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Comment by grecy | Hacker News Reader

This reminds me of my buddies beating a casino. It goes like this:

Play roulette, start with a low bet ($5) on black or white (50/50). If you win, you've profited the amount of the original bet. If you lose, double your bet and play again. Repeat until you win and you will have profited the amount of the original bet. Repeat.

This works so long as you have enough cash to keep doubling the bet. Hitting the maximum allowed bet on the table is not a problem, you just split it in half and keep going.

My buddies at one point had ~$60k on the table, and didn't have enough to go to ~$120k if they lost...

They did this for about two weeks straight, profiting something like $10k. One morning when they tried to enter the casino, the guards at the door said they were not welcome, and if they didn't leave immediately the police would be called. They assume they had been spotted on camera, or the table operator reported them.

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For anyone interested, this strategy is called the [1]Martingale betting system. It works great if a gambler has infinite money, but no gamblers do. It can deplete your bankroll very quickly, due to the exponential nature of the betting system. Your expected profit from this game style is still slightly below zero, due to the relatively unlikely event of running out of bankroll before winning and losing a catastrophic amount of money.

[1] http://en.wikipedia.org/wiki/Martingale_(betting_system)

EDIT: Everyone seems to have beaten me to this answer... :p

Not only that, but the 0 (and 00 if applicable) also push the odds against you.

The Martingale simply does not work. An infinitely wealthy gambler employing this strategy over an infinite time horizon on a fair game has a neutral expectation. For every gambler who comes out ahead, another one comes out behind. Additionally, real life gamblers aren't infinitely wealthy and casino games are negative expectation.

If it "works" for you, you're just the survivor bias.

> For every gambler who comes out ahead

That's only true in games where the only winnings are the bets of the players. Roulette, and blackjack, is different because your winnings on success are set and paid by the house.

He's not saying that there is literally one winner per loser, but that statistically the group of winners and group of losers will be about the same size, for a fair game.

I agree it doesn't work but with infinite money you can win any finite amount of money. Your assertion assumes that you don't stop after a win.

If you profited $10K for two weeks of work, you'd be getting all kinds of free stuff to get you to stick around longer and/or come back. (You'd also probably be laughed at behind your back since that's a pretty lousy take for a hell of a lot of work and a lot of risk)

Winning $10K from a casino is background noise. It's nothing that will get you kicked out.

That's not cheating..... it's a perfectly fine, perfectely efficient way for the casino to make money.

If you are splitting your bets among players to get around table limits, they might frown on that - but that's not because you are "winning" it's because you are circumventing their table limits.

This is called http://en.wikipedia.org/wiki/Martingale_%28betting_system%29

Thanks, I just found that.

Interesting they say that casino betting limits eliminate the strategy. I don't think that's true.

Let's say you have $100k on the table, which is the maximum allowed, and you lose. All you need to is play multiple tables with the doubled bet ($200k) split up across those tables. Once you've played all of those to conclusion (maybe even splitting again...) you will have effectively "won" the line of play that they tried to stop you when you hit the $100k limit.

Betting $100,000 on two tables has a lower probability of returning $400,000 than betting $200,000 on one table. Also a lower probability of returning zero, but winning one of those bets and losing the other doesn't help. Needing to win two independent (consecutive or simultaneous) negative-EV bets to beat a losing streak of a certain length increases the probability that combination of events won't happen, and if you lose both bets at the table limit (which is slightly more probable than winning both) you'll need to spread your bets across even more tables and hope even more independent events fall in your favour.

The Martingale strategy is not viable.

If winning at casinos is your goal, you're going to need to look elsewhere.

But this obviously fails in exactly the same way when there are no more tables. The strategy simply doesn't work.

Go to another casino and continue

It is pretty basic maths that will demonstrate that this system doesn't work (as in it doesn't "beat" the casino).

You say you won $10k, but how much money did you have? You said at one point you had $60k on the table so let's assume you had just that - if you put the entire 60k on something which has 7:6 odds then the odds of you winning are high but exactly what you would expect given the winnings compared with the bet.

When you play with the martingale strategy your odds of winning aren't any better, you just think they are because you don't realise your entire pot of money is actually at stake.

I may be wrong, but I don't know if that works at a lot of casinos because of the zeros and double zeros on the wheel. I think that gives the house an edge.

That's called Martingaling, and it isn't beating a casino because eventually you'll hit a losing streak and either run out of money or hit table limits.

http://en.wikipedia.org/wiki/Martingale_(betting_system)

The Martingale only wins in the long run if you have unlimited wealth and time. http://en.wikipedia.org/wiki/Martingale_%28betting_system%29

I don't see how this betting scheme can be of advantage if each game round is independent of the previous. Plus many casinos put a maximum bet limit anyway if you could somehow make it work.

Except for limits (be it imposed by the casino or your bank account), it's a no-loss situation, even with slightly less than half winning chance (eg due to 0).

Every time you lose, you make up by increasing the potential earning: $1 lost, $2 lost ($-3 total), $4 lost ($-7 total), $8 won ($1 total)

The only problem is that these theoretical limits are really limiting in practice ;-) In case of the GPs buddies, if they started at $15, playing at ~$60k means that they lost 12 times in a row, and if they finally won that round, they still only gained $15.

I just bet using my lucky numbers (no, you may not have them). Guess I beat them too.

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