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You have two dices. There are two players. You each pick a number. The person who picks the number closest or equal to the sum of the roll of the dices is the winner. What is the strategy to optimize chances of winning. Also, is it always better to pick the number that has the highest chance of being rolled? This situation does not apply to the rules of this game. For example, this question could apply to the rules when the two numbers on the die are multiplied rather than added.
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Assistant Trader

Interviewed at Jane Street

4.4★
Jan 16, 2015

You have two dices. There are two players. You each pick a number. The person who picks the number closest or equal to the sum of the roll of the dices is the winner. What is the strategy to optimize chances of winning. Also, is it always better to pick the number that has the highest chance of being rolled? This situation does not apply to the rules of this game. For example, this question could apply to the rules when the two numbers on the die are multiplied rather than added.

Similar to question about coins however it was about beads that were then not replaced. So For example there are 6 $10 chips in Urn A and 6 $1 Chips. 3 $10 chips in Urn B and 9 $1 chips. Given that the chip picked is $10, what is the probability of picking a $10 chip again and what is the estimated value of this pick.
avatar

Assistant Trader

Interviewed at Jane Street

4.4★
Jul 15, 2015

Similar to question about coins however it was about beads that were then not replaced. So For example there are 6 $10 chips in Urn A and 6 $1 Chips. 3 $10 chips in Urn B and 9 $1 chips. Given that the chip picked is $10, what is the probability of picking a $10 chip again and what is the estimated value of this pick.

I have 100 green marbles and 100 red marbles and I can divide them up however I want between 2 bags. There has to be 1 marble in each bag, other than that no restrictions. You do not know how I divide them up or which bag you are getting. If you pick a green marble I pay you 100 dollars, If you pick a red, I pay nothing. What is a fair price for this game?
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Assistant Trader

Interviewed at Jane Street

4.4★
Feb 20, 2011

I have 100 green marbles and 100 red marbles and I can divide them up however I want between 2 bags. There has to be 1 marble in each bag, other than that no restrictions. You do not know how I divide them up or which bag you are getting. If you pick a green marble I pay you 100 dollars, If you pick a red, I pay nothing. What is a fair price for this game?

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