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person A has a 30 sided and person B has a 20 sided die. both players role and the person with the highest role win (on a draw B wins). the loser pays the winner the value of the winners die. 1. calculate expected value of this game for player A (easy) 2. how does this value change if player B can re-roll and when should he re-roll. 3. now how much is it worth for player A to get a re-roll option in this scenario. 4. remove player A reroll. how many re-rolls do player B need in order for him to be a favorite in the game. i believed i solved 4 and 2 I had a decent idea but 3 is very difficult since optimal strategy might change based on opposing players optimal strategy.
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Assistant Trader

Interviewed at Jane Street

4.4★
Apr 4, 2014

person A has a 30 sided and person B has a 20 sided die. both players role and the person with the highest role win (on a draw B wins). the loser pays the winner the value of the winners die. 1. calculate expected value of this game for player A (easy) 2. how does this value change if player B can re-roll and when should he re-roll. 3. now how much is it worth for player A to get a re-roll option in this scenario. 4. remove player A reroll. how many re-rolls do player B need in order for him to be a favorite in the game. i believed i solved 4 and 2 I had a decent idea but 3 is very difficult since optimal strategy might change based on opposing players optimal strategy.

You have a dart board thats split in half. If you hit the left half, you get 2 points, if you hit the right half, you get 3 points. If you have an 80% chance of hitting the dart board on any given throw and a 70% chance of hitting the side you're aiming for (given that you hit the dartboard so a 30% chance you hit the side you aren't aiming for), if you have an unlimited number of throws, what's the probability you get a score of exactly 7
avatar

Assistant Trader

Interviewed at Jane Street

4.4★
Mar 3, 2014

You have a dart board thats split in half. If you hit the left half, you get 2 points, if you hit the right half, you get 3 points. If you have an 80% chance of hitting the dart board on any given throw and a 70% chance of hitting the side you're aiming for (given that you hit the dartboard so a 30% chance you hit the side you aren't aiming for), if you have an unlimited number of throws, what's the probability you get a score of exactly 7

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