The basic flaw with the "martingale" system, which is the one I'm describing, can be summarized as follows: you're usually going to win, but eventually you will lose many times in a row and lose really big. So if someone uses this strategy consistiently in casinos over the course of his life he is likely to end up losing more money than he wins.

The reason that the above strategy is different is as follows: the amount of money the player is trying to win is small compared to his bankroll. The bankroll, versus a small amount of desired winnings, allows for a large number of consecutive failures to be dealt with. Since the player is only trying to win a little bit of money and not continuing indefinitely the odds of a long string of consecutive losses are low.

So while a player using the strategy above has a probability of losing big, it seems more likely that he'd succeed in making a small amount of money if he stops playing as soon as he is reached his goal, and only gambles once or twice in his life instead of doing it regularly.

No, actually, they're just counting on someone feeding something back in. Naive blackjack (without counting cards, or with too many decks to count) gives the house an incredibly small advantage over a good player, but casinos don't play a few dozen games against a small handful of players a day—they play millions of games against thousands of players. It's the Law of Large Numbers in action.

Anyway, while it has some variance at the small-possible-repetitions end of the spectrum, IIRC the proper way to apply the bet-doubling strategy is to make your initial bet what you want to win. From there, you just make your bankroll large enough to ensure that you can wait until your number will most likely come up. There are, however, other things that make it impractical (like having a sufficiently large bankroll, or the possibility of a bet limit which would start requiring you to win multiple times).

It should be noted that there is at least one casino game at which you can, if you're good enough, expect to reliably make money and not get kicked out. That game is poker, and the reason is because no matter what happens, the house gets its cut—you're playing against the other players, and only against the house to the degree that you need to win enough to outweigh the loss of the rake. The same would hold true of any game where the payout comes from the other players rather than from the casino and where skill can gain at least enough advantage to outweigh the rake. On the other hand, you then have to play against the unknown skill of the other players instead of against a known set of odds for the house…

~J

You're assuming most people can calculate the math. We're already an odd bunch here on the forums, one dedicated to an rpg... it's a different demographics compared to the rest of the population.

Yeah, I agree, many places the thinness of the house margin is actually an incentive to go there. Poker players definitely prefer a milder rake all things being equal.

Hmmm, my math doesn't seem to be working right, 'cause I keep figuring that you should pay anything to get into this game, but that seems wrong.
I need to recheck this.


edit: Is that the trick of it? The expected value is infinite?

If the amount you pay makes no difference why is it not totally basic that you pay the least possible amount to get the goods, i.e. find the least-valued banknote in the entire world and pay that?

The idea is to, if you come across someone offering entrance to this lottery at $n, determine whether you should enter the lottery or not. You don't get to choose the price the person is offering

~J

Oh, I see. So even if he's asking for billyuns and billyuns of dollars you should pay that if you have the ability to do so.

I marvel at your ability to make that problem so complicated.
That's.......a slightly different approach than I took.