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Question 1 : We play a game with coins. Player 1 wins if HHT is before HTT. Player 2 wins if HTT is before HHT. Which one is more likely to win ? I choose to bet on HHH. Is there a 3-sequence that beat it ? Question 2 : 2 players : you (player 1) and an other player (player 2). You select a number between 1 and 100 and the one that tells the bigger number has to pay the lower number to the other player. The player 2 says a random number between 1 and 100. What is the optimal strategy ? A third player comes in the game. Now the bigger number has to pay to the 2 other players the number that each one has told. We suppose that the third player is smart. Which strategy to beat him ?
avatar

Trader intern

Interviewed at Jane Street

4.4★
Oct 20, 2019

Question 1 : We play a game with coins. Player 1 wins if HHT is before HTT. Player 2 wins if HTT is before HHT. Which one is more likely to win ? I choose to bet on HHH. Is there a 3-sequence that beat it ? Question 2 : 2 players : you (player 1) and an other player (player 2). You select a number between 1 and 100 and the one that tells the bigger number has to pay the lower number to the other player. The player 2 says a random number between 1 and 100. What is the optimal strategy ? A third player comes in the game. Now the bigger number has to pay to the 2 other players the number that each one has told. We suppose that the third player is smart. Which strategy to beat him ?

4 players in a game, rolling dice. The one with the largest value and the one with the smallest value team up. The others team up as well. The winning team is the team with the biggest sum of the dice values. The payoff is the difference between the sums.
avatar

Quant Trader Intern

Interviewed at Jane Street

4.4★
Oct 4, 2021

4 players in a game, rolling dice. The one with the largest value and the one with the smallest value team up. The others team up as well. The winning team is the team with the biggest sum of the dice values. The payoff is the difference between the sums.

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