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Old 09-16-2020, 04:28 PM   #1
David Sklansky
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Martingale With An Infinite Bankroll

I'm starting this thread because I worry that someone may misconstrue something that heehaww pointed out elsewhere and perhaps go on to do something foolish. Also what I am about is counter intuitive and may start an interesting discussion.

The martingale system for even money bets means you start off betting, say a dollar, and keep doubling up after each loss and go back to a dollar after a win. When you do win, your bankroll has increased by one dollar compared to when you started the sequence.

If you are betting on something that is less than 50% and have a limited bankroll you will eventually hit a streak so bad that it will wipe out your staring bankroll plus all your accumulated dollar wins. (That would not necessarily happen if you were over 50% because your accumulation pace outruns bad luck chances.)

But if you have an unlimited bankroll each one dollar increase must eventually happen. Even if the bet is well below 50%. (As long as it remains the same odds throughout.) So, as heehaww pointed out, you are essentially 100% to reach any goal you set for yourself. With an unlimited bankroll you will eventually be a trillion dollars ahead betting on 49% shots.

But what about the principle that a group of bets that are all negative EV has a negative EV? This seems to violate that.

But it doesn't. Here is why:

If George has an unlimited bankroll and embarks on the martingale system for 49% shots and you interrupt him and ask him how he is doing overall at that precise moment, whether it be after one flip or a googol flips, his possible answers average out to a negative number. Do you see why?
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Old 09-17-2020, 01:16 AM   #2
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Re: Martingale With An Infinite Bankroll

I'm going to elaborate a little. Suppose I decide to check on you after your millionth flip. At that point you will most likely be up about $490,000. Every one of your winning flips moves your bankroll up one dollar, (compared to where it was after your previous winning flip).

If your millionth flip was a winner, you are at a new peak as to how much you are ahead.

But if your millionth flip was a loser, you will be below your peak. Well below if you are in the midst of several consecutive losses. It is even theoretically possible that the losing streak has temporarily wiped out your profit to that point. This of course doesn't bother you because when the losing streak ends you will have overcome the terrible loss and be at another new peak. But if you knew I was lurking nearby and might interrupt things you might feel differently.
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Old 09-17-2020, 10:36 AM   #3
robert_utk
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Re: Martingale With An Infinite Bankroll

Isnít this what Phil Laak means when he answers:

Iím up...

Or

Iím stuck...

Or

Iím upstuck...
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Old 09-17-2020, 02:54 PM   #4
David Sklansky
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Re: Martingale With An Infinite Bankroll

I should add one more thing. The inevitability that somewhere in your adventure you hit a streak that wipes out your accumulated gains does NOT apply when you are betting on 51% shots rather than 49% shots. A losing streak of any size will eventually happen but even with an infinite number of flips it is not certain that any of those losing streaks wipes out you win up to that point and your overall EV martingaling good bets is positive, just as you would expect.
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Old 09-18-2020, 06:40 AM   #5
U shove i call
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Re: Martingale With An Infinite Bankroll

Nowhere has unlimited table limits so the point is moot.
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Old 09-18-2020, 01:30 PM   #6
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Re: Martingale With An Infinite Bankroll

Quote:
Even if the bet is well below 50%. (As long as it remains the same odds throughout.)
On infinity tries does it even matter what the odds are?

Like martingaling on something like a 0.00..1% chance of a win per flip (however many 0s you wanna add as long as it's not infinitely small.) Would you not reach the same "being up a trillion" at some point if you martingale flip infinity, and if not what is the impossibility threshold for the odds.
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Old 09-18-2020, 03:12 PM   #7
David Sklansky
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Re: Martingale With An Infinite Bankroll

Quote:
Originally Posted by OWLS View Post
On infinity tries does it even matter what the odds are?

Like martingaling on something like a 0.00..1% chance of a win per flip (however many 0s you wanna add as long as it's not infinitely small.) Would you not reach the same "being up a trillion" at some point if you martingale flip infinity, and if not what is the impossibility threshold for the odds.
There is no threshold. The OP was not written for gamblers but rather for the ten percent of the population who become concerned that something is going on that seems to break a law of logic. Or to put it differently, 80% of those who have had, or have a chance to make a major impact on the world.
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Old 09-24-2020, 02:41 PM   #8
daringly
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Re: Martingale With An Infinite Bankroll

Of course, if your bankroll is infinite and your starting tier 1 wager is finite, your return on your capital must be 0%, no matter how many you win or lose.

But yes, Martingale is a terrible way to throw your life away.
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Old 10-06-2020, 09:13 AM   #9
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Re: Martingale With An Infinite Bankroll

Why the Martingale strategy seems to work
There is a very nice logical explanation why Martingale should work. If you keep doubling your initial bet, the roulette ball must sooner or later land on a number which grants you a win. Right?

Yes, that’s true. With the number of attempts approaching infinity, the probability of overall failure approaches 0. That means that with infinite resources and no limitations from the casino, you will eventually manage to win and finish a cycle with net winnings of $1.

With infinite resources and no limitations from the casino, the entire system would work. However, as you have probably already guessed, these two conditions are never met in the real world.

source: Roulette scams strategies
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