Comment on Is there a house advantage in a "double-or-nothing" coin flip game?
HandwovenConsensus@lemm.ee 2 months agoRight, and as the chain continues, the probability of the player maintaining their streak becomes infinitesimal. But the potential payout scales at the same rate.
If the player goes for 3 rounds, they only have a 1/8 chance of winning… but they’ll get 8 times their initial bet. So it’s technically a fair game, right?
All the house needs to do is to create an overall situation where more people push until they fail than cashing out whilst ahead. And that’s where the disparity in bank rolls comes in. The bank has a cap so large that it doesn’t come in to play the vast majority of times, so they just keep raising the stakes to give people another chance to fail.
And as long as more people push than don’t, in the end, it works out of the house
rowinxavier@lemmy.world 2 months ago
If everyone has the same amount of starting capital it is a fair game assuming both can opt out at any time.
That said, the house appears to not be able to opt out (they definitely can, you just don’t think about that part), and the house has more capital. For them each time someone plays a round there are only 3 possible outcomes. Half are the player loses, then a quarter are the player wins and plays another round, and lastly a quarter are the player wins and ends the game. The only case where the player wins is option 3, in all other cases, so 75%, the house wins because the next round has another chance to make the player lose directly at a 50/50 chance or play another round.