A Less Obvious Martingale Fallacy - Page 5

jason1990 · #41 07-17-2005, 12:10 PM

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Certainly the expected number of flips you would make before finding yourself ahead by one dollar at that point in time is not infinite.

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It is infinite. I mean exactly that.

Mayhap · #42 07-17-2005, 12:19 PM

I agree. Even if you have a stated goal, like 500,000 bets,
you may not ever achieve it.

The Martigale system is perfectly complemented by alcoholic beverages.

PairTheBoard · #43 07-17-2005, 12:23 PM

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During those periods when you are behind it makes no sense to say, "It doesn't matter that I'm behind now because I know I'm going to be ahead again in the future." If it did make sense then the opposite could be said when you are ahead, "It doesn't matter that I'm ahead now because I know I will be behind again in the future."

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Isn't this exactly how we decide whether or not to continue playing in a poker game?

We figure our Sklansky bucks based on the situation and go from there, right?

If you know that you are going to be ahead in the future, and that the win will overtake the loss, then this is a +EV situation.

I don't see why this is any different than say entering a pot from LP with a small PP hoping to spike a set and recover the PF 'mistake' through implied odds on the flop. You have taken a -EV individual situation and given it a +EV spin by using implied odds.

The Martingale seems to have implied odds that will cover all of your losses + 1 unit.

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With Sklansky implied odds, it means you are going to get paid off on future bets where you are a big favorite or even a lock to win the bets. In this game you are a dog on all the bets.

Try looking at it from the Casino's point of view. While you are marking "special" times after wins when you are ahead, the Casino is marking its "special" times when you are way behind and it is way ahead. There's no reason to think that your times for looking at where things are at are any more special than the times the Casino looks at where things are at.

PairTheBoard

felson · #44 07-17-2005, 12:39 PM

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There's no way I am betting my money according to Martingale.

F.E.F.

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Do you ever say anything that is even remotely useful or insightful on this board? Seriously, you must be the number 1 rank troll on 2+2.

Lawrence

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You sound quite angry. I'm sorry that you feel that way.

PairTheBoard · #45 07-17-2005, 12:46 PM

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Certainly the expected number of flips you would make before finding yourself ahead by one dollar at that point in time is not infinite.

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It is infinite. I mean exactly that.

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It's true that there is no number of flips, N, such that after N flips you expect to be ahead by one dollar or more. But that is not what I said. And it's not what you said when you used the phrase "expected value of the number of flips".

Let N be the random variable which counts the number of flips at which you first go ahead by one dollar. I don't believe the Expected Value of N is infinite. If that's your assertion, I need to see a proof.

PairTheBoard

jason1990 · #46 07-17-2005, 01:01 PM

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Let N be the random variable which counts the number of flips at which you first go ahead by one dollar. I don't believe the Expected Value of N is infinite. If that's your assertion, I need to see a proof.

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It is my assertion. If you really want to see a proof, PM me and I will direct you to a textbook. But here's a pseudo-proof:

Let S(n) be your bankroll after the n-th flip (with S(0)=0). If E[N] is finite, then by Wald's identity, E[S(N)]=E[one flip]*E[N]. But S(N)=1, so E[S(N)]=1; and yet E[one flip]=0, a contradiction.

It's a pseudo-proof because I haven't stated or proved Wald's indentity, but perhaps it seems reasonable without it.

If you don't believe it and think I'm mistaken (which I've been known to be), then perhaps you might want to try and prove it's finite.

PairTheBoard · #47 07-17-2005, 02:05 PM

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Let N be the random variable which counts the number of flips at which you first go ahead by one dollar. I don't believe the Expected Value of N is infinite. If that's your assertion, I need to see a proof.

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It is my assertion. If you really want to see a proof, PM me and I will direct you to a textbook. But here's a pseudo-proof:

Let S(n) be your bankroll after the n-th flip (with S(0)=0). If E[N] is finite, then by Wald's identity, E[S(N)]=E[one flip]*E[N]. But S(N)=1, so E[S(N)]=1; and yet E[one flip]=0, a contradiction.

It's a pseudo-proof because I haven't stated or proved Wald's indentity, but perhaps it seems reasonable without it.

If you don't believe it and think I'm mistaken (which I've been known to be), then perhaps you might want to try and prove it's finite.

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Damn I guess you're right. The "Wald Identity" I have is for stopping times for Brownian Motion. The idea being that you can't change the zero expected value of Brownian Motion using a stopping time with finite mean. I imagine it works like you say in the discrete case as well.

So the expected number of flips to win a dollar is infinite. That's kind of amazing.

PairTheBoard

slickpoppa · #48 07-17-2005, 02:31 PM

You clearly misunderstand what it means to have an infinite bankroll. As long as you are always wagering a finite amount, your bankroll after using the martingale will be the same: infinity. Infinity - 6918624892374691286489127469278468927467892346 = infinity

PairTheBoard · #49 07-17-2005, 02:33 PM

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You clearly misunderstand what it means to have an infinite bankroll. As long as you are always wagering a finite amount, your bankroll after using the martingale will be the same: infinity. Infinity - 6918624892374691286489127469278468927467892346 = infinity

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We're measuring success or failure by how much we are ahead or behind.

PairTheBoard

Dov · #50 07-17-2005, 03:01 PM

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With Sklansky implied odds, it means you are going to get paid off on future bets where you are a big favorite or even a lock to win the bets. In this game you are a dog on all the bets.

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Maurile explained in a previous post how the longer you play, the more likely you are to to win a given bet. Your probability approaches infinity over time.

The difference in poker is that you can't recover all of your previous losses when you 'get lucky' and catch your miracle.

Here, when you do catch your miracle, you recover all of your losses plus a profit.

I understand that you are trying to isolate each individual bet as a separate event. I don't think that you can do that here, though, because the system has a defined relationship between the previous bet and the next one. Ignoring this aspect of the system is the part that puzzles me, I guess.