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| | | Supreme Being
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Last Login: 8/3/2008 2:38:40 PM
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| | I'm pretty sure there's some proof out there that shows that the Martingale gives you no better or worse long term expectation than betting the same amount on each bet. I know I can show it for a very simple situation, but not for more complex situations. The difference is that with a flat betting structure, you're risking a small amount every time. With the Martingale, you often risk a lot more at a time (though when you win you make up for your losses faster). But this requires an infinite bankroll and no table max, or else as we already know you can hit that long losing streak and not make it all back. But if you had an infinite bankroll, you wouldn't mind losing (and I don't know why you'd be gambling anyway).
"You have to put yourself in position to get lucky."
--Tom McEvoy |
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| | | Supreme Being
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Last Login: 9/25/2007 5:19:42 AM
Posts: 332, Visits: 562 |
| | No, there's a mathematical proof that the Martingale gives a guaranteed return, even in a -ve expectation game like Roulette. The only problem is, that the assumption of infinite bankroll is a touch optimistic.
-- FToP says everytime you are outdrawn giving the wrong odds, you actually won something! If only the accountants at my Poker Site would agree. Money men think so short term... |
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| | | Supreme Being
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Last Login: 8/3/2008 2:38:40 PM
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| robnotts (4/7/2006)
No, there's a mathematical proof that the Martingale gives a guaranteed return, even in a -ve expectation game like Roulette. The only problem is, that the assumption of infinite bankroll is a touch optimistic. Are you actually suggesting that if you make enough bets that all have a -EV, you can end up with an overall positive EV? Surely you see the paradox in this. I don't have time now, but later I'll show what I have for this.
"You have to put yourself in position to get lucky."
--Tom McEvoy |
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| | | Supreme Being
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Last Login: 9/25/2007 5:19:42 AM
Posts: 332, Visits: 562 |
| As I said there's a mathematical proof, it's not 'my suggestion'. It falls down in real world because the assumptions are unrealistic.
-- FToP says everytime you are outdrawn giving the wrong odds, you actually won something! If only the accountants at my Poker Site would agree. Money men think so short term... |
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| | | Forum Newbie
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Last Login: 6/6/2006 6:00:20 AM
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| | Hi all, Firstly, i'm new to this site and forum, so hello. There's interesting threads, and it's a very good work skive. Secondly, I was interested in flashmans martingale system for 3 card poker, but was very sure that it was overall a losing system. However, I was a bit bored at work and wanted to find out exactly how unprofitable (or profitable) the system was, so I coded up a simulation using more or less the same system that Flashman proposed. And here's what I found.... The percentage chance of winning with certain hands are as follows: Pair = 21.6% Flush = 6.3% Straight = 3.3% Set = 0.7% Straight Flush = 0.2% Overall winning percentage = 32.1% The chance of losing for 9 hands in a row is (1-0.321)^9 = 3.07*10^-3, or 3.07%. You should expect a losing run every ~33 attempts on average. At this point I was absolutely convinced the system would be unprofitable. I ran a few simulations of 10000-10000000 trials (a trial being series of hands, doubling up until you win or lose 9 times in a row). Amazingly it seems the system is profitable and has an expectation of ~$3.5 per trial. I am still looking over my coding of the simulation, trying to find the bug, but I am beginning to growing more confident that it's correct. My understanding is that the Martingale system for roulette doesn't have an overall positive expectation with a finite bankroll. If you don't have an infinite bankroll you will eventually and inevitably have a losing streak that will wipe you out. I think this system might work because of the few times when you hit a big hand when the stakes are high. The downside is that the variance is huge, and after as many as 1000 trials it seems you can be more than $10000 up or down. If anyone wants to see some graphs of typical bankroll fluctuations, or wants to see the coding of the simulation then you can pm me. NB, the only difference between my system and Flashmans is that I exactly double up each time ($0.5|$1|$2|$4|$8|$16|$32|$64|$128), whereas Flashman talked about $50 bets. ****NB I am not 100% sure that my simulation is correct, so don't try this system out, lose lots of money and blame it on me!!!! |
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| | | Forum Newbie
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Last Login: 6/6/2006 6:00:20 AM
Posts: 8, Visits: 42 |
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| | | Forum Newbie
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Last Login: 6/6/2006 6:00:20 AM
Posts: 8, Visits: 42 |
| | Whoops!!! I didn't read the rules of the game properly. You've got to beat the dealer!!! In that case i'm sure it isn't a profitable stategy. Shame, it would have been nice. I guess casinos don't give their money away. |
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| | | Forum Newbie
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Last Login: 6/6/2006 6:00:20 AM
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| | Just for the record, there was a bug in my simulation... This IS now correct and Martingale doesn't work. ## 3card poker Martingale System ### Initial Bankroll = $0 1000000 Trials 3632653 hands dealt 615197 pairs 16.94% 180549 flushes 4.97% 118380 straights 3.26% 8575 sets 0.24% 7692 str8flsh 0.21% 930393 wins 25.61% Lost 69607 trials Final Bankroll = -$746700.5 Expectation = -$0.7467/trial ## Standard 3card poker :: $1 bet ### Initial Bankroll = $0 10000000 hands dealt 1693106 pairs 16.93% (expected 16.94%) 496389 flushes 4.96% (expected 4.96%) 326340 straights 3.26% (expected 3.26%) 23694 sets 0.24% (expected 0.235%) 21843 str8flsh 0.22% (expected 0.217% 2561372 wins 25.61% Final Bankroll = -$217386 Expectation = -$0.0217/hand |
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| | | Supreme Being
Group: Forum Members
Last Login: 8/3/2008 2:38:40 PM
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