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### Optimal Strategy for a new twist on Rock/Paper/Scissors

Posted: Thu Jun 01, 2017 8:00 pm UTC
You are playing an opponent for a large but indeterminate number of rounds. Standard Rochambeau hand throw rankings apply, except your opponent is told before the game starts whether his goal is to win the most rounds, or to lose the most, determined by a fair coin toss. You are not told in advance if he is trying to win or lose. You may not discuss strategy in advance with your opponent, but you can presume he is perfectly logical.

Is there an optimum strategy that you and your opponent can employ where the game is:

a) adversarial; if your opponent wins more rounds, then they get a prize and you lose that prize
b) cooperative; if your opponent wins more rounds, then they get a prize and you win a prize as well

When I say "wins" that means they are successful based on their coin-flip-determined goal; either to "win" each round or to "lose" each round. You and your opponent both do know if the overall game is adversarial or cooperative.

### Re: Optimal Strategy for a new twist on Rock/Paper/Scissors

Posted: Thu Jun 01, 2017 8:38 pm UTC
Just my quick thoughts on this:

In the adversarial case, the best I can think of is to select a random throw each round. I don't know of any strategy that would allow you to consistently best a perfectly logical opponent, even without the twist of a random victory condition. This strategy should result in ~50/50 win/loss overall.

In the cooperative case, you want to throw the same thing every round. Your opponent will pick up on this quickly and knows his win condition, and thus you will both win.

It doesn't seem to matter whether your opponent's goal is to win or lose; really, all this introduces is a chance that the throw rankings are reversed.

### Re: Optimal Strategy for a new twist on Rock/Paper/Scissors

Posted: Thu Jun 01, 2017 8:40 pm UTC
Well, the co-operative version sounds fairly easy. Your opponent wants to achieve their objective, so they get a prize. You want to help them, so you get a prize too. They know the objective, you don't. So, let them decide the result. Just throw "rock" every time. They will throw "paper" or "scissors" every time as appropriate, and you'll both win prizes.

How can I be sure that this will work? Given their logic, they will realize that you want them to "win", and you are effectively playing to lose. The surest way to lose RPS is to be predictable, and what's more predictable than playing the same thing every turn? Why rock? It's the most common throw. Even if they misjudge your strategy to begin with, it will only take them a few turns to see what you're doing.

Or even simpler, since you only banned discussing strategy in advance, just ask them what the objective is and what they're going to throw each turn...

### Re: Optimal Strategy for a new twist on Rock/Paper/Scissors

Posted: Thu Jun 01, 2017 8:44 pm UTC
SteelCamel wrote:Or even simpler, since you only banned discussing strategy in advance, just ask them what the objective is and what they're going to throw each turn...

This doesn't work, since the opponent will always tell you co-operative regardless of what their actual objective is.

### Re: Optimal Strategy for a new twist on Rock/Paper/Scissors

Posted: Thu Jun 01, 2017 9:00 pm UTC
LaserGuy wrote:
SteelCamel wrote:Or even simpler, since you only banned discussing strategy in advance, just ask them what the objective is and what they're going to throw each turn...

This doesn't work, since the opponent will always tell you co-operative regardless of what their actual objective is.

You already know if the game is adversarial or cooperative. The secret information your opponent has is whether their goal is to win the most rounds or lose the most rounds.