I’m looking at the game as a whole. The player has a 1 in 8 chance of winning 3 rounds overall.
I’m looking at the game as a whole. The player has a 1 in 8 chance of winning 3 rounds overall.
But the odds of the player managing to do so are proportionate. In theory, if 8 players each decide to go for three rounds, one of them will win, but the losings from the other 7 will pay for that player’s winnings.
You’re right that the house is performing a Martingale strategy. That’s a good insight. That may actually be the source of the house advantage. The scenario is ideal for a Martingale strategy to work.
Well, they have to start over with a $1 bet.
I don’t know if that applies to this scenario. In this game, the player is always in the lead until they aren’t, but I don’t see how that works in their favor.
You’re saying that the player pays a dollar each time they decide to “double-or-nothing”? I was thinking they’d only be risking the dollar they bet to start the game.
That change in the ruleset would definitely tilt the odds in the house’s favor.
Right, 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?
Not quite the same, since in my scenario the player loses everything after a loss while in the St. Petersburg Paradox it seems they keep their winnings. But it does seem relevant in explaining that expected value isn’t everything.