A Less Obvious Martingale Fallacy

[MMMMMM]

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The question is, is it possible for the player to begin a series that will never end in a win. And the answer is no, it is not.

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Firstly, that is not the main point of the thread.

Secondly, even if that is true, and even if it is a hinging point, the following is then also true (with a fair coin not a roulette wheel):

P= probability of no win by N trials

1 Loss in a row----> P=1/2, financial loss = $1

3 Losses in a row--> P=1/8, financial loss = $7

5 Losses in a row--> P=1/32, financial loss = $31

Infinite losses in a row-->P=Zero, financial loss = $Infinity

So the certainty point of which you speak also corresponds to losing infinite dollars.

With a fair coin.

Not a roulette wheel.

[MMMMMM]

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I really think everyone is starting to totally misunderstand the point.

Forget the betting. The betting doesn't matter. You are betting with funny money. It is just an inconvenience... irrelevant to your goal, which is to complete series. You always win when you complete a series, and every series completes NECESSARILY.

Stop thinking about each individual bet, and the terrifically mind-boggling exponentially large amounts of money that are lost on many of them. Your probability of eventually winning a bet, and therefore recouping ALL of that lost money is 1.

You can increase the house edge of the bet even. Play Pai Gow Poker if you like. Sic Bo. Let it Ride. Whatever your poison. So long as the house edge is less than 100%, your probability of completing a series is 1. You always complete a series. And you always win when you complete a series. Now that you are looking at it in terms of series, and not in terms of whatever individual bets comprise the series, you realize that you can never ever lose.

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But to reach that certainty, you have to be willing to risk INFINITE money.

In other words, even if you have infinite money, you can't reach that CERTAINTY of which you speak, unless you are willing to risk losing it ALL.

Whether that is practically possible is not the issue. You are forced by the system to must a commensurate amount to the chance of failure or success of the entire series. And if you project enough trials in to make that chance of failure ZERO, the corresponding risk is your ENTIRE infinite bankroll.

You can't bet for eternity at ever-increasing amounts without risking an infinite bankroll. The one infinity is not greater than the other (and in this case they are highly correlated).

[drudman]

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The question is, is it possible for the player to begin a series that will never end in a win. And the answer is no, it is not.

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Firstly, that is not the main point of the thread.

Secondly, even if that is true, and even if it is a hinging point, the following is then also true (with a fair coin not a roulette wheel):

P= probability of no win by N trials

1 Loss in a row----> P=1/2, financial loss = $1

3 Losses in a row--> P=1/8, financial loss = $7

5 Losses in a row--> P=1/32, financial loss = $31

Infinite losses in a row-->P=Zero, financial loss = $Infinity

So the certainty point of which you speak also corresponds to losing infinite dollars.

With a fair coin.

Not a roulette wheel.

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But when you reach the point of certainty, your loss is infinity dollars, and your win is infinity + 1 dollars.

[MMMMMM]

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The question is, is it possible for the player to begin a series that will never end in a win. And the answer is no, it is not.

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Firstly, that is not the main point of the thread.

Secondly, even if that is true, and even if it is a hinging point, the following is then also true (with a fair coin not a roulette wheel):

P= probability of no win by N trials

1 Loss in a row----> P=1/2, financial loss = $1

3 Losses in a row--> P=1/8, financial loss = $7

5 Losses in a row--> P=1/32, financial loss = $31

Infinite losses in a row-->P=Zero, financial loss = $Infinity

So the certainty point of which you speak also corresponds to losing infinite dollars.

With a fair coin.

Not a roulette wheel.

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But when you reach the point of certainty, your loss is infinity dollars, and your win is infinity + 1 dollars.

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Um, I don't think so. Because you haven't won it back yet. And you just bet infinity dollars AND LOST.

[maurile]

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And you just bet infinity dollars AND LOST.

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That's got to hurt.

[PairTheBoard]

drudman --
"Mr. M has net gain of $1, and Mr. C has a net loss of $1, and as such I would say that Mr. M is the winner.

What if I put it this way:

You put $1 mil in a savings account, and one year later withdraw it, plus interest. Have you not made (won) money? "

You say Mr. M has a net gain and Mr. C has a net loss of a dollar. Yet you ignore your exact next point in that Mr. M has lost the 1 year's savings account interest on that $1 million and Mr. C has gained it, which amounts to much more than $1.

So now, who won and who lost that bet, and which side of it would you take; the gained $1 or the gained year's interest on the $1 million.

And the relation to the Martingaler is that although there is zero probabilty the Quiting Martingaler will not "win" $1, there is a non-zero Positive probability that he will run so bad doing it that it will amount to the scenario of giving up a year's interest on $1 million or worse.

PairTheBoard

[PairTheBoard]

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drudman --
"Okay, so the pro-Martingalers are arguing that there cannot be an infinite series of losses.

The anti-Martingalers are arguing that there can be."

No. I think MMMMMMMMMMMM is getting off base with that argument.

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Maybe so; I worried about that; off main point at least. Yet can anyone tell me WHY (without just meaning 100% "for all practical intents and purposes")

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You know, MMMMMM, as I recall my studies it's kind of tricky handling infinite trials type scenarios. But I'm pretty sure you can say that when flipping coins, Heads will come up infinitely often. If a heads is required for the Martingaler's win, that should mean he will win with probabilty 1. I'm real fuzzy on the details for probabilties with infinite trials though. It's a lot easier to look at probability statements for finite trials.

PairTheBoard

[PairTheBoard]

EliteNinja --
"The more important question is:
Why bother playing Roulette if one has an infinite bankroll?"

I guess we're having fun doing it. We don't seem to care that it doesn't really impact our bankroll. We're just trying to figure out whether we're winning or losing if we do it.

PairTheBoard

[SheetWise]

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In other words, even if you have infinite money, you can't reach that CERTAINTY of which you speak, unless you are willing to risk losing it ALL.

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I was just curious, how long of a losing streak would that take? [img]/images/graemlins/wink.gif[/img]

[mosta]

you know they invented something called "math" for questions like this.