A Less Obvious Martingale Fallacy - Page 12

SomethingClever · #**111** 07-18-2005, 05:58 PM

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Bottom line... if you can always bet 2x after a loss, you can choose to be a winner as long as you stop on a win.

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You cannot have it both ways. You can't have the game go on for infinite and have the ability to stop on a win. Since if you stop it is no longer an infinitly long game. So stopping at any point is not valid. What people are doing is coming up with a way to measure who is winning, since you cannot reasonably use a single point in time to do this.

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Agreed. If you play infinitely, you will lose money on average.

However, unless you are the one case out of infinity that literally never wins a bet, you will win if you stop.

Also, you can "virtually" assure yourself a win even if you do multiple stop wins over a career of indeterminate length.

This is because assuming an infinite bankroll, etc... the odds that you will ever hit the infinity-long losing streak are infinitely improbable.

Yes, I'm a big HH2G fan.

drudman · #**112** 07-18-2005, 06:18 PM

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.

I really have a hard time believing the anti-Martingalers. It keeps being brought up that if an infinite number of players use this strategy, there will always be players who have not won yet. I'm not sure if I buy this, because you can only check to see how many players have yet to win at finite numbers of trials... isn't this right?

Also, doesn't 1/2^n=0 when n goes to infinity? Because this represents the odds of losing n bets in a row. Didn't we establish this in the "Hawking Infinite Series" thread?

MMMMMM · #**113** 07-18-2005, 06:35 PM

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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.

I really have a hard time believing the anti-Martingalers. It keeps being brought up that if an infinite number of players use this strategy, there will always be players who have not won yet. I'm not sure if I buy this, because you can only check to see how many players have yet to win at finite numbers of trials... isn't this right?

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This can get complicated and over my head at some point, so just let me say that I'm NOT saying there WILL ALWAYS be players who have not won yet--just that there CAN be. And you have no way of knowing FOR SURE that there WON'T be.

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Also, doesn't 1/2^n=0 when n goes to infinity? Because this represents the odds of losing n bets in a row.

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I don't know, but if it does, couldn't the same argument be applied at that point by saying you have already lost infinite money (since your losses double at the same rate that 1/2^n goes to infinity).

SomethingClever · #**114** 07-18-2005, 06:45 PM

If you play perpetually, you will lose money on average in a game where the house has a slight edge.

Of course it won't matter with your infinite bankroll.

If you decide that you will have 1 stopping point and you have an infinite bankroll, it is almost infinitely probable that you will win.

Adding several other stopping points along the way will very slightly increase the chance that you will go on an infinitely long losing streak, but it's still almost infinitely improbable.

PairTheBoard · #**115** 07-18-2005, 07:00 PM

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. SomethingClever has it right. In the beginning MMMMMMMMM was talking about the case where the Martingaler continues playing forever. In that case the pro-Martingalers argue that he will just chalk up 1 chip after another as each Martingale series completes. The con-Martingalers argue that the Casino will chalk up stacks of chips after stacks of chips as one long streak after another happens, and that on average the Casino will be Ahead by more chips per unit time than the Martingaler.

But if you change this scenario to one where the Martingaler quits after he wins say 1 chip then it's true that he will Quit a Winner with Probabilty One. However, QUITING A WINNER DOES NOT NECESSARILY MAKE HIM A WINNER. If he has to go into Debt for a Huge Amount of Money for a Long Period of time, you cannot count him a winner.

Consider this result of a Bet and tell me who do you think lost the Bet. As a result of the bet Mr. M loans Mr. C $1 million for 1 year. At the end of the year Mr. C must pay Mr. M back $1 million and $1. Did Mr. M win the bet because he gets an extra dollar back at the end of the year? Or did Mr. C win the bet?

PairTheBoard

jason1990 · #**116** 07-18-2005, 07:22 PM

If you have infinitely many players, each repeatedly playing some game, then after the n-th trial (with probability one, no matter what n is), there will be infinitely many players who have not won yet.

But...if you look at any fixed player, then (with probability one) he will eventually win.

Sorry that I'm not explaining why, but I just wanted to point out something subtle which can cause confusion and apparent paradoxes.

drudman · #**117** 07-18-2005, 07:33 PM

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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. SomethingClever has it right. In the beginning MMMMMMMMM was talking about the case where the Martingaler continues playing forever. In that case the pro-Martingalers argue that he will just chalk up 1 chip after another as each Martingale series completes. The con-Martingalers argue that the Casino will chalk up stacks of chips after stacks of chips as one long streak after another happens, and that on average the Casino will be Ahead by more chips per unit time than the Martingaler.

But if you change this scenario to one where the Martingaler quits after he wins say 1 chip then it's true that he will Quit a Winner with Probabilty One. However, QUITING A WINNER DOES NOT NECESSARILY MAKE HIM A WINNER. If he has to go into Debt for a Huge Amount of Money for a Long Period of time, you cannot count him a winner.

Consider this result of a Bet and tell me who do you think lost the Bet. As a result of the bet Mr. M loans Mr. C $1 million for 1 year. At the end of the year Mr. C must pay Mr. M back $1 million and $1. Did Mr. M win the bet because he gets an extra dollar back at the end of the year? Or did Mr. C win the bet?

PairTheBoard

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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?

MMMMMM · #**118** 07-18-2005, 07:38 PM

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If you decide that you will have 1 stopping point and you have an infinite bankroll, it is almost infinitely probable that you will win.

Adding several other stopping points along the way will very slightly increase the chance that you will go on an infinitely long losing streak, but it's still almost infinitely improbable.

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Agreed. However that "almost infinitely improbable" corresponds to an "almost infinitely large" loss.

Likewise if you round it off as "zero chance" then you must round off the loss as "infinitely large". So at the hypothetical "zero chance point" (whether rounded or otherwise derived) you have ALREADY lost infinite money.

MMMMMM · #**119** 07-18-2005, 08:01 PM

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If you have infinitely many players, each repeatedly playing some game, then after the n-th trial (with probability one, no matter what n is), there will be infinitely many players who have not won yet.

But...if you look at any fixed player, then (with probability one) he will eventually win.

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True one, or just rounded-off or assumed or otherwise derived one?

Dov · #**120** 07-18-2005, 08:06 PM

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Special relativity and quantum mechanics as we understand them today state that it is impossible to retrieve any matter from a black hole. Ergo, your chips will be lost forever.

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I don't think this is true. I saw something a couple of weeks ago about how Steven Hawking is advancing a theory that black holes actually emit some kind of particle.