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Comment by fatbird | Hacker News Reader

I was able to play martingale in a casino in a video game, so a limited wallet wasn't my problem, and I made money in the long run, but it exposed a subtler problem with Martingale: You only ever win your initial bet back; the rest is covering losses. If you have the cash to withstand 20 losses, then the initial bet, in comparison to your stake, is basically a rounding error. Who cares about winning $1 when you have $1 billion to martingale it?

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Yes -- this is what is commonly misunderstood about Martingale. What Martingale really does is change the probability distribution of outcomes to be heavily weighted toward winning a very small amount of money.

You can, for a given number of plays, use Martingale to make the odds of winning greater than the odds of losing. However what you can't do, is change the expected value of that set of plays. So what you've really done is created a situation where you have a high chance of winning a small amount of money, and a low chance of losing a lot of money.

Yeah, I'm running the Martingale simulator in OP, and getting frequent outcomes where I was able to gamble 10+ days starting with $10000. I suspect that's what gamblers really like about it -- not more money, but more gameplay.

(There's also the gambler's calculus that while they're losing money playing, they're being comped drinks/rooms/meals/shows/etc at a resort.)

What's kind of funny is that lots of people talk about playing the Martingale, which is dumb, but no one ever talks about playing the reverse Martingale - which is also dumb and losing, but at least has what I'd argue is a more favorable outcome distribution. Basically, with a reverse Martingale you'll usually lose a moderate amount (which, I mean, is what you'd expect since...casino) but occasionally win a larger amount when you hit your winning threshold and get, say, 6 positive results in a row.

Plenty of people play like this accidentally, moving up stakes when they are winning.

Yes, that is also a problem. When you lose, your risk increases exponentially. Given an unlimited wallet and no casino rules, that's ok. But the real world unfortunately doesn't work like that. (And if you had an unlimited wallet, who cares if you lose?)

No matter what you bet, your take is only equal to your initial bet * number of rounds/hands played.

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