HandwovenConsensus

One thing I remember when I saw this discussed before is that it doesn't take into account whether or not those vacant properties are inhabitable.

Well, I only know how it tends to work in China, where the traditional calendar is used for cultural events such as festivals, while the Gregorian calendar is used for just about everything else, including domestic business. I assumed it's the same in most modern cultures with a different traditional calendar, but maybe I'm wrong.

Is it? I know some cultures have a traditional lunar calendar, but I didn't know there were many that didn't also use the Gregorian calendar for business.

Which cultures have the seven day week without the solar year?

The plummeting should take care of itself from that point. You might need assistance with the rotation though.

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.

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?

I feel like he was working up to a punchline about haven mistaken a toy for an electric school bus, but for some reason failed to get there.