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BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BINGO PROBABILITY STATISTICS ANALYSIS AND GRAPHS 1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called. 2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called. 3) In a 50 board game there is a 0.088966 probability someone### will get a

BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

### POKER PROBABILITIES

One Pair 1,098,240 .4225690276. High card only 1,302,540 .5011773940. Total 2,598,960 1.0000000000. (See Probabilities for 5 card poker hands with misc. wild cards for additional details.) The first calculation that must be made is to determine the total possible poker### hands.

GUARANTEED PROFITS IN STOCK MARKET OPTIONS? X13 = 35. In English this means: For each package (mixed strategy) that includes 1/4 of an option contract as indicated above, you are guaranteed to make a profit of at least $35. This solution technique can be used on any family of options as long as they are HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split SUPERIMPOSITION RAPID/PEARCE FERRY RAPID The silt-laden Colorado River exits from the Grand Canyon (lower right quadrant) into Lake Mead. Pearce Bay is in the lower left portion of the lake, and what will become the location for Superimposition Rapid is just to the right of the two points of land that stick out into the lake just to the north of Pearce Bay. ORIGIN AND FORMATION OF GLENWOOD CANYON, COLORADO Origin and Formation of Glenwood Canyon, Colorado. The Chronology on how the Colorado River formed Glenwood Canyon. View to the west from Dotsero to Glenwood Springs, Colorado. Contour intervals are 100 feet. The major highway is I-70. The Colorado River cuts through the south side of the White River Plateau to form Glenwood Canyon. ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

MONOPOLY BOARD LOCATION PROBABILITIES (STATISTICS, FREQUENCY) Monopoly Probabilities Monopoly Board Location Probabilities (Statistics, Frequency) What is the probability your board piece (token) will be on any given board space at the end of a turn? BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I BINGO PROBABILITY STATISTICS ANALYSIS AND GRAPHS 1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called. 2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called. 3) In a 50 board game there is a 0.088966 probability someone### will get a

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I BINGO PROBABILITY STATISTICS ANALYSIS AND GRAPHS 1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called. 2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called. 3) In a 50 board game there is a 0.088966 probability someone### will get a

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

### POKER PROBABILITIES

One Pair 1,098,240 .4225690276. High card only 1,302,540 .5011773940. Total 2,598,960 1.0000000000. (See Probabilities for 5 card poker hands with misc. wild cards for additional details.) The first calculation that must be made is to determine the total possible poker### hands.

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

GUARANTEED PROFITS IN STOCK MARKET OPTIONS? X13 = 35. In English this means: For each package (mixed strategy) that includes 1/4 of an option contract as indicated above, you are guaranteed to make a profit of at least $35. This solution technique can be used on any family of options as long as they are BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ORIGIN AND FORMATION OF GLENWOOD CANYON, COLORADO Origin and Formation of Glenwood Canyon, Colorado. The Chronology on how the Colorado River formed Glenwood Canyon. View to the west from Dotsero to Glenwood Springs, Colorado. Contour intervals are 100 feet. The major highway is I-70. The Colorado River cuts through the south side of the White River Plateau to form Glenwood Canyon. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the MONOPOLY BOARD LOCATION PROBABILITIES (STATISTICS, FREQUENCY) Monopoly Probabilities Monopoly Board Location Probabilities (Statistics, Frequency) What is the probability your board piece (token) will be on any given board space at the end of a turn? BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I BINGO PROBABILITY STATISTICS ANALYSIS AND GRAPHS 1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called. 2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called. 3) In a 50 board game there is a 0.088966 probability someone### will get a

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I BINGO PROBABILITY STATISTICS ANALYSIS AND GRAPHS 1) A single board has a 0.00488136 probability of producing a Bingo when the 20th number is called. 2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called. 3) In a 50 board game there is a 0.088966 probability someone### will get a

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

### POKER PROBABILITIES

One Pair 1,098,240 .4225690276. High card only 1,302,540 .5011773940. Total 2,598,960 1.0000000000. (See Probabilities for 5 card poker hands with misc. wild cards for additional details.) The first calculation that must be made is to determine the total possible poker### hands.

LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

GUARANTEED PROFITS IN STOCK MARKET OPTIONS? X13 = 35. In English this means: For each package (mixed strategy) that includes 1/4 of an option contract as indicated above, you are guaranteed to make a profit of at least $35. This solution technique can be used on any family of options as long as they are BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE BRIDGE SUIT SPLIT COMBINATORICS/PROBABILITY We note that the sum of the number of combinations equals the 10,400,600 total that we calculated earlier (COMBIN (26,13)). To get the probability of any particular split we just divide the number of combinations for the split by the total number of hands. Thus: Split ORIGIN AND FORMATION OF GLENWOOD CANYON, COLORADO Origin and Formation of Glenwood Canyon, Colorado. The Chronology on how the Colorado River formed Glenwood Canyon. View to the west from Dotsero to Glenwood Springs, Colorado. Contour intervals are 100 feet. The major highway is I-70. The Colorado River cuts through the south side of the White River Plateau to form Glenwood Canyon. LA PLATA MOUNTAINS, UPPER DOLORES RIVER, AND ANCESTRAL SAN La Plata Mountains, Upper Dolores River, and Ancestral San Juan River. by. Bill Butler. The history of the La Plata Mountains and nearby terrain to the south and west is significant as it controls the history of the San Juan River as well as local features near Durango. The first uplift of the La Platas resulted from igneous intrusions 65### to 70

SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the MONOPOLY BOARD LOCATION PROBABILITIES (STATISTICS, FREQUENCY) Monopoly Probabilities Monopoly Board Location Probabilities (Statistics, Frequency) What is the probability your board piece (token) will be on any given board space at the end of a turn? BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

DURANGO BILL'S HOME PAGE Bill Butler. E-mail: lisabill@wcenturywlink.net (Remove both "w"s for a valid E-mail address.) Note: The author (Bill Butler) of this website is a magna cum laude, Computer Science graduate of Brown University. The photo above shows the author’s home near Durango, CO. For a 4 minute aerial video, please see. LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

THE N-QUEENS PROBLEM Expanding the Problem to “N” Queens on an NxN ChessboardAlso, include “Superqueens ”. If we increase the size of the chessboard beyond 8 rows/columns, we might want to find how many solutions exist for any arbitrary board size “N”. For example, if “N” = 10,### then there are

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. SUPERIMPOSITION RAPID/PEARCE FERRY RAPID The silt-laden Colorado River exits from the Grand Canyon (lower right quadrant) into Lake Mead. Pearce Bay is in the lower left portion of the lake, and what will become the location for Superimposition Rapid is just to the right of the two points of land that stick out into the lake just to the north of Pearce Bay. FORMATION AND ORIGIN OF DESOLATION / GRAY CANYON, UTAH Formation and Origin of Desolation / Gray Canyon, Utah. This view of the main part of Desolation Canyon shows the full, nearly 5,000-ft. depth of the canyon. Here in the deepest part of the canyon, the Roan Cliffs (early Tertiary deposits) flank both sides and rise to over 9,000 feet above sea level. The Green River flows from north to south ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

DURANGO BILL'S HOME PAGE Bill Butler. E-mail: lisabill@wcenturywlink.net (Remove both "w"s for a valid E-mail address.) Note: The author (Bill Butler) of this website is a magna cum laude, Computer Science graduate of Brown University. The photo above shows the author’s home near Durango, CO. For a 4 minute aerial video, please see. LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

THE N-QUEENS PROBLEM Expanding the Problem to “N” Queens on an NxN ChessboardAlso, include “Superqueens ”. If we increase the size of the chessboard beyond 8 rows/columns, we might want to find how many solutions exist for any arbitrary board size “N”. For example, if “N” = 10,### then there are

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. SUPERIMPOSITION RAPID/PEARCE FERRY RAPID The silt-laden Colorado River exits from the Grand Canyon (lower right quadrant) into Lake Mead. Pearce Bay is in the lower left portion of the lake, and what will become the location for Superimposition Rapid is just to the right of the two points of land that stick out into the lake just to the north of Pearce Bay. FORMATION AND ORIGIN OF DESOLATION / GRAY CANYON, UTAH Formation and Origin of Desolation / Gray Canyon, Utah. This view of the main part of Desolation Canyon shows the full, nearly 5,000-ft. depth of the canyon. Here in the deepest part of the canyon, the Roan Cliffs (early Tertiary deposits) flank both sides and rise to over 9,000 feet above sea level. The Green River flows from north to south ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

BRIDGE PROBABILITIES Using this analysis, a player counts 4 points for every Ace in his hand, 3 points for Kings, 2 points for Queens, and 1 point for Jacks. The total becomes the point count. A hand that has no honors (not even a 10) is frequently referred to as a "Yarborough" (9 high or worse). There are 347,373,600 "Yarboroughs" (COMBIN (32, 13)), and I think I "SHUT THE BOX" ANALYSIS 12-Box Shut the Box. Another variation of Shut the Box uses 12 boxes instead of 9. There are no standard rules for the 12 box version, but the analysis given here assumes that you always use 2 dice. As shown below, it is much more difficult to shut all 12 boxes. The probability of winning is only 0.3622 percent. BRIDGE PROBABILITIES AND STATISTICS For example you could have all 13 cards in any one of the 4 suits. The “Probability” column shows the probability of getting a bridge hand with the indicated distribution. This probability is equal to the Total Hands for the distribution divided by the total possible hands. The total number of hands must sum to COMBIN (52, 13 BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 HOW TO CALCULATE BINGO PROBABILITY STATISTICS (Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.) The key to calculating Bingo statistics is the Single Board Cumulative Probability of getting Bingo on or before the "Nth"### number is called.

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. HOW TO CALCULATE THE MONOPOLY STATISTICS There are 3 steps required to calculate the statistics given in the tables and illustrated in the graphs. 1) For each board space, run an exhaustive tree search of all possible Monopoly moves (including consequences of doubles, Chance, Community Chest, Go to Jail, etc.). For each possible path that starts on a given board space and ends on SUPERIMPOSITION RAPID/PEARCE FERRY RAPID Pearce Ferry Rapid. (Also please see Lower Superimposition Rapid) A chronology of transitions from: 1) Lake Mead. 2) To a new superimposed path for the Colorado River. 3) Which became a “riffle” near the old Pearce Ferry take-out. 4) This “riffle” became a moderately severe rapid in late 2007. 5) The combination of silt deposited by the ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

DURANGO BILL'S HOME PAGE Bill Butler. E-mail: lisabill@wcenturywlink.net (Remove both "w"s for a valid E-mail address.) Note: The author (Bill Butler) of this website is a magna cum laude, Computer Science graduate of Brown University. The photo above shows the author’s home near Durango, CO. For a 4 minute aerial video, please see. LAPLATA - DURANGO BILL'S HOME PAGE This area to the west and southwest of Durango has one of the most complex histories of any area in the Rockies. There was an initial uplift of the La Plata Mountains due to igneous intrusions some 65 to 70 million years ago. When the San Juan Basin (to the south and southeast off the lower edge of the picture) rebounded in the Eocene,### the

BRIDGE PROBABILITIES AND STATISTICS The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck. Note: For all combinations, there are COMBIN (26,13) = 10,400,600 possible hands for a specific opponent after 26 ENUMERATION OF BINARY TREES The diagram above illustrates all possible binary trees that can be created with 3 vertices. If we want to consider binary trees that are structurally different, then trees 1, 2, 4, and 5 are structurally the### same.

THE N-QUEENS PROBLEM Expanding the Problem to “N” Queens on an NxN ChessboardAlso, include “Superqueens ”. If we increase the size of the chessboard beyond 8 rows/columns, we might want to find how many solutions exist for any arbitrary board size “N”. For example, if “N” = 10,### then there are

BRIDGE PROBABILITIES AND STATISTICS The table below shows the number of ways any possible point count total could occur and the probability of each of these possibilities. Bridge Honor Count Combinations for 26 cards (2 hands) The total number of possible combined hands is: COMBIN (52, 26) = 495,918,532,948,104. Honor Total Honor Count Cumulative Avg. Nbr. SUPERIMPOSITION RAPID/PEARCE FERRY RAPID The silt-laden Colorado River exits from the Grand Canyon (lower right quadrant) into Lake Mead. Pearce Bay is in the lower left portion of the lake, and what will become the location for Superimposition Rapid is just to the right of the two points of land that stick out into the lake just to the north of Pearce Bay. FORMATION AND ORIGIN OF DESOLATION / GRAY CANYON, UTAH Formation and Origin of Desolation / Gray Canyon, Utah. This view of the main part of Desolation Canyon shows the full, nearly 5,000-ft. depth of the canyon. Here in the deepest part of the canyon, the Roan Cliffs (early Tertiary deposits) flank both sides and rise to over 9,000 feet above sea level. The Green River flows from north to south ANCESTRAL RIVERS IN THE EASTERN UNITED STATES The Delaware Water Gap was an important route for early settlers that were headed west. Over geologic time the Delaware River had eroded a path though upturned layers of hard rock, and it was much easier to build an early road near the river as opposed to climbing over 1,000 feet to go over the mountain. PICTURES OF THE ANIMAS RIVER FLOOD The pictures below were taken about noon on May 23, 2005. River flow was about 8,400 cubic feet per second (revised upward from the original report of 8,000 cfs)) with a river gauge height at about 7.37 feet. The extreme crest came on 5/25/05 at 7.4 feet and 8,500 cubic### feet

Durango Bill's Home Page### Featuring

Origin & Formation of the Grand Canyon Evolution of the Colorado River (Geology) 3-D Grand Canyon Geologic Tour Ancestral Rivers of the World Probability Analysis of Popular Games Graph Theory Enumeration Global Warming / Climate Change (3-D image of Durango, CO generated by Google Earth### .)

Durango, Colorado is located in the Animas River Valley just a few miles southeast of the 13,000-ft. high La Plata Mountains. Local attractions include the Durango & Silverton Narrow Gauge Railroad, Purgatory Resort (skiing), Mesa Verde National Park, and some of the world’s most frightening highways and jeep “roads”. e.g. Black Bear Road / Black Bear Pass: http://en.wikipedia.org/wiki/Black_Bear_Road “You don’t have to be crazy to drive this road - but it helps”. For some grizzly info, check http://www.telluridenews.com/the_watch/news/article_052cefa1-4595-57ec-a438-94308e7fdead.html or run a Google search using: “saw a car that seemed to fall out of the sky”. Also check “Black Bear Pass” videos at YouTube. About the author's previous home where: Sometimes it Snows in the Mountains (I currently live near the center of the above picture and about 300 feet below the viewpoint for the photo at the top of the page.)### Links to Topics

Videos by the author The author has uploaded several dozen videos to YouTube### .

Paleogeography / Historical Geology Evolution of the Colorado River A model of the geologic history of the Colorado River and its tributaries starting with the Late Cretaceous through the present. Includes origin and formation of the Grand Canyon. 3-D aerial tour of the Grand Canyon 3-D end-to-end geologic tour of the Grand Canyon An end-to-end aerial geologic tour of the Grand Canyon. Sequencing through the pages simulates a nearly 300-mile trip starting with Glen Canyon Dam at Page, AZ., and continues past the Grand Wash Cliffs to### Lake Mead.

Recommended Grand Canyon Videos Norman Beerger's The Grand Canyon In 1982 Norman Beerger filmed and produced what is probably the best video ever made for anyone that would like an armchair scenic aerial tour of the Grand Canyon. Both the 1-hour and 2-hour versions are helicopter tours accompanied by a classical music sound track. The included notes can be used as a mile-by-mile guide for either the 1-hour or 2-hour versions.### Geology/Glaciology

Rio Chama Rockfall### - A pictorial study

A large rockfall occurred in a remote area of the upper Rio Chama headwaters sometime between Sept. 1998 and June 2005. There appears to be no available information about the rockfall, and the author happened to find it while browsing with Google Earth.### The Taku Glacier

### - What it is

and What is going to happen to it All of the glaciers that exit from the Juneau Icefield are retreating - except the Taku Glacier. It appears that this anomaly of the Taku Glacier is about to end as the Taku appears to be going into retreat. Alaska's Melting Glaciers### - Alaska's

glaciers are melting due to Global Warming A pictorial tour of 3 of Alaska's tidewater glaciers (Harriman, Surprise, and Barry) that are retreating. These glaciers can be easily seen via the "26 Glacier Cruise" Ancestral Rivers of the World An illustrated world tour with examples of river systems that cut through mountain ranges instead of taking easier routes around them. The geologic processes involved are “antecedence” and “superimposition”.### Geodes

Amethyst geodes and cathedrals are fascinating members of the quartz### family.

Creationism, “Intelligent Design Evangelism”, Religious Cultists Creationism = Willful Ignorance A brief review of the fallacies of Creationism and “Intelligent Design Evangelism”. Noah’s Flood is physically impossible, but that doesn’t stop Creationists from perverting reality in an attempt to force their religious beliefs on everyone else. Is the willful ignorance of the Creationists a result of fear? Patriot Bible “University” Very few people have had a chance to see the current location of Kent Hovind’s alma mater - mostly because it’s a long way from any other “educational institution”. George Bush Misrepresents Science and Knowledge Is George W. Bush one of the ignorant Young Earth Creationists? What might happen if you combined Ignorance and Power? If the Ignorant Armies gained control, what steps might these Creationists take to throw us back into the Dark Ages of Religious### Theocracy?

Some highlights from a paper endorsed by a large number of Nobel### Laureates.

New Orleans Underwater The funds that were supposed to be spent reinforcing New Orleans’ levee system were instead diverted to the Iraq war and the figurehead Department of Homeland Security. Thus New Orleans did not have the protection it could have had when hurricane Katrina hit. What causes a Creationist to be a Creationist? The answer is: Fear! 1) Fear of evolution. 2) Fear and hatred toward gays/lesbians.### 3) Fear of women.

### 4) Fear of death.

5) Fear of losing their “All Powerful Father”. Militant Protests by Religious Cultists against “Planned Parenthood” in Durango, Colorado A small militant group of abortion protesters has been active at Planned Parenthood in Durango, Colorado. The group is run by “Michaela Dasteel, director of LifeGuard” - as reported in the March 16, 2007 Durango Herald.### Game Analysis

Bingo Probability and Statistics The statistics, probabilities, and odds involved with the popular game of Bingo. Includes algorithms for the computations. Bridge Combinatorics and Probabilities The statistics, combinatorics, and probabilities for the various point counts, suit distributions, and suit splits for Bridge hands. Includes “How To” mathematics. Round Robin and Whist Tournament analysis and schedules The Integer Brick Problem Also know as the Euler Brick problem. No solutions out to odd side <= 3.0 Trillion (3.0E12). Monopoly Probabilities and Statistics End-of-turn and "Land on" statistics/frequency analysis for Parker Brothers Monopoly Game. All the "What is the chance of landing on ..." statistics. Also, there are up to 50,083 ways to "Go To Jail". N-Queens Problem How many queens (and/or superqueens) can be placed on an arbitrarily sized chessboard without any of them attacking another queen? Queens to N = 26, Superqueens to N = 23. Peg Solitaire (All pages include number of solutions) 15 Hole Peg Solitaire This version is for a triangular pattern with 5 holes (peg positions) per side. 33 Hole Peg Solitaire Sold commercially as Hi-Q 577,116,156,815,309,849,672 possible Hi-Q games 40,861,647,040,079,968 different ways to win Hi-Q 37 Hole Peg Solitaire This version is popular in France 41 Hole Peg Solitaire This lesser known version is extremely difficult### Pig (Pig-out)

Optimal strategy for two versions of this dice game Poker Probabilities Probabilities for 5 to 10 card hands (including misc. wild cards),### lowball Poker,

and optimal strategy for Video Poker. Shut the Box - Optimal Strategy Includes a prototype for a casino version. Solitaire Chinese Checkers The minimum number of moves to move a set of ten marbles from one side to the other is 27. Graph Theory / Number Theory (Valid for 47 states but not in Kansas, Louisiana, or Texas where all math/science “theories” are being thrown out as “not### Biblical”.)

### Trochoids

Epitrochoids and Hypotrochoids are curves generated by rolling one circle around another stationary circle. Examples and graphical illustrations are given.### Partitions

How many ways are there to subdivide a set containing "N" items? Rooted (oriented) trees A rooted tree has a single vertex (node) desiginated as a "root" (usually at the top). Travel along any of the edges is directed toward the "root". A table is given showing how many structurally different, rooted trees exist given "N" vertices. Non rooted (free) trees A non-rooted tree has a free form where no vertex has priority. A non-rooted tree can be twisted, deformed, contorted, etc. into many shapes without altering its structure. Again, a table is given showing how many structurally different, non rooted trees exist given "N"### vertices.

Ordered Binary trees A binary tree is rooted tree where each vertex can have a maximum of two edges that connect to lower portions of the tree. The "root" is normally depicted at the top. Edges from any vertex in the tree will descend either to the left (left branch) or to the right (right### branch).

Structurally different binary trees How many structurally different binary trees exist given "N" vertices? Structurally different graphs An unlabeled graph may have an arbitrary number of vertices with none, one, or more edges connecting some or all of the vertices. If you have "V" vertices and "E" edges, how many structurally different graphs can### be constructed?

### Ramanujan Numbers

Ramanujan Numbers and the Taxicab Problem. The simplest of these solution groups is: 1^3 + 12^3 = 9^3 + 10^3 = 1729. Includes graphs showing 2-way, 3-way, 4-way, and the 193 known 5-way solutions. 24,153,319,581,254,312,065,344 has been confirmed as Taxicab(6) Analysis of Sorting Algorithms A common task for computers is to sort data as an aid to analyzing it. Time trials and source code are provided for: Bubble Sort, Insertion Sort, Median-of-three Quicksort, Multiple Link List Sort, and Shell### Sort.

The search for a counterexample to Beal's Conjecture### Does the equation:

### Ax + By = Cz

have any solution where: 1) A, B, C, are positive integers 2) x, y, z are positive integers > 2 3) and A, B, C have no common factor? If you can answer the above question (with either a “Yes” or a “No”), the American Mathematical Society has a $1,000,000 prize### waiting for you.

Bad News - there are no counterexamples up through Cz <= 1.0E28 (and### counting).

### Magic

### Squares

Magic Squares exist for many different sizes and may have various qualifications on the numbers they contain. We will look at simple 3x3 Magic Squares and take a brief look at the “3x3 Magic Square of### Squares” problem.

### Applied Mathematics

Guaranteed Profits in Stock Market Options? This is a demo model illustrating how a linear programming system can be used to find an optimal profit for arbitrage positions in stock### options.

Mega Millions Odds & how to calculate them Updated for the pick 5 from 70 / pick 1 from 25 version. Powerball Odds and how to calculate them The standard odds, probabilities for multiple winners, calculations for “Power Play Multiplier”, and expected “Return on investment” are all included as well as the math operations that are used to calculate these numbers. Global Warming - and those people with closed minds that blindly deny### it

“The Great Global Warming Swindle” is itself a Fraud and a### Swindle

“The Great Global Warming Swindle” is a pseudo-documentary in which British television producer Martin Durkin has fraudulently misrepresented both the data involved and scientists who have researched global climate. Movie director Durkin has willfully misrepresented the facts about global warming just to advocate his own### agenda.

Global Warming Denial - Liars Global Warming Deniers misrepresent the scientific facts of Global Warming / Climate Change in multiple ways. The misrepresentations can take the form of paid political propaganda, ignorance, outright lies, etc. The people responsible for these misrepresentations can vary from “think tanks” and lobbyists that are financed by large corporations down to ignorant individuals. In particular: The Oregon Institute of Science and Medicine is in reality - a farm, and Christopher Monckton - A vociferous Global Warming Denier Liar. Roger Cohen’s proposed $5,000 bet A (retired) Exxon Mobil executive’s attempt to use money to promote his personal agenda. (Which is to deny “Global Warming”.) The “Global Warming Stopped in 1998” Lie One of the false claims that Global Warming Deniers have been making in recent years is that “Global Warming Stopped in 1998”. As per usual, this claim is another deliberate GWD falsehood that can be easily debunked by looking at the actual observations. http://www.durangobill.com/GwdLiars/FabiusMaximusIgnorance.html The Fabius Maximus Website is an example of a Global Warming Denier website. A look at the evidence that GWDs lie, they are willfully ignorant, and they are wrong. Durango History via Topo Maps Historical snapshots of Durango, CO via Topo maps. The featured areas extend northward to include Animas City and westward to include the Rafter J subdivision.### Fight DMCA Abuse

How to fight back against DMCA abuse The Digital Millennium Copyright Act has been used abusively to suppress legitimate criticism of cultists and other “questionable activities”. Here’s an outline on how to fight back if you are ever a victim of a DMCA attack.### Fee Demo

### Fee Demo Complaint

U. S. National Forests are a national responsibility - illustrated with a Beetle Bailey cartoon. We now have to pay additional fees to access our National Forest lands. This is in addition to the federal taxes that we all pay. Previously this tax money was used for maintenance of these publicly owned lands.### Animas River Flood

The winter of 2004/2005 had a much above normal snow-pack over the San Juan Mountains. A heat wave in mid/late May melted large amounts of it### all at once.

A Giant Sequoia grove near Durango, Colorado A log of the author's effort (and a general “How to” guide) to get a Giant Sequoia grove to grow next to the author's home west of### Durango, Colorado

### Genealogy/Ancestry

The Inishowen Butlers http://durangobill.com/InishowenButlers/InishowenButlers.html### Website Hits

Over 6.0 million page hits since start-up March 13, 2001. The pages most frequently visited are (some variation with### time):

“The Great Global Warming Swindle” is itself a Fraud and a Swindle Powerball (Visits increase sharply when large jackpots exist) Mega Millions (Visits increase sharply when large jackpots exist)### Poker

### Home page

Evolution of the Colorado River (Parker Brothers) Monopoly### Grand Canyon Tour

### Bingo

N_Queens (A surprisingly popular classic puzzle) Creationism (& related pages)### Donald Trump

And who is responsible for the mess that has resulted from the government’s shutdown? Trump: “I am proud to shut down the government” Trump: “I will be the one to shut it down” Video: https://www.youtube.com/watch?v=4ElVqRvEvMQ Q: And why would Trump want to "Shut down the government? A: (Hint: "temper tantrum") For information on why the author of this website can not, and will not support Mr. “I alone can fix it” ( https://www.youtube.com/watch?v=KGenVcak5nI ); please see: 'MALIGNANT NARCISISSM': DONALD TRUMP DISPLAYS CLASSIC TRAITS OF MENTAL ILLNESS, CLAIM PSYCHOLOGISTS http://www.independent.co.uk/life-style/health-and-families/donald-trump-mental-illness-narcisissm-us-president-psychologists-inauguration-crowd-size-paranoia-a7552661.html### and/or

Donald Trump's malignant narcissism is toxic: Psychologist https://www.usatoday.com/story/opinion/2017/05/04/trump-malignant-narcissistic-disorder-psychiatry-column/101243584/### and/or

President Trump exhibits classic signs of mental illness, including 'malignant narcissism,' shrinks say http://www.nydailynews.com/news/politics/shrinks-break-silence-president-trump-exhibits-traits-m-article-1.2957688### etc.

https://www.google.com/search?q=donald+trump+%22Malignant+narcissism%22 Malignant narcissism https://en.wikipedia.org/wiki/Malignant_narcissism > "Malignant narcissism is a psychological syndrome comprising an > extreme mix of narcissism, antisocial personality disorder, > aggression, and sadism. Often grandiose, and always ready to raise > hostility levels, the malignant narcissist undermines organizations > in which they are involved, and dehumanizes the people with whom > they associate." "A narcissist is a pathological liar who will lie about anything and everything for the sole purpose of gleefully watching you sift through### the word garbage."

http://www.thenarcissisticpersonality.com/the-pathological-liar/ And a quote from Ted Cruz: "I'm going to tell you what I really think of Donald Trump. This man is a pathological liar" https://www.bbc.com/news/av/election-us-2016-36198532/ted-cruz-donald-trump-is-a-pathological-liar “I HATE EVERYONE IN THE WHITE HOUSE!”: TRUMP SEETHES AS ADVISERS FEAR THE PRESIDENT IS “UNRAVELING” https://www.vanityfair.com/news/2017/10/donald-trump-is-unraveling-white-house-advisers Narcissistic Rage: What Causes Narcissists To Rage? http://narcissisticbehavior.net/what-causes-narcissistic-rage/ > “Narcissistic rages are not reactions to stress, but rather based > on the underlying fear of not getting their needs meet, a fear so > great that it will endure even after the threat is gone (Vaknin). > Because the narcissist is hypervigilant to narcissistic injury, he > is constantly on the lookout for slights, insults, criticisms, or > disagreements (real or imagined), all of which are experienced by > him as complete and humiliating rejection, to which he will > automatically and instantly fly into a rage. The raging > narcissists usually perceive their reaction to have been triggered > by an intentional provocation to cause them injury, or prevent them > from accomplishing their grandiose fantasies. Their response to > such insult and injury is to detach from the person, direct his rage > towards the person in a cold and aggressive manner, and to devalue > the person as they go; to other people, the rage is incoherent and > unjust. This rage impairs the narcissist’s cognition, therefore > impairing their judgment. During the rage they are prone to > shouting, fact distortion and making groundless accusations with > punitive and hate-filled malice.”### Also, please see:

"How to Recognize a Malignant Narcissist" https://www.psychologytoday.com/blog/neurosagacity/201702/how-recognize-malignant-narcissist > "I am so smart! My IQ is above140."### >

> Self-enhancement is a prominent feature of narcissistic personality > disorder, regardless of the dimension. They view themselves in an > overly positive light and believe they are unique and superior to### > others.

Cartoon by Tom Curry https://www.youtube.com/watch?v=LCQ5LtDDNWU As of Dec. 2019 the "Donald's Lies" count is up to 15,413 as tabulated by the Washington Post with a physical demonstration of the magnitude of 15,413 as measured by "How many gumballs?" as shown on CNN. https://www.youtube.com/watch?v=KmhUOQsCv5A DONALD TRUMP ON GOLF Quotes from Rick Reilly - Author of “Commander in Cheat: How Golf### Explains Trump”

> “To say “Donald Trump cheats” is like saying “Michael Phelps > swims.” He cheats at the highest level. He cheats when people are > watching, and he cheats when they aren’t. He cheats whether you > like it or not.”### >

> “I’ve found that to be true with golf. The guy who plays slowly > on the course is going to be molasses in meetings. The guy who’s > generous with compliments on the course is going to do the same at > dinner. And the guy who cheats on the course is going to cheat in > business, or on his taxes or, say, in politics.”### >

> “Why cheat? Why lie? Why exaggerate his handicap, his scores, his > club championships? “Because he has to,” says Harvard > psychiatrist Dr. Lance Dodes, co-author of The Dangerous Case of > Donald Trump. He needs to be the best at everything. He can’t > stand not winning, not being the best.” https://www.golf.com/news/features/2019/04/02/how-why-president-trump-cheats-golf-playing-tiger-woods/ Cartoon by Chris Britt And finally, as to why Trump supporters are perfectly willing to accept a president who is an insane madman, please see: “A neuroscientist explains what could be wrong with Trump supporters’ brains” https://www.rawstory.com/2018/04/neuroscientist-explains-wrong-trump-supporters-brains/ "Rethuglican" Ignorance and Hatred - This is why we have a "Rethuglican" terrorist problem Rethuglican: https://en.wiktionary.org/wiki/Rethuglican TRUMP: “I COULD STAND IN THE MIDDLE OF FIFTH AVENUE AND SHOOT SOMEBODY, AND I WOULDN’T LOSE ANY VOTERS, OK? IT’S, LIKE,### INCREDIBLE.”

https://www.cbsnews.com/news/what-do-trump-supporters-see-in-their-candidate/### Also, please see:

"Just What Were Donald Trump's Ties to the Mob?" https://www.politico.com/magazine/story/2016/05/donald-trump-2016-mob-organized-crime-213910### and/or

"Is Donald Trump the First Gangster President?" http://observer.com/2018/04/donald-trump-gangster-president/### and/or

"Comey is exactly right about Trump being like a mob boss" https://www.cnn.com/2018/04/13/opinions/comey-right-about-trump-opinion-love/index.html### and/or

Just run a Google search using: "Donald Trump" organized crime The above cartoon was created by Dave Whamond in Sept. 2019. It depicts Trump's extortion attempt where he withheld $400 million that was supposed to go the Ukraine unless the Ukrainians agreed to "3### favors".

https://www.vice.com/en_us/article/9ked3d/the-three-favors-trump-asked-the-ukrainian-president-in-new-transcript Trump/Tillerson/“F***ing Moron” Coronavirus/Stock Market https://www.cnbc.com/2017/10/04/tillerson-called-trump-a-moron-says-report.html### and/or

https://www.gq.com/story/rex-tillerson-spot-the-lie As for Trump's ability to control the Coronavirus (COVID-19) and/or manage the U. S. economy, here is a headline from the New York Post as of Feb. 24, 2020. Here is Trump's Feb. 24, 2020 Twitter post. You can check the recent death count of U.S. citizens for the latest “under control” total. As for Trump's advance “planning” for this pandemic: “The Trump administration fired the U.S. pandemic response team in 2018 to cut costs.” https://www.snopes.com/fact-check/trump-fire-pandemic-team/### Also, please see

https://www.snopes.com/fact-check/experts-officials-pandemic-2018/ > “When the next pandemic occurs (and make no mistake, it will) and > the federal government is unable to respond in a coordinated and > effective fashion to protect the lives of US citizens and others, > this decision by John Bolton and Donald Trump will be why.” As for claims that the Trump administration is being unfairly blamed for an “unexpected” pandemic, the 29 January 2019 report from the Office of the Director of National Intelligence states: > We assess that the United States and the world will remain > vulnerable to the next flu pandemic or large-scale outbreak of a > contagious disease that could lead to massive rates of death and > disability, severely affect the world economy, strain international > resources, and increase calls on the United States for support.### >

> https://www.dni.gov/files/ODNI/documents/2019-ATA-SFR---SSCI.pdf### On Jan. 29, 2020:

https://news.yahoo.com/trade-adviser-warned-white-house-122107510.html > A top White House adviser starkly warned Trump administration > officials in late January that the coronavirus crisis could cost the > United States trillions of dollars and put millions of Americans at > risk of illness or death.### >

> The warning, written in a memo by Peter Navarro, President Donald > Trump’s trade adviser, is the highest-level alert known to have > circulated inside the West Wing as the administration was taking its > first substantive steps to confront a crisis that had already > consumed China’s leaders and would go on to upend life in Europe > and the United States.### >

> “The lack of immune protection or an existing cure or vaccine > would leave Americans defenseless in the case of a full-blown > coronavirus outbreak on U.S. soil,” Navarro’s memo said. “This > lack of protection elevates the risk of the coronavirus evolving > into a full-blown pandemic, imperiling the lives of millions of### > Americans.”

For a more complete list that Donald Trump was warned in advance about a possible pandemic, please see: > Trump says 'nobody' could've predicted a pandemic like coronavirus. > Here are all the times he was warned about it and refused to take### > action.

> https://www.businessinsider.com/coronavirus-all-the-times-trump-was-warned-about-pandemic-2020-3 After the Coronavirus (COVID-19) was officially declared to be a pandemic by the World Health Organization### ,

when asked about the incident, Trump's reply was “I DON’T KNOW ANYTHING ABOUT IT,” (Click here for source### )

Here's what the S&P 500 stock average looked like as of the opening on the morning of Feb. 25, 2020. You can also check just about any financial news source to see what happened immediately after Trump's assurance that the stock market “looks 'very good'”. It is this author's sincerest hope that the opening upward blip on Feb. 25, 2020 was a result of all of Trump's patrons buying into the market with their life's savings. Note that the S&P was at 3,246.85 at the time. In 2016 the National Safety Council prepared a “White House Playbook” outlining what the president should do if a pandemic appeared likely. “Playbook for Early Response to High-Consequence Emerging Infectious Disease Threats and Biological Incidents” https://www.politico.com/news/2020/03/25/trump-coronavirus-national-security-council-149285 Did President Trump pay any attention to it? Nope. How many lives would have been saved if Donald Trump had followed what the experts had recommended vs. Trump's own ignorance and arrogance? In October 2019 the Center for Disease Control ran a simulation of a pandemic and documented: > “that officials at the Departments of Homeland Security and Health > and Human Services, and even at the White House’s National > Security Council, were aware of the potential for a respiratory > virus outbreak originating in China to spread quickly to the United > States and overwhelm the nation.” https://www.nytimes.com/2020/03/19/us/politics/trump-coronavirus-outbreak.html### Nothing was done.

(Click on the picture for a large image) The picture above is a Print Screen copy of Johns Hopkins University's COVID-19 coronavirus web page as of March 26, 2020. If you check the above display, it shows that as of March 26, 2020, the United States had 83,507 confirmed cases of COVID-19 with 1,178 deaths. If you check these numbers with any subsequent totals, you will get an idea of how fast the disease is spreading. For reference purposes, on March 1, 2020, the U. S. had only 30 confirmed cases. https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/cases-in-us.html A quote from Donald Trump from a press conference on Feb 26, 2020: > And again, when you have 15 people , and the 15 within a couple of days is going to be down to > close to zero, that’s a pretty good job we’ve done. (Link to White House Press Conference### )

The picture above shows the status of Covid 19 cases in the U. S. and for the state of Colorado as of April 22, 2020. (Data sources: Johns Hopkins University and CO Dept. of Public Health) The dots show the daily number of new cases for the disease. The solid black line shows the total number of U. S. deaths as of each date. The curve lines are least squares, sum of two normal distribution ("Bell" distribution) curves fitted to the daily observations. Future curve plots are NOT valid forecasts of the expected number cases. The future number of cases for both curves will tend to extend horizontally to the right as opposed to dropping to the zero level. (If "social distancing" controls are relaxed before an alternate method of controlling the virus is in place, all 3 data metrics would rocket off the top of the graph.) All of the above blunders by Donald Trump were “duly rewarded” by March 26, 2020. The U.S. became NUMBER 1 in the world - as measured by the greatest number of people that had become victims of the COVID-19 coronavirus. China has far more people than the U. S., but their government listened to expert advice and stopped the spread of the virus in China. In the U. S., ignorance and arrogance were in charge, and guess what the result was? Finally, we have Donald Trump's advice on how to avoid catching the COVID-19. From the New York Post https://nypost.com/2020/03/31/trump-says-people-can-wear-a-scarf-to-prevent-coronavirus/ > WASHINGTON — President Trump says people can “wear a > scarf” over their face if they want to avoid catching the### > coronavirus.

### >

> “You know, you can use a scarf,” Trump said Tuesday at a > White House press conference. “A lot of people have scarves. And > you can use a scarf. A scarf would be very good.” And there's always the "medical advice" (promoted by Donald Trump and Fox "News") that Hydroxychloroquine and Chloroquine are effective medicines and a "game changer" in the fight against COVID-19. Trump: "What have you got to lose?". Turns out that "What have you got to lose?" is your life. From the Journal of the American Medical Association: "Here we present analyses until day 13, with lethality as the primary outcome." ( Link### )

Also "Study finds no benefit, higher death rate in patients taking hydroxychloroquine for Covid-19". ( Link### )

Rex Tillerson said it best - “F***ing Moron” Note: The air spaces between the fibers in a scarf are much too large to filter out the coronavirus microbes. As for “why” the wheels are about to come off the U. S. economic system, Rush Limbaugh (see http://www.durangobill.com/GwdLiars/GwdLiarsIndex.html ) worked for years cultivating an “ignorance is a virtue” and “hatred against fellow Americans is good” system. He convinced enough Americans so that Donald Trump was elected to finish the job of destroying what used to “make America great”. The process was somewhat like setting up a long row of dominoes. The Coronavirus tipped the first### domino over.

Note to those compiling Donald Trump's "Enemies List(s)" and "Fake### News List(s)":

Please add my name to your lists. Information About the Website Author### Contact

### Bill Butler

E-mail: lisabill@wcenturywlink.net (Remove both "w"s for a valid E-mail address.) Note: The author (Bill Butler) of this website is a _magna cum laude_, Computer Science graduate of Brown University. The photo above shows the author’s home near Durango, CO. For a 4 minute aerial video, please see https://vimeo.com/119921726### or

https://www.youtube.com/watch?v=VW9oiNnO8wM (Click on the full screen icon in the lower right corner for best### resolution.)

For a 10:46 video set to Liszt's 2nd Hungarian Rhapsody, see: https://www.youtube.com/watch?v=3_LVY--_IDU&feature=youtu.be The author of this web page supports "STEM" education The picture above is from NASA’s Adopt the Planet promotion. https://climate.nasa.gov/adopt-the-planet/#/ It shows the location of the randomly generated 3,076 sq. mile plot that the author has “adopted” as part of NASA’s Earth Day 2017### program.

We are living in an age where many people think that anti-intellectualism and ignorance are virtues. The author of this website takes a contrary view. If America is to maintain its “Great” status in the future, we must educate our people so that they are competent in the fields of science, technology, engineering, and mathematics. If instead, our goal is to revive the coal industry so that more of our citizens will die of Black Lung Disease, America will not be “Great Again”. The author supports NASA’s efforts to learn about our planet so that we can make it a better place to live. The author supports the ideal that our voters should be an “Informed Electorate”. Thomas Jefferson - “A properly functioning democracy depends on an informed electorate.”### The Puppy Dog

And finally, we have “The Puppy Dog” Subtitle: “Here comes trouble” Web page generated via Sea Monkey's Composer HTML editor within a Linux Cinnamon Mint 18 operating system.### (Goodbye Microsoft)

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