Mathematical Proof that Progressions will never Overcome a Negative Expectation Game

[aslan]

Originally Posted by QFIT

Why would anyone risk an infinite amount of money for one bet? If you lose, you would be condemned to sit at the table for all eternity.

The fool who persists in his folly shall become wise. - William Blake

Some of us enjoy the social aspects of blackjack, although conversing with an unlimited number of people from an infinite number of places might prove a bit taxing even for the most outgoing of us. I wonder if we get to sit at an infinite number of casinos as well? That, at least, might break up the monotony.

 

[johndoe]

Why would I bore myself playing a silly game when I could take the unlimited credit and live an unlimited lifestyle.

The credit is only good at the game.

 

[johndoe]

Why would anyone risk an infinite amount of money for one bet? If you lose, you would be condemned to sit at the table for all eternity. This is what's wrong with these ridiculous attempts at twisting reality into making progressions systems "work." You have to keep piling ridiculous assumption on top of ridiculous assumption until no one can recognize the original question.

What are the chances of losing "for eternity"? Infinitesimal. For all practical purposes, zero.

What are the chances of winning any amount you like? The exact same odds as winning a single roll within whatever timeframe you can tolerate. How long would you need to wait to hit "red" once on roulette? Sure, you can't formally guarantee it mathematically at any given time, but the odds difference between "eternity" and "a day" is negligible. And it doesn't require an infinite bet, either. (Just a reeeally big one!)

I'm not claiming that martingale would work in any realistic condition, because no casino would offer unlimited credit and table limits. But if they did, I agree with Thorp's statement that such a system would be entirely "reasonable".

 

[zengrifter]

Wait a minute. He said "unlimited credit," not unlimited bankroll or cash. I read into that the ability to borrow without limit, either from the casino or a private source. Do you mean to use the credit and never pay it back? Shame on you, Qfit! :laugh: :whip:

He's just thinking like a too big to fail bank, govt, Fed, Goldman, etc. zg

 

[zengrifter]

What are the chances of losing "for eternity"? Infinitesimal. For all practical purposes, zero. What are the chances of winning any amount you like?

I'm not claiming that martingale would work in any realistic condition, because no casino would offer unlimited credit and table limits. But if they did, I agree with Thorp's statement that such a system would be entirely "reasonable".

I say ALMOST SURELY! z:laugh:g

 

[zengrifter]

[/INDENT]I was ...what's the word...flabbergasted... by the amount of attention that has been given by serious mathematicians to the concept of martingales in infinite and finite random series. Aslan, In awe of mathematicians

I confess that thanks to Dr. iCountN's thread here I have a new-found respect for progressions
in general and martingales in particular! Thanks Doc! You can lock'her up now! zg

 

[aslan]

Wait! Just one minute!

i say almost surely! Z:laugh:g

View attachment 7108

And please don't call me surely! :flame: In memoriam: Leslie Nielsen, 1926 - 2010

 

[QFIT]

Of course all of these discussions are pointless. Every person with a basic knowledge of grade school math should realize that a negative number times a positive number always results in a negative number. I get sucked into these discussions on occasion because some of the concepts are interesting. But, I have to draw the line at hypotheticals that require the complete suspension of reality. End of my participation on this thread.

 

[zengrifter]

I have to draw the line at hypotheticals that require the complete suspension of reality.

Its a little late for that, Dr. QFIT. zg

 

[aslan]

Of course all of these discussions are pointless. Every person with a basic knowledge of grade school math should realize that a negative number times a positive number always results in a negative number. I get sucked into these discussions on occasion because some of the concepts are interesting. But, I have to draw the line at hypotheticals that require the complete suspension of reality. End of my participation on this thread.

View attachment 7113 The party's over ....

View attachment 7112

Pointless, perhaps, but not without value. Despite all the fun and games, I think readers learned a lot from ICountNTrack, k c, johndoe, Renzy, yourself and others who contributed their knowledge of this rarely discussed area of mathematics. So, thanks to all, even if it did get a little too drawn out, off-track, and exasperating to some.

 

[johndoe]

Of course all of these discussions are pointless. Every person with a basic knowledge of grade school math should realize that a negative number times a positive number always results in a negative number. I get sucked into these discussions on occasion because some of the concepts are interesting. But, I have to draw the line at hypotheticals that require the complete suspension of reality. End of my participation on this thread.

A negative times a positive is always a negative, but that has absolutely nothing to do with this discussion.

The original issue was a dispute of the claim that it was "mathematically proven" that a martingale would not work for both finite and infinite bankrolls, and that Thorp was therefore proven wrong. That proof for the infinite case was not provided, and I pointed out why. The "suspension of reality" was initiated by claiming that the proof applied to both cases.

As for the recent hypothetical (my bet in a casino), it was an additional thought experiment that had some pretty reasonable conditions, none of which required a "suspension of reality" (only a really dumb casino!) I'm not surprised that you could not counter it with a reasoned response, because in reality, it would be a perfectly fine proposition under the stated conditions. It's a good bet, and perfectly reasonable. Exactly as Thorp had described when he wrote about it way back when.

It's handy to have a proof that under finite credit/table limit conditions, no progression will ever "work". However, with unlimited credit and no table limits, you just have to have one win, which will "almost surely" occur.

 

[aslan]

A negative times a positive is always a negative, but that has absolutely nothing to do with this discussion.

The original issue was a dispute of the claim that it was "mathematically proven" that a martingale would not work for both finite and infinite bankrolls, and that Thorp was therefore proven wrong. That proof for the infinite case was not provided, and I pointed out why. The "suspension of reality" was initiated by claiming that the proof applied to both cases.

As for the recent hypothetical (my bet in a casino), it was an additional thought experiment that had some pretty reasonable conditions, none of which required a "suspension of reality" (only a really dumb casino!) I'm not surprised that you could not counter it with a reasoned response, because in reality, it would be a perfectly fine proposition under the stated conditions. It's a good bet, and perfectly reasonable. Exactly as Thorp had described when he wrote about it way back when.

It's handy to have a proof that under finite credit/table limit conditions, no progression will ever "work". However, with unlimited credit and no table limits, you just have to have one win, which will "almost surely" occur.

I was playing with the numbers and discovered that if you are very unlucky you get into the billions quite fast using a $100 min as a base bet. Many on the Forum have reported multiple times when they experienced 20 consecutive losses. That's a million to one shot on an even bet, but of course, bj is not an even bet. If one had billions, would they really be motivated to try something that could actually bust them in say, 30, maybe fewer, consecutive losses?

 

[zengrifter]

If one had billions, would they really be motivated to try something that could actually bust them in say, 30, maybe fewer, consecutive losses?

Thet just did, but they had downside protection >>

The Global Collapse was a MARTINGALE Play​

 

[k_c]

How about this question, then:

If a casino offered you (truly) unlimited credit, no table limits, and no time limit (you alone choose when to stop), on a game with known -EV (say, roulette), would you play it?

I sure as heck would! I think anyone would be a fool not to.

As for "almost surely", QFIT, would you then agree that Martingale would "almost surely" work, or at least has an infinitesimal chance of failure? Or, similarly precisely, that martingale will be successful with a probability of 1?




What are the chances of losing "for eternity"? Infinitesimal. For all practical purposes, zero.

What are the chances of winning any amount you like? The exact same odds as winning a single roll within whatever timeframe you can tolerate. How long would you need to wait to hit "red" once on roulette? Sure, you can't formally guarantee it mathematically at any given time, but the odds difference between "eternity" and "a day" is negligible. And it doesn't require an infinite bet, either. (Just a reeeally big one!)

I'm not claiming that martingale would work in any realistic condition, because no casino would offer unlimited credit and table limits. But if they did, I agree with Thorp's statement that such a system would be entirely "reasonable".

I think the missing element is the odds. For example if someone had a million unit bankroll and wanted to use a martingale starting with a 1 unit bet in order to win 1 unit then it is an even game if his probability of failure is 1/1000000. It is a negative EV game if chance of failure > 1/1000000 and positive EV if failure rate < 1/1000000.

In a martingale for a modestly negative game and a very large bankroll the probability of winning 1 unit before going belly up approaches 1 but is always less than 1. Since it's a negative EV game, a martingaler is always risking more than it's worth to try for a 1 unit profit.

Martingale proponents say if you play long enough with an endless bankroll you can be guaranteed a 1 unit profit, even in a negative EV game. In a modestly negative game he may have an almost certain probability of winning 1 unit. However the probability of a win is never quite certain and a martingaler is ALWAYS RISKING MORE THAN IT'S WORTH WITH ANY BANKROLL to try for a 1 unit profit in a negative EV game.

 

[QFIT]

As for the recent hypothetical (my bet in a casino), it was an additional thought experiment that had some pretty reasonable conditions, none of which required a "suspension of reality" (only a really dumb casino!) I'm not surprised that you could not counter it with a reasoned response, because in reality, it would be a perfectly fine proposition under the stated conditions.

An "unlimited credit line" is reasonable? In what Universe?

 

[aslan]

In a martingale for a modestly negative game and a very large bankroll the probability of winning 1 unit before going belly up approaches 1 but is always less than 1. Since it's a negative EV game, a martingaler is always risking more than it's worth to try for a 1 unit profit.

So even though it approaches one but is always less than one, it is still not comparable to a RoR of less than 1% as we would figure it for an acceptable risk at card counting? Another way of saying it, would one require a +EV to have a less than 1% RoR equivalence?

 

[aslan]

An "unlimited credit line" is reasonable? In what Universe?

Yes, johndoe, let's bring it into a reasonable real life perspective. We've all had fun with the infinite prospects; propose now a real life scenario where we have some finite amount of bankroll and the very wealthy house grants a no limit playing environment. Even this hardly seems real life, but just imagine it as a publicity stunt. Is the risk warranted? Is Thorp correct in this context?

 

[zengrifter]

Yes, johndoe, let's bring it into a reasonable real life perspective. We've all had fun with the infinite prospects; propose now a real life scenario where we have some finite amount of bankroll and the very wealthy house grants a no limit playing environment. Even this hardly seems real life, but just imagine it as a publicity stunt. Is the risk warranted? Is Thorp correct in this context?

Yes, Thorp is correct - it doesn't work... (((yawn)))

But, did we ever see the proof that it won't work in a theoretically unbounded state? zg

 

[aslan]

Yes, Thorp is correct - it doesn't work... (((yawn)))

But, did we ever see the proof that it won't work in a theoretically unbounded state? zg

You can go back and review the old thread. Let us know what you find. Thanks.

 

[zengrifter]

You can go back and review the old thread. Let us know what you find. Thanks.

Did not find.

So my question is - If martingale will always succeed in the absence of limits,
is that some sort of paradox or violation of commonly held probability understanding? zg