A quick and dirty, shallow one, that I just opted to brute force out of curiosity.
An online game I play includes an optional two player Russian Roulette type feature (non-fatal). I got to wondering if there was an optimal betting percentage to use, if you set aside some money as a betting seed. So I spent time coding up a really ugly brute force "just run lots of games and see".
Pretty much the answer is you'll lose more often than you win, looks like your best bets are around 2% of whatever money you have left of your betting money.
If you play 75 games, at 2% of your betting pool, you'll come out ahead only about 49.8% of the time.
There's more efficient ways of working that out than I bothered to do, which was to create a basic abstraction for a gun. For example, your odds of winning is essentially 50%, given two players. For every "game" I simulated, I could have just picked a random integer between 0 and 1 instead. Faster and the same effect.
As best as I could find, there are no good betting strategies on a coin toss (which is what this really is)
An online game I play includes an optional two player Russian Roulette type feature (non-fatal). I got to wondering if there was an optimal betting percentage to use, if you set aside some money as a betting seed. So I spent time coding up a really ugly brute force "just run lots of games and see".
Pretty much the answer is you'll lose more often than you win, looks like your best bets are around 2% of whatever money you have left of your betting money.
If you play 75 games, at 2% of your betting pool, you'll come out ahead only about 49.8% of the time.
There's more efficient ways of working that out than I bothered to do, which was to create a basic abstraction for a gun. For example, your odds of winning is essentially 50%, given two players. For every "game" I simulated, I could have just picked a random integer between 0 and 1 instead. Faster and the same effect.
As best as I could find, there are no good betting strategies on a coin toss (which is what this really is)