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Person A has a 20-sided dice and person B has three 6-sided dice. They both roll their dice and whoever gets a bigger number/sum of numbers wins the game. Is it a fair game? Same game with one more player C who has a 20-sided dice. Is this new game fair? (all dice are fair; a 20-sided dice has number 1,2,…, 20 on each of its 20 sides) 作者：匿名用户 链接：https://www.zhihu.com/question/29364614/answer/216229840 来源：知乎 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。 Person A and B are going to play a coin toss game. There is an initial score 0, and whenever a head/tail appears, the score +1/-1. Repeating the coin toss until one wins, that is, when the score reaches +2/-2, A/B wins the game. There is also an initial stake $1 for the game and person A has the option to double the stake every time before a coin toss. When one person wins the game, the other player needs to pay the amount of dollars on the stake to the winner. The question is: if you are person A, what is your strategy and what is your highest expected payoff of the game?
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Quantitative Trader

Interviewed at Jane Street

4.4★
Dec 10, 2020

Person A has a 20-sided dice and person B has three 6-sided dice. They both roll their dice and whoever gets a bigger number/sum of numbers wins the game. Is it a fair game? Same game with one more player C who has a 20-sided dice. Is this new game fair? (all dice are fair; a 20-sided dice has number 1,2,…, 20 on each of its 20 sides) 作者：匿名用户 链接：https://www.zhihu.com/question/29364614/answer/216229840 来源：知乎 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。 Person A and B are going to play a coin toss game. There is an initial score 0, and whenever a head/tail appears, the score +1/-1. Repeating the coin toss until one wins, that is, when the score reaches +2/-2, A/B wins the game. There is also an initial stake $1 for the game and person A has the option to double the stake every time before a coin toss. When one person wins the game, the other player needs to pay the amount of dollars on the stake to the winner. The question is: if you are person A, what is your strategy and what is your highest expected payoff of the game?

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