7 11 Dice
2021年7月23日Register here: http://gg.gg/vhk7m
*7-11 Dice Games
*7 11 Dice Drinking Game
After the come point has been established you win if it is a 2 or 3 and lose for 7 or 11. 12 is a tie and other dice rolls will make you win only if a 7 appears before them on the following throws. Place Bets - This bet works only after the point has been determined. 7 / 11 dice game. While loops and with p. 7 / 11 dice game. While loops and with points and stuff. Write your question here. So i have this project. A gambling game played with two dice in which a first throw of 7 or 11 wins, a first throw of 2, 3, or 12 loses the bet, and a first throw of any other number (a point) must be repeated to win before a 7 is thrown, which loses both the bet and the dice. A losing throw in this game. Also called crap2. No-one will be fooled by the trick dice. One is all fives, and the other is half sixes and half twos. So, yes, you will always roll a 7 or 11, but even a quick glance at the dice reveals their ’secret.’ Only a blind person might be tricked by this.
In front of you are two fair dice.
One is a 7-sided dice with faces -3, -2, -1, 0, 1, 2, 3.
The other is an 11-sided dice with faces -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
You pick a dice, and I will get the other one. We will roll together, and the person with the larger number wins. If the two dice show the same number, we roll again until someone wins.
Which dice should you pick, if you want to maximize your chance of winning?
Bonus: solve the game for the generalized case: one dice has integer sides from –n to n and the other dice has integer sides from –m to m, where n < m.
Watch the video for a solution.
Or keep reading.
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.
’All will be well if you use your mind for your decisions, and mind only your decisions.’ Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .
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Answer To 7 Vs 11 Sided Dice Game Riddle: Who Wins?
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
I saw this puzzle at Puzzling StackExchange and the answer initially surprised me until I read the excellent solution from hexomino.
First let’s solve the 7 vs 11 case directly. There are 7 equally likely ways to roll the 7 sided dice, and 11 equally likely ways to roll the 11 sided dice, for a total of 7 x 11 = 77 equally likely events.
We can visualize the sample space as an ordered pair (i, j) for rolling (7 sided dice, 11 sided dice).
There are 7 possible ways both dice show the same number:
(-3, -3), (-2, -2), (-1, -1), (0, 0), (1, 1), (2, 2), (3, 3)
For any other roll, the game ends with a win for some player. Thus there are 77 – 7 = 70 equally likely rolls in which the game ends.
Out of these, exactly 35 will be a win for the person rolling the 7-sided dice, which we can enumerate:
(-3, -5), (-3, -4)
(-2, -5), (-2, -4), (-2, -3)
(-1, -5), (-1, -4), (-1, -3), (-1, -2)
(0, -5), (0, -4), (0, -3), (0, -2), (0, -1)
(1, -5), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0)
(2, -5), (2, -4), (2, -3), (2, -2), (2, -1), (2, 0), (2, 1)
(3, -5), (3, -4), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (3, 2)
We can also use a table to represent the outcomes:
So the 7-sided dice wins with a 35/70 = 50 percent probability. And since the other game-ending outcomes are a win for the other dice, this means the 11-sided dice also wins with a 35/70 = 50 percent probability.
In other words, it doesn’t matter which dice you pick: the game is fair! Pat sajak family. There is a 50 percent chance of either player winning, and this is true even for the general case of an n dice versus an m dice for n < m.
General proof7-11 Dice Games
There’s a neat trick to see why each dice has the same chance of winning.
Consider the roll (i, j) = (player 1 rolls n dice, player 2 rolls the m dice).
Player 1 wins if and only if i > j.7 11 Dice Drinking Game
But for every such winning pair, there will also be a roll (-i, –j) because if a dice has a face labeled x it also has the face labeled –x. And this roll is a win for player 2 since i > j implies –i < –j.
And we can make the same argument for player 2 as well! Player 2 wins on a roll (i, j) if and only if i < j. But for every such winning pair, we can find the paired outcome (-i, –j) which is a win for player 1.
Thus, the mapping (i, j) to (-i, –j) is a bijection between the winning rolls between the two players. Player 1 and 2 have exactly the same number of winning outcomes, and the game ends in a win for some player, implying each person has a 50 percent chance of winning.
The game is fair, and it doesn’t matter which dice you pick, even in the general case!
Source
Problem adapted from Puzzling StackExchange. Best online poker machines. Post by athin, 11 sided vs 41 sided dice. Solution from hexomino.
https://puzzling.stackexchange.com/questions/77557/a-short-dice-puzzle
Achilles and Ajax Playing Dice, 6th Century BCE Greecian Pottery
7 In the first month, which is the month of Nisan, in the twelfth year of King Ahasuerus, they cast Pur– which means “the lot”– before Haman for the day and for the month, and the lot fell on the thirteenth day of the twelfth month, which is the month of Adar. 8 Then Haman said to King Ahasuerus, “There is a certain people scattered and separated among the peoples in all the provinces of your kingdom; their laws are different from those of every other people, and they do not keep the king’s laws, so that it is not appropriate for the king to tolerate them. 9 If it pleases the king, let a decree be issued for their destruction, and I will pay ten thousand talents of silver into the hands of those who have charge of the king’s business, so that they may put it into the king’s treasuries.” 10 So the king took his signet ring from his hand and gave it to Haman son of Hammedatha the Agagite, the enemy of the Jews. 11 The king said to Haman, “The money is given to you, and the people as well, to do with them as it seems good to you.”
The dice are rolled, the lot is cast for the date that will come to be Purim. It will be a day of reversals, but at this point in the story it is foreshadowed as a date that will bring disaster to the Jewish people. The king once again receives bad advice from an advisor, advice that will have long lasting consequences and the king never once asks a question or attempts to probe Haman’s motives. The king trusts Haman and is willing for an enormous pile of money (a ridiculous sum, 375 tons of silver, this is roughly 2/3 of the annual Persian kings’ income) to put his authority behind it. Perhaps in both the ancient world and the modern world enough money seems to make something evil more appealing.
This last thought reminds me, in a way, of the plot of the movie the Boxwhere a man and a woman are given a box with a button where if they push it they will receive one million dollars, but someone they don’t know will die and so they are entered into the ethical dilemma of whether their own very real monetary needs outweigh the life of a stranger. Now it is not the greatest movie, but the ethical question of the power of money to cause a horrible decision, especially when you don’t have to carry it out, more appealing. The king never carries out his decision, he is always insulated and while his ring may mark the life or death of many, he allows others to be the executioners.
The king not only takes the advice of Haman, he seems to compel it along even more so. The king’s authority is placed behind the plot of Haman. One man’s revenge now becomes imperial policy and the story’s crisis is set in motion. This is a strange story since the Persian empire was actually pretty benevolent as far as ancient empires go toward their subject people maintaining their own laws, religions and traditions so long as the empire is served (remember Cyrus, also a Persian emperor is lifted up as a ‘messiah’ in Isaiah 45 and the Jewish story is in general very favorable towards Persia). But this story turns on the conflict between Mordecai and Haman, and the plot is moving.
Register here: http://gg.gg/vhk7m
https://diarynote-jp.indered.space
*7-11 Dice Games
*7 11 Dice Drinking Game
After the come point has been established you win if it is a 2 or 3 and lose for 7 or 11. 12 is a tie and other dice rolls will make you win only if a 7 appears before them on the following throws. Place Bets - This bet works only after the point has been determined. 7 / 11 dice game. While loops and with p. 7 / 11 dice game. While loops and with points and stuff. Write your question here. So i have this project. A gambling game played with two dice in which a first throw of 7 or 11 wins, a first throw of 2, 3, or 12 loses the bet, and a first throw of any other number (a point) must be repeated to win before a 7 is thrown, which loses both the bet and the dice. A losing throw in this game. Also called crap2. No-one will be fooled by the trick dice. One is all fives, and the other is half sixes and half twos. So, yes, you will always roll a 7 or 11, but even a quick glance at the dice reveals their ’secret.’ Only a blind person might be tricked by this.
In front of you are two fair dice.
One is a 7-sided dice with faces -3, -2, -1, 0, 1, 2, 3.
The other is an 11-sided dice with faces -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
You pick a dice, and I will get the other one. We will roll together, and the person with the larger number wins. If the two dice show the same number, we roll again until someone wins.
Which dice should you pick, if you want to maximize your chance of winning?
Bonus: solve the game for the generalized case: one dice has integer sides from –n to n and the other dice has integer sides from –m to m, where n < m.
Watch the video for a solution.
Or keep reading.
.
.
’All will be well if you use your mind for your decisions, and mind only your decisions.’ Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .
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Answer To 7 Vs 11 Sided Dice Game Riddle: Who Wins?
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
I saw this puzzle at Puzzling StackExchange and the answer initially surprised me until I read the excellent solution from hexomino.
First let’s solve the 7 vs 11 case directly. There are 7 equally likely ways to roll the 7 sided dice, and 11 equally likely ways to roll the 11 sided dice, for a total of 7 x 11 = 77 equally likely events.
We can visualize the sample space as an ordered pair (i, j) for rolling (7 sided dice, 11 sided dice).
There are 7 possible ways both dice show the same number:
(-3, -3), (-2, -2), (-1, -1), (0, 0), (1, 1), (2, 2), (3, 3)
For any other roll, the game ends with a win for some player. Thus there are 77 – 7 = 70 equally likely rolls in which the game ends.
Out of these, exactly 35 will be a win for the person rolling the 7-sided dice, which we can enumerate:
(-3, -5), (-3, -4)
(-2, -5), (-2, -4), (-2, -3)
(-1, -5), (-1, -4), (-1, -3), (-1, -2)
(0, -5), (0, -4), (0, -3), (0, -2), (0, -1)
(1, -5), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0)
(2, -5), (2, -4), (2, -3), (2, -2), (2, -1), (2, 0), (2, 1)
(3, -5), (3, -4), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (3, 2)
We can also use a table to represent the outcomes:
So the 7-sided dice wins with a 35/70 = 50 percent probability. And since the other game-ending outcomes are a win for the other dice, this means the 11-sided dice also wins with a 35/70 = 50 percent probability.
In other words, it doesn’t matter which dice you pick: the game is fair! Pat sajak family. There is a 50 percent chance of either player winning, and this is true even for the general case of an n dice versus an m dice for n < m.
General proof7-11 Dice Games
There’s a neat trick to see why each dice has the same chance of winning.
Consider the roll (i, j) = (player 1 rolls n dice, player 2 rolls the m dice).
Player 1 wins if and only if i > j.7 11 Dice Drinking Game
But for every such winning pair, there will also be a roll (-i, –j) because if a dice has a face labeled x it also has the face labeled –x. And this roll is a win for player 2 since i > j implies –i < –j.
And we can make the same argument for player 2 as well! Player 2 wins on a roll (i, j) if and only if i < j. But for every such winning pair, we can find the paired outcome (-i, –j) which is a win for player 1.
Thus, the mapping (i, j) to (-i, –j) is a bijection between the winning rolls between the two players. Player 1 and 2 have exactly the same number of winning outcomes, and the game ends in a win for some player, implying each person has a 50 percent chance of winning.
The game is fair, and it doesn’t matter which dice you pick, even in the general case!
Source
Problem adapted from Puzzling StackExchange. Best online poker machines. Post by athin, 11 sided vs 41 sided dice. Solution from hexomino.
https://puzzling.stackexchange.com/questions/77557/a-short-dice-puzzle
Achilles and Ajax Playing Dice, 6th Century BCE Greecian Pottery
7 In the first month, which is the month of Nisan, in the twelfth year of King Ahasuerus, they cast Pur– which means “the lot”– before Haman for the day and for the month, and the lot fell on the thirteenth day of the twelfth month, which is the month of Adar. 8 Then Haman said to King Ahasuerus, “There is a certain people scattered and separated among the peoples in all the provinces of your kingdom; their laws are different from those of every other people, and they do not keep the king’s laws, so that it is not appropriate for the king to tolerate them. 9 If it pleases the king, let a decree be issued for their destruction, and I will pay ten thousand talents of silver into the hands of those who have charge of the king’s business, so that they may put it into the king’s treasuries.” 10 So the king took his signet ring from his hand and gave it to Haman son of Hammedatha the Agagite, the enemy of the Jews. 11 The king said to Haman, “The money is given to you, and the people as well, to do with them as it seems good to you.”
The dice are rolled, the lot is cast for the date that will come to be Purim. It will be a day of reversals, but at this point in the story it is foreshadowed as a date that will bring disaster to the Jewish people. The king once again receives bad advice from an advisor, advice that will have long lasting consequences and the king never once asks a question or attempts to probe Haman’s motives. The king trusts Haman and is willing for an enormous pile of money (a ridiculous sum, 375 tons of silver, this is roughly 2/3 of the annual Persian kings’ income) to put his authority behind it. Perhaps in both the ancient world and the modern world enough money seems to make something evil more appealing.
This last thought reminds me, in a way, of the plot of the movie the Boxwhere a man and a woman are given a box with a button where if they push it they will receive one million dollars, but someone they don’t know will die and so they are entered into the ethical dilemma of whether their own very real monetary needs outweigh the life of a stranger. Now it is not the greatest movie, but the ethical question of the power of money to cause a horrible decision, especially when you don’t have to carry it out, more appealing. The king never carries out his decision, he is always insulated and while his ring may mark the life or death of many, he allows others to be the executioners.
The king not only takes the advice of Haman, he seems to compel it along even more so. The king’s authority is placed behind the plot of Haman. One man’s revenge now becomes imperial policy and the story’s crisis is set in motion. This is a strange story since the Persian empire was actually pretty benevolent as far as ancient empires go toward their subject people maintaining their own laws, religions and traditions so long as the empire is served (remember Cyrus, also a Persian emperor is lifted up as a ‘messiah’ in Isaiah 45 and the Jewish story is in general very favorable towards Persia). But this story turns on the conflict between Mordecai and Haman, and the plot is moving.
Register here: http://gg.gg/vhk7m
https://diarynote-jp.indered.space
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