Mathematical Proof that Progressions will never Overcome a Negative Expectation Game

[aslan]

Okay, you play martingale and win a bet after three hands. Then you stop and say it works. There you have it. It does work after all these arguments. What else can I say. You have the profit to prove it.

Are you saying, "Don't spend it all in one place?" :laugh:

 

[johndoe]

Okay, you play martingale and win a bet after three hands. Then you stop and say it works. There you have it. It does work after all these arguments. What else can I say. You have the profit to prove it.

Because for this hypothetical case the bet size and bankroll are unlimited, you can set your win target as whatever you want, and repeat that process as many times as you wish. This leads to an arbitrary profit that costs only time.

Yes, it does work in this specific non-real-life case.

 

[aslan]

Because for this hypothetical case the bet size and bankroll are unlimited, you can set your win target as whatever you want, and repeat that process as many times as you wish. This leads to an arbitrary profit that costs only time.

Yes, it does work in this specific non-real-life case.

What if the very first time you begin your martingale, you never win for eternity? Odds, Schpodds! In an infinity, this can happen. Say it, you L ... ... ...! :celebrate:celebrate:band::band2::toast::juggle::band::celebrate

 

[QFIT]

Because for this hypothetical case the bet size and bankroll are unlimited, you can set your win target as whatever you want, and repeat that process as many times as you wish. This leads to an arbitrary profit that costs only time.

Yes, it does work in this specific non-real-life case.

Yes, it works. If you ignore the case where it doesn't work. This is the consistent error of progression thinking.

 

[aslan]

Yes, it works. If you ignore the case where it doesn't work. This is the consistent error of progression thinking.

The specific case where it doesn't work can happen at any time! You can't ignore it!!! This is a consistent error of martingalers. Either a case always words or it doesn't. We're not talking about practicality here. We're talking about whether it is a sure thing-- always wins-- never loses-- the nuts-- a lock-- Katie bar the door-- fuhgetaboutit-- the immortals-- no escape-- nothing can go wrong-- gotcha-- believe it or not-- gotem by the balls-- hell freezes over-- the Alamo-- Custard's last stand-- the little train that never did-- ground zero-- money in the pocket-- no way out-- this way to the egress-- seven come eleven-- I got you Babe-- don't even think about it-- a deal you can't refuse-- lock city-- jail time-- time to kiss yo ass goodbye-- bend over and grab your cheeks-- it's only money-- just a dream-- ain't that a shame-- anyway, you had the best of it-- couldn't happen to a nicer guy-- oooooh, s~it!-- born to lose-- pay up, sucka-- whaddya know, a home run-- outa da ballpark-- touchdown!-- all she wrote-- ain't life wonderful?-- there's no tomorrow-- out of the blue-- why me?-- it's unreal!-- who'd a guessed?-- that just goes to show ya-- what a revoltin' development this turned out to be!-- I can't believe it!-- it's impossible!-- Did I ever f_ck up!!!-- that's all folks!!!

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[johndoe]

Yes, it works. If you ignore the case where it doesn't work. This is the consistent error of progression thinking.

Again, the only case where it can't work is if your bankroll runs out, which is impossible, per the conditions posed in this hypothetical case ('unlimited bankroll'). The specific case if it not working, which you cite, has a probability of zero of occurring.

Unlike the case where table limits are established, the bankroll does not asymptotically reduce as time goes on; it's a divergent, oscillating series that increases in amplitude with time. Stop on a high point, which you can "almost certainly" do, and you're a winner.

 

[aslan]

Again, the only case where it can't work is if your bankroll runs out, which is impossible, per the conditions posed in this hypothetical case ('unlimited bankroll'). The specific case if it not working, which you cite, has a probability of zero of occurring.

Unlike the case where table limits are established, the bankroll does not asymptotically reduce as time goes on; it's a divergent, oscillating series that increases in amplitude with time. Stop on a high point, which you can "almost certainly" do, and you're a winner.

Well, I'm happy to see you've admitted that it doesn't always work.

And to win anything significant comparable to what you are risking, it is NEVER justified! Like, who would risk the universe for a $1 gain??? But I know you've addressed that and you don't care.

I mean if you put a stipulation on it that you will always win, I guess under those circumstances you will always win!!! :laugh::laugh::laugh:

 

[johndoe]

Well, I'm happy to see you've admitted that it doesn't always work.

And to win anything significant comparable to what you are risking, it is NEVER justified! Like, who would risk the universe for a $1 gain??? But I know you've addressed that and you don't care.

I mean if you put a stipulation on it that you will always win, I guess under those circumstances you will always win!!! :laugh::laugh::laugh:

Well, for one, the gain is whatever you want it to be. Certainly doesn't have to be a dollar. But if you think of it in terms of credit line, rather than bankroll, it makes a little more sense.

The stipulation is that the game is winnable - the odds of winning are nonzero. If this is the case, then you're certain to win eventually. That's all. Obviously martingale wouldn't work on a game that had zero chance of ever winning.

Risking the universe is easy when you have an "almost certain" chance of winning, and no limits. But remember I'm just refuting a claim made about a mathematical proof here.

But what about that hypothetical example I offered earlier: Unlimited credit line, no table limits, no time limit, betting on roulette. Would you take it?

 

[Machinist]

Yes, it works. If you ignore the case where it doesn't work. This is the consistent error of progression thinking.

Well hell QFIT!!!!!!!!! When you put it that way!!!!!!!!!!!!! " The one time it doesn"t work!!! "

Now if you could only persuade one of these guys to understand that one simple sentence....
Kinda like asking a gambler how he did at his last trip to a casino....They can ramble on about how much money they had won.........if only they had quit and went home with it...:whip:
Machinist

 

[21gunsalute]

Again, the only case where it can't work is if your bankroll runs out, which is impossible, per the conditions posed in this hypothetical case ('unlimited bankroll'). The specific case if it not working, which you cite, has a probability of zero of occurring.

Unlike the case where table limits are established, the bankroll does not asymptotically reduce as time goes on; it's a divergent, oscillating series that increases in amplitude with time. Stop on a high point, which you can "almost certainly" do, and you're a winner.

And if you split an infinite amount of hairs an infinite number of times for all of eternity this conversation would still be meaningless and irrelevant to anything that exists in the real world. :whip:

 

[psyduck]

Well, for one, the gain is whatever you want it to be. Certainly doesn't have to be a dollar. But if you think of it in terms of credit line, rather than bankroll, it makes a little more sense.

The stipulation is that the game is winnable - the odds of winning are nonzero. If this is the case, then you're certain to win eventually. That's all. Obviously martingale wouldn't work on a game that had zero chance of ever winning.

Risking the universe is easy when you have an "almost certain" chance of winning, and no limits. But remember I'm just refuting a claim made about a mathematical proof here.

But what about that hypothetical example I offered earlier: Unlimited credit line, no table limits, no time limit, betting on roulette. Would you take it?

Martingale worked for me last night. I won a unit after 4 hands. Fortunately I stopped there and am enjoying my profit. If I start again, I may keep losing until the end. Call me a chicken. I figured the sum of my wins will be finite, but one infinite losing streak will put me back in red, infinite red. I'm done with BJ!

 

[aslan]

I don't believe in progressions, but sometimes I will double my bet in a neutral or near neutral count for cover purposes only. If I win, sometimes I will place the same double bet again, and so on as long as I continue to win. Originally, the move was meant for cover, but as it proceeds and continues to win, it becomes very lucrative. Sometimes, I have even let it ride, that is, double the double up (4X). My main focus is always on betting higher when I have the advantage, and I expect these minor excursions will even out over time in neutral counts.

 

[QFIT]

Again, the only case where it can't work is if your bankroll runs out, which is impossible, per the conditions posed in this hypothetical case ('unlimited bankroll'). The specific case if it not working, which you cite, has a probability of zero of occurring.

Unlike the case where table limits are established, the bankroll does not asymptotically reduce as time goes on; it's a divergent, oscillating series that increases in amplitude with time. Stop on a high point, which you can "almost certainly" do, and you're a winner.

Frankly, I cannot understand why you keep repeating this. "Almost certainly" is NOT certainly. You are falling for the trap that all progressionists for centuries have fallen into. Small chances occur. In an infinity situation, infinitesimal chances occur. Forever expanding bankrolls and time and whatever other problems get in the way of attempting to reverse simple math does not change the equation.

Suppose we play Russian Roulette. One in, say six, chance you will lose. OK, expand it. The gun has 100 chambers. 1 in 100. OK, say the gun has an infinite number of chambers. 1 in infinty. That's "zero." BUT, you can still die on the first pull. And, if you keep playing, you WILL die. If an infinite number of players play, one will die. (Actually, an infinite number will die, but that's getting deeper into infinity.)

If an infinite number of players use a Martingale, with an inifinte bankroll and infinite time, at least one will lose. And, in a negative EV game, the loser(s) will lose more than all other players win. Martingale does not work.

Like all progressions, they work if you ignore the cases where they do not work. That is called denial.

 

[aslan]

Where am I going wrong? Isn't it possible to play a shoe with a positive EV and lose every hand? If yes, then, doesn't it follow that we can play an infinite number of hands using card counting techniques and basic strategy perfectly applied with good pen and still have a run in which we lose every hand? Would we then say categorically that card counting doesn't work? Isn't that precisely what we are saying with regards to progressions? Again, I am not trying to be argumentative, but inquiring minds want to know, so I beg the smarter members' indulgence.

 

[johndoe]

Frankly, I cannot understand why you keep repeating this. "Almost certainly" is NOT certainly. You are falling for the trap that all progressionists for centuries have fallen into. Small chances occur. In an infinity situation, infinitesimal chances occur. Forever expanding bankrolls and time and whatever other problems get in the way of attempting to reverse simple math does not change the equation.

Suppose we play Russian Roulette. One in, say six, chance you will lose. OK, expand it. The gun has 100 chambers. 1 in 100. OK, say the gun has an infinite number of chambers. 1 in infinty. That's "zero." BUT, you can still die on the first pull. And, if you keep playing, you WILL die. If an infinite number of players play, one will die. (Actually, an infinite number will die, but that's getting deeper into infinity.)

If an infinite number of players use a Martingale, with an inifinte bankroll and infinite time, at least one will lose. And, in a negative EV game, the loser(s) will lose more than all other players win. Martingale does not work.

Like all progressions, they work if you ignore the cases where they do not work. That is called denial.

I think your (quite justified) disdain for progressionists is blinding you a bit to my point. Once again, I'm only taking issue with the statement that it was "proven" that a martingale won't work with an infinite bankroll. This has nothing to do with real life.

Your russian roulette example proves my point exactly, but you have it backwards. The single bullet (pointed elsewhere!) is more accurately described as the "win", not the "infinite loss". Just like you say, no matter how many chambers you have, eventually, you WILL win. The infinite loss would be analogous to the bullet never firing, which, you admit, cannot ever happen.

Again:

1. There is a zero possibility of losing your whole bankroll, per the statement of the problem. It will never, ever happen. It's unlimited.

2. There is a nonzero chance of winning a trial.

Therefore, eventually, there will be a win, and you'll be ahead. This is by your very own analogy.

 

[DDutton]

Your russian roulette example proves my point exactly, but you have it backwards. The single bullet (pointed elsewhere!) is more accurately described as the "win", not the "infinite loss". Just like you say, no matter how many chambers you have, eventually, you WILL win. The infinite loss, cannot ever happen.

Again:

1. There is a zero possibility of losing your whole bankroll, per the statement of the problem. It will never, ever happen.

At least almost surely it will not, says ZG. LOL!

 

[psyduck]

Again:

1. There is a zero possibility of losing your whole bankroll, per the statement of the problem. It will never, ever happen. It's unlimited.

Zero possibility of losing your whole bankroll does not mean profit for you. In the end your unlimited bank will become your unlimited debt (sure if you stop playing after a win in 4 hands as I did, that's another story).

 

[psyduck]

Where am I going wrong? Isn't it possible to play a shoe with a positive EV and lose every hand? If yes, then, doesn't it follow that we can play an infinite number of hands using card counting techniques and basic strategy perfectly applied with good pen and still have a run in which we lose every hand? Would we then say categorically that card counting doesn't work? Isn't that precisely what we are saying with regards to progressions? Again, I am not trying to be argumentative, but inquiring minds want to know, so I beg the smarter members' indulgence.

I do not consider myself smart, but refer to the last equation in the very first post in this thread by ICNT. It explains everything! You can't be more mathematical than that!

 

[aslan]

I do not consider myself smart, but refer to the last equation in the very first post in this thread by ICNT. It explains everything! You can't be more mathematical than that!

But I am not smart enough to follow it in math language. I was looking for some good old plain English.

 

[johndoe]

Zero possibility of losing your whole bankroll does not mean profit for you. In the end your unlimited bank will become your unlimited debt (sure if you stop playing after a win in 4 hands as I did, that's another story).

Yes it does, if your next bet is larger than your cumulative loss. It only takes one win to be ahead, and, if you wish, that's the end. Or just keep going until the next time you win.