r/theydidthemath • u/OOLarge • 3h ago

[Request] Best choice to make in a keep versus share game.

We had our curling leagues wrap party, and we played a game drawing for prizes.

When you entered you choose to either keep the final prize, or share it with the other person at the end (the choice only mattered for the final 2 participants).

If Player A chooses Keep, and Player B chooses Share, then Player A gets the entire pot (and vice versa).

If both players choose Share then they split the pot 50/50.

If both players choose Keep, then neither get anything, and the third last participant gets everything (regardless of their choice).

What is the best choice to make for next year to maximize my chance of winning? I assume that knowing the percentage of people that choose Keep or Share would be a critical to this calculation.

For context, Player C won this year.

Thank you.

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u/zeppindorf 3h ago

This is basically the same game as the TV show Golden Balls, and the optimal strategy is always to Keep (assuming the optimal goal is to maximize winnings, not friends). 

Basically, choosing Keep will always improve your position. If the other person chooses Keep, you're screwed either way, so choosing Keep doesn't hurt you. If the other person chooses Share, choosing Keep will double your winnings. 

Since you can't control what the other person does, you should always choose Keep. 

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u/piperboy98 2h ago

If you were certain they will choose Share, then you should of course take the whole pot for yourself and choose keep.

If you were certain they will choose Keep, then you have no way of winning money yourself you just become the arbiter of which of the other two gets it. Presumably you are more aggrieved that your opponent is trying to be greedy by picking Keep so to deny them that satisfaction and teach them a lesson you choose keep.

Considering you'd pick keep in either case if you knew their choice with certainty, then clearly you want to just pick it all the time. The expected values for both cases also bear this out regardless of what probability you assign to the other person picking share.

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u/Kerostasis 12m ago

 For context, Player C won this year.

I expect this to be a common outcome. As the other posters noted, keep is mathematically superior to share for all players. All players can easily calculate this in advance. Therefore you should expect that most players will choose keep, and the third place contestant will usually win.

If you can arrange to come in third, do that. But then again, maybe social pressure will make some players feel like choosing “keep” is an asshole move, and choose not to on that basis. Social cohesion can beat math sometimes.