Failure of Gambling Systems under Unfavorable Odds

http://www.naturalspublishing.com/files/published/93j7s7uo121d1g.pdf

Do you guys know of other papers or books where this is actually proved?

EDIT: Not sure why the link doesn't seem to work. It worked in the preview version just fine.

EDIT 2: I am first author.

Quote:jmp116Right, I'm not expecting it to convince a devotee of systems. I just think it is mathematically interesting. While the result seems pretty obvious to me, it's harder to prove than I expected.

I think its interesting that in your first post ever here you tried to post a link here to something written by someone with your exact initials, but posted as it was just a random article you found.

Any chance you could figure out the mathematical odds on that? Gotta be a longshot...

ZCore13

Hi, and welcome.Quote:jmp116Yes, I'm the author. I wasn't trying to hide or draw attention to it either. I edited my first post so it is no longer unintentionally sneaky.

Normally, promoting your own site in a first post is often perceived here as spam. But I've read your paper and since you don't seem to be monetizing it, and it is on topic, I'll link to it for you.

Mathematical Analysis of The Failure of Gambling Systems

we should take bets on when the next brand new martingaler - or some variation thereof - with a winning system - shows up here

here's how the bets should be priced:

within one day...................................4/1

within 4 days..................................................................5/2

within one week............................................................................................................even money

within one month.................1/20

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Quote:OnceDearHi, and welcome.

Normally, promoting your own site in a first post is often perceived here as spam. But I've read your paper and since you don't seem to be monetizing it, and it is on topic, I'll link to it for you.

Mathematical Analysis of The Failure of Gambling Systems

Thanks, bud! Right, it isn't my site and I get no money from it. I just thought it was of interest to people who like debunking systems. But I do understand the reason for policy for new posters like me.

Quote:onenickelmiracleSomeone just telling me about a betting system for horse racing trifectas yesterday, it was hard not to laugh and I sure did. Laughed even more when I was told it looks better on paper. :) Seems you have to win a 20 to 1 shot first, then bet a hot jockey and a hot horse and hot trainer and you cannot lose because you're starting out winning $40 on the first horse. Me talking about asking how to overcome a 25% edge didn't matter to them, they just went back to the spiel. Maybe I'll ask them to come on to explain it.

That sounds like a sure thing. I would get them to show it to me on paper though :)

Quote:daveyandersen1it seems to me that ANY betting system is dependent on the[ person betting] needing a majority of winning bets for it to erein lies the problem with them..I stay away from any betting system...OR am I being obtuse????

It just depends on the type of system. If you're doing one of the more common negative progression systems like the Martingale (Double up), in which you increase the bet after losing, then you may only need one or a few big wins to make up for all the previous losses. But this short winning streak may not happen before you go broke, so you are in effect risking a lot to win a little.

If it is a positive progression, you raise your bet after wins, so it is important to have more wins than losses. You are risking a little hoping to have a big winning streak. But you have to "know when to quit". Which is the problem. Who actually knows when to quit? It can only be decided retrospectively.

I wouldn't risk any substantial amount on a betting system. It might be ok to do for fun. As part of my "research", I tried using a system at an online roulette game. I have to admit, it was really fun for a while, when I was "winning". Then I lost my whole deposit (about $80) on a short losing streak. That was less fun :)

Quote:daveyandersen1it seems to me that ANY betting system is dependent on the[ person betting] needing a majority of winning bets for it to work...therein lies the problem with them..I stay away from any betting system...OR am I being obtuse????

No. Plenty of betting systems require less than 50% rate of winning bets to come out ahead. That’s the nature of a negative progression. But a long losing streak can quickly wipe out your bankroll still.

I've always said that the secret is to get really good at guessing numbers. Once you've got that down pat: profit!

Quote:SOOPOOjmp.... I guess it’s just simple to me.... the ‘proof’ is that no series of negative expectation bets can ever add up to a positive expectation. I don’t need more ‘proof’ than that!

Maybe there could be a game designed to better illustrate the idea. Like 2 games you play at the same time. One has a positive expectation and the other a negative. To win at the positive you must lose. And as usual, to win at the negative you have to win.

It’s based on the idea that you can see something better with contrast present.

Not sure, if that’s the right way to go about it though.

Quote:rxwineMaybe there could be a game designed to better illustrate the idea. Like 2 games you play at the same time. One has a positive expectation and the other a negative. To win at the positive you must lose. And as usual, to win at the negative you have to win.

It’s based on the idea that you can see something better with contrast present.

Not sure, if that’s the right way to go about it though.

You could play any casino game you want and just play with a full house bank and a player back and see where you end up after 10,000 hands, which might take 25 hours or so, depending on the game. Not much of a time investment to test a brilliant theory. If it wins, do it again.

ZCore13

Quote:SOOPOOjmp.... I guess it’s just simple to me.... the ‘proof’ is that no series of negative expectation bets can ever add up to a positive expectation. I don’t need more ‘proof’ than that!

I agree. I'm not really any more convinced that systems don't work, because I was already convinced. But in my limited reading, all I saw for "proof" was authoritative statements from "PhD mathematicians" assuring that systems can't work (since then I've seen the very good simulations done by Wizard, which should convince anyone). This is the legit kind of appeal to authority, because these people have actually earned their expertise. But appeals to authority only sound good to those already converted. So they rarely do any good. And the one proof I did come across (actually a proof sketch given in the exercises of a probability textbook) is apparently based on a flawed assumption that the amounts won on different trials are independent.

Another question to ask is, what is the justification for thinking expectation tells you whether a bet is good or bad? It's true that a bunch of negative expectation bets add up to one big negative expectation bet, but so what? I believe the reason expectation is a reasonable measure of the favorableness of a bet is the strong law of large numbers, which converts expectations into long term near certainties about the win rate. But I found it hard to apply any of the simple versions of the law of large numbers to general betting systems, where you can change your bet in any way based on previous outcomes. For these reasons, it seemed like an interesting problem.

However, system believers fear math and logic like a vampire fears a wooden cross.

Quote:WizardFor me, the Central Limit Theorem is all you need to know to prove betting systems not only can't work, they can't even dent the house edge.

However, system believers fear math and logic like a vampire fears a wooden cross.

That's enough for me, too. I really didn't need a formal proof to know that such systems are about as likely to work as perpetual motion machines. But to play devil's advocate just a little, the version of the CLT everyone learns about applies to the sample mean of a sequence of independent, identically distributed random variables. If you are allowed to choose your bet sizes in any way based on previous outcomes, then the sequence of amounts won ( or lost) is generally not independent or identically distributed. So if you ran into the unlikely system adherent who knew that much, what do you say?

Quote:jmp116Quote:WizardFor me, the Central Limit Theorem is all you need to know to prove betting systems not only can't work, they can't even dent the house edge.

However, system believers fear math and logic like a vampire fears a wooden cross.

That's enough for me, too. I really didn't need a formal proof to know that such systems are about as likely to work as perpetual motion machines. But to play devil's advocate just a little, the version of the CLT everyone learns about applies to the sample mean of a sequence of independent, identically distributed random variables. If you are allowed to choose your bet sizes in any way based on previous outcomes, then the sequence of amounts won ( or lost) is generally not independent or identically distributed. So if you ran into the unlikely system adherent who knew that much, what do you say?

That's all known info. It's why card counting in blackjack works. And why it doesn't work in dice and roulette. Previous results have zero correlation to the next in dice rolls and random ball spins.

ZCore13

Quote:Zcore13Quote:jmp116Quote:WizardFor me, the Central Limit Theorem is all you need to know to prove betting systems not only can't work, they can't even dent the house edge.

However, system believers fear math and logic like a vampire fears a wooden cross.

That's enough for me, too. I really didn't need a formal proof to know that such systems are about as likely to work as perpetual motion machines. But to play devil's advocate just a little, the version of the CLT everyone learns about applies to the sample mean of a sequence of independent, identically distributed random variables. If you are allowed to choose your bet sizes in any way based on previous outcomes, then the sequence of amounts won ( or lost) is generally not independent or identically distributed. So if you ran into the unlikely system adherent who knew that much, what do you say?

That's all known info. It's why card counting in blackjack works. And why it doesn't work in dice and roulette. Previous results have zero correlation to the next in dice rolls and random ball spins.

ZCore13

The outcomes of spins of the roulette wheel are independent (thus uncorrelated). The amounts you win on those different spins generally are not. It's the amounts that determine whether you have a get rich quick scheme or not.

Quote:jmp116Quote:Zcore13Quote:jmp116Quote:Wizard

However, system believers fear math and logic like a vampire fears a wooden cross.

That's enough for me, too. I really didn't need a formal proof to know that such systems are about as likely to work as perpetual motion machines. But to play devil's advocate just a little, the version of the CLT everyone learns about applies to the sample mean of a sequence of independent, identically distributed random variables. If you are allowed to choose your bet sizes in any way based on previous outcomes, then the sequence of amounts won ( or lost) is generally not independent or identically distributed. So if you ran into the unlikely system adherent who knew that much, what do you say?

That's all known info. It's why card counting in blackjack works. And why it doesn't work in dice and roulette. Previous results have zero correlation to the next in dice rolls and random ball spins.

ZCore13

The outcomes of spins of the roulette wheel are independent (thus uncorrelated). The amounts you win on those different spins generally are not. It's the amounts that determine whether you have a get rich quick scheme or not.

The amounts are created to have a negative expectation. There is no get rich quick scheme that can work unless you have a biased wheel or can "clock" spins that do not vary the speed.

ZCore13

Quote:The amounts are created to have a negative expectation. There is no get rich quick scheme that can work unless you have a biased wheel or can "clock" spins that do not vary the speed.

Sorry, by amounts I didn't mean the payout odds. I'm talking about the actual amount you win or lose on a given trial, which also depends on how much you decided to bet. That depends on what has happened previously, assuming you are following a system.

it's fun - for me anyway - to think about a reverse martingale

instead of doubling after a loss - double after any win and keep doubling until you lose

just as in a traditional martingale you will occasionally run into a very long losing streak - if it's a low HA advantage game you would have to at some time - even it's very seldom - run into a very long winning streak

and run into the table limit

at which point you either go home with a juicy win

unless you're really an addict you just go into the high rollers pit and look for a table with a much higher limit and keep doubling

until you can't go home with any money.............................(~:\......................then the progressive system player is finally satisfied............................................(~:\

*

It's actually amusing to actually do it, and is no better or worse than regular marty. Instead of your bankroll chart looking like a nice upward staircase with an eventual but not inevitable plunge, you get a steady downward ramp with a not-inevitable leap.Quote:lilredrooster.......................

it's fun - for me anyway - to think about a reverse martingale

instead of doubling after a loss - double after any win and keep doubling until you lose

It shouldn't be, but can be a bit distressing, because you're repeatedly 'letting it ride' and each time you lose, your bankroll drops to an all time low. Unlike a marty, where each win takes you to an all time high.

e.g imagine you start with a bankroll of 16 units Regular marty

wager 1: win => Br=17

wager 1: lose=>Br=16 wager 2 next time

wager 2: lose=>Br=14 wager 4 next time

wager 4: lose=>br=10 wager 8 next time

wager 8: win =>br=18 phew! BR at all time high.

Now do it the reverse way

wager 1: win => Br=17 wager 2 next time

wager 2: lose=>Br=15 wager 1 next time BR at all time low

wager 1: lose=>Br=14 wager 1 next time BR at all time low

wager 1: lose=>br=13 wager 1 next time BR at all time low

wager 1: win =>br=14 phew! let's carry on wager 2 next time

wager 2: win => Br=16 wager 4 next time

wager 4: win => Br=20 wager 8 next time

wager 8: lose => Br=12 wager 1 next time BR at all time low AGAIN

You see your BR hit an all time low and then hopefully recover, time after time.

Funny how psychology applies to these systems.

.

one of the most fun systems to me - and of course it's not a long runner winner - is this one:

first bet 3 units - if win next bet 2 units - if win next bet 3 units - if win next bet 4 units

if you win the first bet, then depending on when and whether you tap out you either win 1 or 2 or 4 or (Praise the Lord) 12 units

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Quote:jmp116But to play devil's advocate just a little, the version of the CLT everyone learns about applies to the sample mean of a sequence of independent, identically distributed random variables. If you are allowed to choose your bet sizes in any way based on previous outcomes, then the sequence of amounts won ( or lost) is generally not independent or identically distributed. So if you ran into the unlikely system adherent who knew that much, what do you say?

The CLT works just fine even if the bets are based on past events. The outcomes of the bets are still independent of each other, which is all you need for the CLT to hold water.

I disagree.Quote:jmp116if it is a positive progression, you raise your bet after wins, so it is important to have more wins than losses.

When playing an even money game that's close to 50/50 with a standard pressing progression, you don't need more wins than losses. In fact, you can survive many more losses than wins, if you have winning streaks that are long enough.

Yes, I realize that's a big "If".

For example, if you bet one unit on an even money game, then press your bet one unit on every win, while restarting at one unit after every loss, you could have 60% losses and break even - provided those 40% wins were four-in-a-row.

It's all about streaks.

A streak of five wins lets you survive 10 losses.

Six wins and you can survive 15 losses.

And it gets exponentially better.

Of course, it all revolves around a winning streak. And the longer the streak, the rarer it occurs.

If, instead, you have a "streak" of flip-flopping, win, lose, win, lose, etc, then this 'system' will really hurt.

So, while no system will ever be foolproof, or even work over the long term, there's something about the short term that can't be beat.

And that's why we gamble.

For the thrill of it.

Quote:WizardThe CLT works just fine even if the bets are based on past events. The outcomes of the bets are still independent of each other, which is all you need for the CLT to hold water.

What do you mean specifically by the outcome of a bet. Whether it's a win or a loss? Or how much is won or lost. The former are independent. The latter are not if you are using a system to choose your next bet size.

Quote:jmp116What do you mean specifically by the outcome of a bet. Whether it's a win or a loss? Or how much is won or lost. The former are independent. The latter are not if you are using a system to choose your next bet size.

Either one.

Quote:WizardEither one.

Hmm, ok. It is the amounts gained on the different spins of the roulette wheel that determine if your system works. And they are not independent or identically distributed. So the simple version of the CLT doesn't apply directly to the analysis of the system.

Quote:jmp116Hmm, ok. It is the amounts gained on the different spins of the roulette wheel that determine if your system works. And they are not independent or identically distributed. So the simple version of the CLT doesn't apply directly to the analysis of the system.

You still seem to think a betting system can work. On a fair game (other than Blackjack), you can't. How much a bet pay makes no difference. It's still a negative expectation bet. The roulette wheel could have not landed on the number 1 for 200 straight spins. If you start betting it only at that point for a 36-1 payout chance, you still have a house advantage of 5.26 on the next spin and loss over the long haul.

ZCore13

Quote:Zcore13You still seem to think a betting system can work.

ZCore13

No, I don't. That is not the point I'm making at all.

Quote:WizardThe CLT works just fine even if the bets are based on past events. The outcomes of the bets are still independent of each other, which is all you need for the CLT to hold water.

So now that you've understood the simple example in the previous post, how do you propose to apply the Central Limit Theorem to the sequence X1, X2, X3, X4, .... of amounts gained on spins 1, 2, 3, 4, ....? Those X's are generally correlated and not identically distributed.

Quote:daveyandersen1I really think variation distribution is all we need to understand .Just hope to hit it when the rolls spins cards or machines are in a favorable mode so we can take advantage of it. I guess I just explained it..You guys probably know this..I just never read much about it here..

How can you tell when a roulette wheel is in a favorable mode?

Quote:jmp116How can you tell when a roulette wheel is in a favorable mode?

You can't. See, I knew you didn't understand something. I thought it was betting systems you thought worked. Now I see it's just dont understand how negative expectation games work and how when every possible bet is negative, it can never equal positive..

ZCore13

Quote:Zcore13You can't. See, I knew you didn't understand something. I thought it was betting systems you thought worked. Now I see it's just dont understand how negative expectation games work and how when every possible bet is negative, it can never equal positive..

ZCore13

Man, you haven't followed a single thing in this thread. If you had, you'd know better. Go do something else.

Quote:jmp116How can you tell when a roulette wheel is in a favorable mode?

That tells me all I need to know.

ZCore13

Quote:WizardThe CLT works just fine even if the bets are based on past events. The outcomes of the bets are still independent of each other, which is all you need for the CLT to hold water.

Wizard, I hope that my example about using a martingale for two rounds convinced you that X1, the amount gained on the first spin, and X2, the amount gained on the second spin, are correlated and not identical in distribution. That they aren't identical is obvious, since they don't even have the same sample space. But maybe you're still on the fence about correlation. So for the sake of math and logic, I'll calculate the covariance of X1 and X2 right here.

First the expectations:

X1 takes value -1 with probability 20/38 and +1 with probability 18/38, so E[X1] = -20/38 + 18/38 = -2/38.

X2 has conditional expectation -2/38 when the first bet wins, and conditional expectation -4/38 when the first bet loses (because we bet twice as much). So E[X2] = (18/38)(-2/38) + (20/38)(-4/38) = (-36-80)/38^2 = -116/38^2

X1*X2 takes value 1*1=1 with probability (18/38)^2, value 1*(-1) = -1 with probability (18/38)(20/38), value -1*2 = -2 with probability (20/38)(18/38), and value -1*(-2) = 2 with probability (20/38)^2. So E[X1*X2] = (18/38)^2 - 3*(18/38)(20/38) + 2*(20/38)^2 = (324 - 1080 + 800)/38^2 = 44/38^2 = 1672/38^3.

Now the covariance:

Cov(X1, X2) = E[X1*X2] - E[X1]*E[X2] = 1672/38^3 - 232/38^3 = 1440/38^3 = 0.026242892

So they are positively correlated. The Central Limit Theorem that you invoked requires that they be independent. That doesn't mean that systems work. They don't. It just means it's harder to prove than you might be aware of.

Quite the opposite. His very first post was to link to a scholarly paper he wrote showing why they *can't*.Quote:Zcore13You still seem to think a betting system can work.

Quote:jmp116How can you tell when a roulette wheel is in a favorable mode?

@Zcore, you're usually spot on the money, but you're way off base here. jmp116's question was *rhetorical*, basically saying that you *can't* know when a roulette wheel is more likely to win for you. You owe him an apology.Quote:Zcore13You can't. See, I knew you didn't understand something....

@jmp116, I linked to your paper in my article on betting systems. Also, since you said that you like simulations, here's a simulation I wrote based on an idea that a forum member here had about how to beat craps.

Quote:MichaelBluejayQuite the opposite. His very first post was to link to a scholarly paper he wrote showing why they *can't*.

@Zcore, you're usually spot on the money, but you're way off base here. jmp116's question was *rhetorical*, basically saying that you *can't* know when a roulette wheel is more likely to win for you. You owe him an apology.

I saw they paper, which is why I was confused on some of his other comments. I guess I misinterpreted/misunderstood what he is trying to say.

Jmp116, if in fact you understand a betting system can not overcome the house edge,, no matter what has occurred during previous spins or throws, I apologize for not understanding that.

ZCore13

Quote:Zcore13I saw they paper, which is why I was confused on some of his other comments. I guess I misinterpreted/misunderstood what he is trying to say.

Jmp116, if in fact you understand a betting system can not overcome the house edge,, no matter what has occurred during previous spins or throws, I apologize for not understanding that.

ZCore13

No worries, man :)

Quote:MichaelBluejayQuite the opposite. His very first post was to link to a scholarly paper he wrote showing why they *can't*.

@Zcore, you're usually spot on the money, but you're way off base here. jmp116's question was *rhetorical*, basically saying that you *can't* know when a roulette wheel is more likely to win for you. You owe him an apology.

@jmp116, I linked to your paper in my article on betting systems. Also, since you said that you like simulations, here's a simulation I wrote based on an idea that a forum member here had about how to beat craps.

Awesome, thank you MichaelBluejay. I will go get some coffee and take a look at both of them!

How about a Labby on Player?

You have a slight influence on tossing dice, either more or less sevens?

Seems it matters more on bankroll than anything else.