A Less Obvious Martingale Fallacy

[Dov]

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

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Why don't you enlighten us as to how you solve this problem mathematically?

[drudman]

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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

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What are you talking about? The situations are analagous. In both, the guy who puts his million on hold gets it and extra back at the end of the year. I think you have confused the analogies.

[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.

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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.

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I'm at my limit of mathematical knowledge, so if you say that you can go bust with an infinite bankroll, I can't really argue.

[SheetWise]

I find Knights and Knaves logic to be a lot easier than Infinity-vs-Infinity.

Earlier I hoped to get a bite in looking at this as a finite situation, even if we had to use somewhat large numbers. While I know the value of running simulations, and I know the value of calculations -- I'm interested in what value you all think using 'infinity' in your hypothetical has.

I have seen the concept of infinity disprove Euclidian geometry -- and while I thought it was interesting, to me Euclidian geometry has bested infinity.

Do all of you believe that because something can occur that it eventually will?

[SomethingClever]

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

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As my losses approached infinity, I would begin to believe that the casino is rigged.

[PairTheBoard]

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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

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What are you talking about? The situations are analagous. In both, the guy who puts his million on hold gets it and extra back at the end of the year. I think you have confused the analogies.

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I think you're confused.

Case 1. M has $1 million. He could put it in a savings account for a year and earn say $20,000 interest. But instead, because he lost a bet, he has to let C use the money for a year. C pays M back $1 million plus $1. But C earns the $20,000 interest on the money. M gets back an extra dollar but loses $20,000 in interest. Clearly, M lost on that bet.

Case 2. M gambles coin flips with C. One flip every 10 days. M plays a martingale system, doubling up after each loss. M goes on a bad run and goes down over $1 billion before he hits a winner after about a years's play, and goes up by $1. In the mean time, C has put all M's losses during the year into short term interest bearing notes and has earned over $1 million in interest. M is up $1 from his "winning" Martingale system but is OUT over $1 million in interest he would have earned had he not gambled and "won".

While there is zero probabilty that M will not "win" his $1, there is a strictly postitive, non-zero probabilty that he will run as bad as described in Case 2 doing it. There is also a non-zero probabilty he will run a Trillion Times Worse.

If you insist on such a scenario really being a "win" for M then I don't see what more can be said to convince you. You just won't be convinced.

PairTheBoard

[MMMMMM]

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I'm at my limit of mathematical knowledge, so if you say that you can go bust with an infinite bankroll, I can't really argue.

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If you can say that a non-zero probability (that of never winning a future bet) is actually a zero probability (by rounding-off, limits, or whatever) then you can't object to a limited but enormous bet being considered an "infinite" bet.

The two infinite amounts are directly correlated.

One is the non-zero probability of never winning another bet, which is doubled with every future spin.

The other is the bet size for that spin, which doubles with every roll.

If you consider the first to be, effectively, ZERO, you have to consider the second to be, effectively, INFINITE.

The two are exactly correlated (with a fair coin).

So advanced knowledge of math has nothing to do with it. If you assign a ZERO probability to an infinitesimally small probability, you have to assign an INFINITE size to the corresponding humungously large bet.

[drudman]

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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

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What are you talking about? The situations are analagous. In both, the guy who puts his million on hold gets it and extra back at the end of the year. I think you have confused the analogies.

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I think you're confused.

Case 1. M has $1 million. He could put it in a savings account for a year and earn say $20,000 interest. But instead, because he lost a bet, he has to let C use the money for a year. C pays M back $1 million plus $1. But C earns the $20,000 interest on the money. M gets back an extra dollar but loses $20,000 in interest. Clearly, M lost on that bet.

Case 2. M gambles coin flips with C. One flip every 10 days. M plays a martingale system, doubling up after each loss. M goes on a bad run and goes down over $1 billion before he hits a winner after about a years's play, and goes up by $1. In the mean time, C has put all M's losses during the year into short term interest bearing notes and has earned over $1 million in interest. M is up $1 from his "winning" Martingale system but is OUT over $1 million in interest he would have earned had he not gambled and "won".

While there is zero probabilty that M will not "win" his $1, there is a strictly postitive, non-zero probabilty that he will run as bad as described in Case 2 doing it. There is also a non-zero probabilty he will run a Trillion Times Worse.

If you insist on such a scenario really being a "win" for M then I don't see what more can be said to convince you. You just won't be convinced.

PairTheBoard

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You are wholly ridiculous. At what point did this argument become a question of whether the Martingaler is losing money that he could have made by doing something else?

[MMMMMM]

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Do all of you believe that because something can occur that it eventually will?

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No, because infinity does not imply infinite diversity.

[PairTheBoard]

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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

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What are you talking about? The situations are analagous. In both, the guy who puts his million on hold gets it and extra back at the end of the year. I think you have confused the analogies.

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I think you're confused.

Case 1. M has $1 million. He could put it in a savings account for a year and earn say $20,000 interest. But instead, because he lost a bet, he has to let C use the money for a year. C pays M back $1 million plus $1. But C earns the $20,000 interest on the money. M gets back an extra dollar but loses $20,000 in interest. Clearly, M lost on that bet.

Case 2. M gambles coin flips with C. One flip every 10 days. M plays a martingale system, doubling up after each loss. M goes on a bad run and goes down over $1 billion before he hits a winner after about a years's play, and goes up by $1. In the mean time, C has put all M's losses during the year into short term interest bearing notes and has earned over $1 million in interest. M is up $1 from his "winning" Martingale system but is OUT over $1 million in interest he would have earned had he not gambled and "won".

While there is zero probabilty that M will not "win" his $1, there is a strictly postitive, non-zero probabilty that he will run as bad as described in Case 2 doing it. There is also a non-zero probabilty he will run a Trillion Times Worse.

If you insist on such a scenario really being a "win" for M then I don't see what more can be said to convince you. You just won't be convinced.

PairTheBoard

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You are wholly ridiculous. At what point did this argument become a question of whether the Martingaler is losing money that he could have made by doing something else?

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At what point? At the point of the first post of this thread actually. Do you agree or disagree with the original point MMMMMM was making IN THE CASE WHERE THE MARTINGALER DOESN'T QUIT? You've never expressed an opinion on that. The reason the non-Quiting Martingaler loses is that time spent being behind is just as important as time spent being ahead. That's what makes the Cosmic Casino a winner and the non-Quiting Martingalers as a whole, losers. The same principle applies to the quiting Martingaler. Time spent being behind matters.

PairTheBoard