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.

Also videos that weren’t intended for kids but superficially looked like they were got involuntarily flagged as such and had their comments removed.

A separate site would have been a much better solution.

Yeah, I can’t speak to the behind-the-scenes drama, but I agree that Pierce was at his best in Season One, where he was a little bit grandiose and a little bit of a jerk but still had moments of wisdom and humanity. I always liked the talk he gave Jeff in the boating episode.

Turning him into a total buffoon villain from season 2 onwards was a change for the worse.

Taiwan had the same concern. What they did is make it so that receipts also work as lottery tickets, to encourage people to ask for them and hold on to them.

What I usually love about musicals is the variety of songs and subject matters, and with the exception of the Klingon song, the songs all felt the same.

If you liked Norsemen, try Lilyhammer.

Forget Sandy Loam. I want to know more about this “silly clay.”

I’m surprised to hear that. When I was in China in the early 2010s I saw it played all the time.

Surely there’s a difference between an animated movie loosely inspired by a traditional story with original songs, character designs, and dialogue, and remaking that movie beat-for-beat with just a few scenes changed for pandering.

Everything about that was puzzling. They changed the story supposedly to be more culturally accurate, but what they came up with wasn’t culturally accurate at all. How did that happen?

Besides, when Chinese people want a culturally accurate Mulan, they watch one of the many Chinese-made adaptions of the story. The animated was appealing because it was a fresh take, a Disney musical that Chinese could relate to. The remake was just a huge miscalculation.

That’s not true. The Hoover Dam contributes to Vegas’s power supply, but it’s nowhere near “almost entirely powered” by the dam, except in Fallout: New Vegas.

Sure, both sides are not the same. But the “good” side is still part of the system that allows the “bad” side to exist.

So by all means, vote for the party that will do less damage in the short term. But oppose FPTP voting at the same time.