# Throwing Poker Chips Close to Wall Game

I just had an interview question involving a two-player game of throwing poker chips closest to the wall. Players take turns throwing chips (of which you start with zero, but chips can be "borrowed"), and each turn a player can choose to pass. The game ends when both players pass. The winner is the player who throws closest to the wall, and he or she wins 20 poker chips. The goal is to maximize the number of chips you end up with. For example, if player 1 throws 14 chips before both players pass and they are closest to the wall, they will end up with 6 chips since they receive 20 chips for winning and have to repay the "borrowed" 14 chips.

The interviewer asked what the optimal strategy for maximizing the number of chips you end up with is and I couldn't come up with anything concrete. Does anyone know the strategy? Is the game even worth playing? Does knowing the distributions of the distance of the players throw change anything?

The game will never end since $$20-\text{borrowed chips}>-\text{borrowed chips}$$. The optimal strategy for both players is: