A Less Obvious Martingale Fallacy - Page 4

Dov · #31 07-17-2005, 03:51 AM

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What matters is who's rack the money is in at any point in time.

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I still don't see why if each individual player comes out 1 unit ahead at the end of a series, and you extend them out to infinity, you think the casino will win in the end.

If this were true, then why put a table limit at all? Why not let people keep doubling the bets?

Are you saying that it would be too risky for a real casino to allow someone to do this?

Wouldn't that contradict what was said earlier about them making more money when more money is wagered?

There must be a reason for table limits. Obviously EV isn't everything.

maurile · #32 07-17-2005, 03:55 AM

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Are you saying that it would be too risky for a real casino to allow someone to do this?

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Yes. Binion's used to be famous for being willing to accept huge bets. It let a guy bet $1 million on craps a couple times, I think. (Back when $1 million meant something.)

But there comes a point where it's definitely too risky. If I bet a few billion or whatever on red at Harrah's, I will own the casino if I win. The board of directors at Harrah's doesn't want to take that risk.

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Wouldn't that contradict what was said earlier about them making more money when more money is wagered?

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No.

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There must be a reason for table limits. Obviously EV isn't everything.

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EV isn't everything. There's variance, too.

PairTheBoard · #33 07-17-2005, 04:13 AM

Dov --
"I still don't see why if each individual player comes out 1 unit ahead at the end of a series, and you extend them out to infinity, you think the casino will win in the end."

I'm not looking at what happens "in the end". We never get to the end. All we can look at is what happens over time as we look at longer and longer measures of time played. Yes, there are times you will be ahead. In fact, most of the time you will be ahead. But there is no point in time where you will be ahead forever. There will always be times in the future when you are behind again. 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." What does matter is how much time you spend ahead or behind AND BY HOW MUCH. If you weight the amount of time spent ahead and behind by the AMOUNT you are ahead or behind and look at future times T then you can say the following. As T gets larger and larger, the Weighted Time you are behind will exceed the Weighted Time you are ahead by an average amount determined by the House Edge.

PairTheBoard

felson · #34 07-17-2005, 05:19 AM

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

F.E.F.

Lawrence Ng · #35 07-17-2005, 08:03 AM

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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

jason1990 · #36 07-17-2005, 09:13 AM

Suppose I repeatedly flip a coin for $1 each time; no doubling strategy. If it's a fair coin, then the swings in my bankroll, both up and down, will grow without bound. That is, for any X, there will come a time when I am $X ahead and a time when I am $X behind. So if I have an unlimited bankroll and an unlimited amount of time, I can make a million dollars. I simply wait until I am a million dollars ahead, which will eventually happen, and then I quit, never to play the game again. But the expected value of the number of flips I must make before winning a million dollars is infinity. And I must *never* play the game again after reaching my goal. I'll leave it as food for thought what, if anything, this has to do with the so-called martingale betting system.

PairTheBoard · #37 07-17-2005, 11:22 AM

Jason1990 --
"But the expected value of the number of flips I must make before winning a million dollars is infinity."

Actually, this expected value would be a finite number. This is easy to see. After only about 100 Trillion flips, being up a million would only amount to being about 1/10 of a standard deviation over the mean of 50 Trillion heads. After a Billion*Billion flips it's almost like a coin flip for you to be ahead by a million dollars.

With a fair coin you will of course spend just as much time on average being behind a million dollars as ahead. This is similiar in principle to what I'm saying would happen with the martingale backed by unlimited funds.

PairTheBoard

jason1990 · #38 07-17-2005, 11:45 AM

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Jason1990 --
"But the expected value of the number of flips I must make before winning a million dollars is infinity."

Actually, this expected value would be a finite number. This is easy to see.

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What you are seeing is an illusion. The expected number of flips it takes to win *one* dollar is infinite.

Dov · #39 07-17-2005, 11:55 AM

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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.

I don't see how you can get around this. I understand you to be saying that when you finally do win, you should be ahead more than 1 unit if your expectation was positive. I also understand that you want to measure each individual bet. I don't think this is entirely accurate, though.

I posted a 44 hand from EP a few weeks ago where each individual action (bet, call fold) was correct, but each STREET had errors on it. (flop, turn, river). Maybe what we should be calculating is the effective odds of the Martingale. You are using pot odds on every bet.

BTW, I know that this is not a viable gambling technique, but it is interesting to consider.

Meh, I have to go now. Be back later.

PairTheBoard · #40 07-17-2005, 12:04 PM

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Jason1990 --
"But the expected value of the number of flips I must make before winning a million dollars is infinity."

Actually, this expected value would be a finite number. This is easy to see.

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What you are seeing is an illusion. The expected number of flips it takes to win *one* dollar is infinite.

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ok. I think you are working with a definition of the word "win" which you have in mind but are not stating. What I took "win" to mean was to "be ahead" by that amount. Certainly the expected number of flips you would make before finding yourself ahead by one dollar at that point in time is not infinite. If you mean to say that being ahead by a dollar doesn't mean you've won a dollar because you keep playing forever then ok. In that case you never "win" anything.

PairTheBoard