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Omni-MATH / Two players, A and B, play a game called "draw the joker card". In the…

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problem

Two players, A and B, play a game called "draw the joker card". In the beginning, Player A has nn different cards. Player B has n+1n+1 cards, nn of which are the same with the nn cards in Player A's hand, and the rest one is a Joker (different from all other nn cards). The rules are i) Player A first draws a card from Player B, and then Player B draws a card from Player A, and then the two players take turns to draw a card from the other player. ii) if the card that one player drew from the other one coincides with one of the cards on his/her own hand, then this player will need to take out these two identical cards and discard them. iii) when there is only one card left (necessarily the Joker), the player who holds that card loses the game. Assume for each draw, the probability of drawing any of the cards from the other player is the same. Which nn in the following maximises Player A's chance of winning the game? n=31n=31, n=32n=32, n=999n=999, n=1000n=1000, For all choices of nn, A has the same chance of winning
Plain-text mathematical notation (without MathML)
Two players, A and B, play a game called "draw the joker card". In the beginning, Player A has n different cards. Player B has n+1 cards, n of which are the same with the n cards in Player A's hand, and the rest one is a Joker (different from all other n cards). The rules are i) Player A first draws a card from Player B, and then Player B draws a card from Player A, and then the two players take turns to draw a card from the other player. ii) if the card that one player drew from the other one coincides with one of the cards on his/her own hand, then this player will need to take out these two identical cards and discard them. iii) when there is only one card left (necessarily the Joker), the player who holds that card loses the game. Assume for each draw, the probability of drawing any of the cards from the other player is the same. Which n in the following maximises Player A's chance of winning the game? n=31, n=32, n=999, n=1000, For all choices of n, A has the same chance of winning
Original LaTeX notation
Two players, A and B, play a game called "draw the joker card". In the beginning, Player A has $n$ different cards. Player B has $n+1$ cards, $n$ of which are the same with the $n$ cards in Player A's hand, and the rest one is a Joker (different from all other $n$ cards). The rules are i) Player A first draws a card from Player B, and then Player B draws a card from Player A, and then the two players take turns to draw a card from the other player. ii) if the card that one player drew from the other one coincides with one of the cards on his/her own hand, then this player will need to take out these two identical cards and discard them. iii) when there is only one card left (necessarily the Joker), the player who holds that card loses the game. Assume for each draw, the probability of drawing any of the cards from the other player is the same. Which $n$ in the following maximises Player A's chance of winning the game? $n=31$, $n=32$, $n=999$, $n=1000$, For all choices of $n$, A has the same chance of winning

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task_id
e2267e43-b71a-50d9-a333-99af27c5c256
task_key
test--e2267e43-b71a-50d9-a333-99af27c5c256
task_revision_id
1
config / split
/ test

Official source

initial import