Mathematical Proof that Progressions will never Overcome a Negative Expectation Game

[paddywhack]

Holy crap

I'd have never guessed this thread would have carried on for so long. I'm dizzy from the circles.....

 

[aslan]

I'd have never guessed this thread would have carried on for so long. I'm dizzy from the circles.....

And I thought mathematics was an exact science. 1 + 1 = 2

 

[aslan]

I "allow" only enough hands to establish a win - not an infinite number. Yes, if an infinite number of hands are played, you'll lose an infinite amount. I agree completely.

But if a win ever occurs, which it "almost certainly" will, the system is a winner. You don't have control over when the win occurs, but you can stop once it does.

Are you saying that your parachute will "almost certainly" open, but sooner or later it will not, but you don't care because you're not going to jump anymore?

And isn't ICountNTrack saying that a positive EV game is equivalent to one long jump from an infinite height that is safer and safer the closer you get to the ground?

The big difference is that you do not have a prescription for "playing" blackjack, but more a prescription for "quitting" blackjack, that is, as soon as you win one unit.

I hate to put it this way, but given equal units in both scenarios, is there any doubt that ICountNTrack's proposition is a bonanza, whereas yours is a dud?

 

[johndoe]

Are you saying that your parachute will "almost certainly" open, but sooner or later it will not, but you don't care because you're not going to jump anymore?

Nope. The possibility is effectively (perhaps exactly) zero.

The big difference is that you do not have a prescription for "playing" blackjack, but more a prescription for "quitting" blackjack, that is, as soon as you win one unit.

I hate to put it this way, but given equal units in both scenarios, is there any doubt that ICountNTrack's proposition is a bonanza, whereas yours is a dud?

All along all I've been arguing is that it there is no proof that the martingale with unlimited table limits and bankroll wouldn't work, and therefore Throp's statement was not disproven. All you need is a single win, which will "almost surely" happen, and you've done it. It works just fine. That win can be any number you want.

Now, some here have argued that there is an infinitesimal (but nonzero) chance of losing every hand for all eternity. I happen to disagree, (and so does QFIT, but he won't admit it! ) for reasons I've stated, but let's say that's the case.

Wouldn't that possibility apply to any system, even those with positive expectations? If the possibility exists, however tiny, of losing eternally disqualifies a system from "working", then no system can be said to "work".

 

[johndoe]

Can an Immovable Object and an Irresistible Force exist in the same universe? If they meet will they destroy each other, or should one assume they can never meet.

Just for fun, here is a great example of that very machine:

http://www.youtube.com/watch?v=5q-BH-tvxEg

 

[QFIT]

Now, some here have argued that there is an infinitesimal (but nonzero) chance of losing every hand for all eternity. I happen to disagree, (and so does QFIT, but he won't admit it! ) for reasons I've stated, but let's say that's the case.

That's it. Now you are calling me a liar.

For the fourth time, I do not agree with this statement. I have repeatedly said that i don't agree, and you repeatedly state I do. It is unacceptable that you continue to put words in my mouth and claim that I agree with something when I don't simply because you do not understand the math.

You are now on my banned list, so I won't see any responses. But, I ask that all here understand that JD does not speak for me.

 

[Machinist]

That's it. Now you are calling me a liar.

For the fourth time, I do not agree with this statement. I have repeatedly said that i don't agree, and you repeatedly state I do. It is unacceptable that you continue to put words in my mouth and claim that I agree with something when I don't simply because you do not understand the math.

You are now on my banned list, so I won't see any responses. But, I ask that all here understand that JD does not speak for me.

Hell you guys!!!!!!!!!,,,, You guys lost me a long time ago......(nonzero)??? huh???
All i know is ...infinity.......well it's a bunch....and Progressions...well....eventually somewhere along the line...at the moment of starting the line and to the infinite end of the line ( of which there is not , supposedly) there will be a losing hand , or a spin...or roll of the dice!!!!

I"m done with this but i'm guessing this thread could go on for infinity!!!!!

Machinist.......not infinite

 

[psyduck]

Nope. The possibility is effectively (perhaps exactly) zero.



All along all I've been arguing is that it there is no proof that the martingale with unlimited table limits and bankroll wouldn't work, and therefore Throp's statement was not disproven. All you need is a single win, which will "almost surely" happen, and you've done it. It works just fine. That win can be any number you want.

Now, some here have argued that there is an infinitesimal (but nonzero) chance of losing every hand for all eternity. I happen to disagree, (and so does QFIT, but he won't admit it! ) for reasons I've stated, but let's say that's the case.

Wouldn't that possibility apply to any system, even those with positive expectations? If the possibility exists, however tiny, of losing eternally disqualifies a system from "working", then no system can be said to "work".

Do you believe the existence of negative expectation games? If you do, what are they by your definition?

 

[johndoe]

That's it. Now you are calling me a liar.

For the fourth time, I do not agree with this statement. I have repeatedly said that i don't agree, and you repeatedly state I do. It is unacceptable that you continue to put words in my mouth and claim that I agree with something when I don't simply because you do not understand the math.

You are now on my banned list, so I won't see any responses. But, I ask that all here understand that JD does not speak for me.

You've had ample opportunity to explain why your russian roulette example, where you said "the gun must fire", doesn't apply to the possibility of a single win, and only applies to the possibility of an infinite loss. I think your example very clearly supports my argument, and you have not said why you disagree.

If you wish to not answer, that's certainly your prerogative, but I did not call you a liar. You were simply caught inadvertently supporting an opposing argument with a very nice analogy.

 

[johndoe]

Do you believe the existence of negative expectation games? If you do, what are they by your definition?

You really don't understand much of what I'm writing, if you're asking this kind of question.

 

[psyduck]

You really don't understand much of what I'm writing, if you're asking this kind of question.

Maybe I do not, so help me out here.

Do you believe negative expectation games exist? If you do, what are they?

 

[johndoe]

Maybe I do not, so help me out here.

Do you believe negative expectation games exist? If you do, what are they?

Of course they do. Absent AP techniques, all casino games are -EV.

 

[QFIT]

Maybe I do not, so help me out here.

Do you believe negative expectation games exist? If you do, what are they?

In fact, JD agrees with everything I have said. And I can prove this by repeating it over and over.

 

[k_c]

Nope. The possibility is effectively (perhaps exactly) zero.



All along all I've been arguing is that it there is no proof that the martingale with unlimited table limits and bankroll wouldn't work, and therefore Throp's statement was not disproven. All you need is a single win, which will "almost surely" happen, and you've done it. It works just fine. That win can be any number you want.

Now, some here have argued that there is an infinitesimal (but nonzero) chance of losing every hand for all eternity. I happen to disagree, (and so does QFIT, but he won't admit it! ) for reasons I've stated, but let's say that's the case.

Wouldn't that possibility apply to any system, even those with positive expectations? If the possibility exists, however tiny, of losing eternally disqualifies a system from "working", then no system can be said to "work".

What I've argued is that there 2 conflicting scenarios, each of which relies upon the same logic.

Scenario A: If probability of a loss is greater than zero then sooner or later a martingale sequence can be expected to experience a 1 unit win. This is because (Prob of loss)^n -> 0 as n -> infinity for n successive losses. The eventuality of experiencing a win is virtually zero and not absolutely equal to zero, however.

Scenario B: If probability of a 1 unit win for a martingale sequence is less than 1 then sooner or later a martingale sequence will experience a disaster where not even 1 win ever occurs. This is because in scenario A if probability of n successive losses is virtually zero as opposed to absolutely equal to zero then probability of a 1 unit win is virtually 1 as opposed to absolutely equal to 1 and (Prob of 1 unit win)^s -> 0 as s-> infinity for s successive sequences.

I really don't think either scenario is exclusively true. After all they are both predicated on the same logic. Either they both are true or they both are false.

Rather what I think the math in this thread shows is a teeter totter effect with respect to winning and losing.

If the probability of a win equals 1/2 then the weights of scenarios A and B are equal and the teeter totter tends to stay balanced as number of sequnces grows endlessly. This seems kind of strange because it would seem either a disaster will happen or it won't. Perhaps what it means is that chance of growing bankroll 1 unit at a time forever equals chance of experiencing a disaster.

If the probability of a win is greater than 1/2 then scenario A outweighs scenario B and the probability of growing bankroll 1 unit at a time forever is greater than the probability of experiencing a disaster. The teeter totter tends to swing toward an infinte number of wins 1 unit at a time. The closer the probability of a win is to 1 the better the probability of avoiding a disaster is.

If the probability of a win is less than 1/2 then scenario B outweighs scenario A and the teeter totter will at some point swing to an infinite number of losses and overcome all accumulated 1 unit wins. The closer the probability of a loss is to 1 the faster the disastrous loss will be expected to come.

 

[psyduck]

Of course they do. Absent AP techniques, all casino games are -EV.

With a large bankroll and no bet limit, I can "beat" all these games as long as I stop playing after seeing a profit. Is it correct to say that all games have +EV?

 

[psyduck]

How a winning system really beats a game

After a large number of hands, a winning system can reach a point after which the cumulative profit stays positive regardless where the player chooses to stop. In contrast, martingale system in a -EV game will never reach such a point. The profit will always oscillate between positive and negative. The player always faces the chance of being in the red if he keeps playing. By my definition at least, such a system does not really work and it does not really beat the game.

What do you think, johndoe?

 

[psyduck]

You've had ample opportunity to explain why your russian roulette example, where you said "the gun must fire", doesn't apply to the possibility of a single win, and only applies to the possibility of an infinite loss. I think your example very clearly supports my argument, and you have not said why you disagree.

All you did was to use Qfit's analogy trying to support your own argument. Qfit never said he agreed with you. I have to say it is funny for you to keep saying he agreed with you evem after he repeatedly emphasized that he did not.

 

[QFIT]

All you did was to use Qfit's analogy trying to support your own argument. Qfit never said he agreed with you. I have to say it is funny for you to keep saying he agreed with you evem after he repeatedly emphasized that he did not.

Thanks. I don’t call it funny – I use the term intellectual dishonesty. You are allowed to debate anything a person says and point out inconsistencies, and even to make the claim that your opponent has made your point. You are not allowed to demand that he agrees with you.

Infinity is different. It isn’t a really, really big number. It is possible in infinity both for something to occur, and for it to never occur. This is because infinity is not a “number.” It is a “concept” of all possibilities. And, this is important, they all theoretically “exist” at once. So, you can lose a Martingale, even if you must win a hand and you stop on a win. And you can both lose every hand and win every hand. It simply does not make sense to use common arithmetic or logic when infinity enters the picture. We use limit theory and calculus to devise practical answers to questions which “approach” infinity. Martingale obviously loses as you approach infinity. I think we all agree on this. To demand that this somehow changes if you “reach” infinity is more than a giant leap. You don’t “reach” infinity. You cannot get from here to there. It isn’t the next step after the “biggest number.” It is fundamentally different. It is a concept, not a number.

"I’m so tired... I was up all night trying to round off infinity."
— Steven Wright

 

[psyduck]

"I’m so tired... I was up all night trying to round off infinity."

LOL! I wonder if he was trying to round up or down!

By the way, what was the biggest bet you used in this martingale simulation? I doubt you could go to infinity:

http://www.blackjackincolor.com/useless4.htm

 

[QFIT]

LOL! I wonder if he was trying to round up or down!

By the way, what was the biggest bet you used in this martingale simulation? I doubt you could go to infinity:

http://www.blackjackincolor.com/useless4.htm

No idea. But, infinitely less than infinity.