Can anyone diprove this math?
A simple Martingale or D'alembert MUST win against the house in the following scenario.
1. Unlimited bankroll.
2. Unlimited bets on the table.
So indeed you can see that both Martingale and D'Almbert were right in their thinking and did in fact beat the tables in europe out of vast sums of money until the houses instituted TABLE LIMITS. These limits are the only thing that can cause these systems to loose given a rich gambler with great resources.
If you wish to beat the game you need to figure out how to beat the table limits...........and have a wad of cash....
Can you prove that this is incorrect?
https://wizardofvegas.com/forum/off-topic/general/4160-infinite-martingale/
And if there was, and you had access to it, why bother - you are already infinitely rich, it just doesn't get any better.
To clarify, I said this was "correct in a way", meaning that there is a sensible way to define "beat the game" that allow a martingale to work if you have unlimited bankroll. But it still does not work with a traditional definition - your bankroll won't become any larger, however long you play.
Quote: Whiskeyjack1. Unlimited bankroll.
Ask yourself this question: What does it mean to increase an unlimited bankroll?
In simulated rullette spins with Martingale totaling two million five hundred thirty two thousand six hundred spins of an american wheel the longest loss streak I could produce was a whopping twenty-six spins where either black or green appeared but as can be certain red finally came on spin twenty seven.
True that betting only 1 unit to start you are wagering a fortune at spin twenty seven still it can not fail to appear.
On a french wheel useing the imprison rule in 800,000 spins i could do no better than 14 losses in a streak.
Let's say that a casino had $100000000000000000000000000000000000000000000000000, which was also its max bet. The Martingale, or any betting system, could still not overcome, or even dent, the house edge, over the long run.
Quote: Wizard*sigh*
Let's say that a casino had $100000000000000000000000000000000000000000000000000, which was also its max bet. The Martingale, or any betting system, could still not overcome, or even dent, the house edge, over the long run.
So useing that number "over the long run" as the max bet how many times in your 1 billion trials has the house overcome the holder of an equal bankroll? Starting with a 1$ bet and moving up. While it's not an impossibility (it may happen one time in thirty trillion events) I can not produce any scenario (particularly on a french wheel w/imprison where the house comes close to winning such a bankroll.
D'Almbert fairs even better as the betting sums are lower and the more trials the colser the results to the true expectation appear.
I'll bet the answer is ZERO
Quote: WhiskeyjackSo useing that number "over the long run" as the max bet how many times in your 1 billion trials has the house overcome the holder of an equal bankroll? Starting with a 1$ bet and moving up. While it's not an impossibility (it may happen one time in thirty trillion events) I can not produce any scenario (particularly on a french wheel w/imprison where the house comes close to winning such a bankroll.
D'Almbert fairs even better as the betting sums are lower and the more trials the colser the results to the true expectation appear.
I'll bet the answer is ZERO
Ok, you're right. Now go and win money using the system. Oh, you say you can't win because the casinos have made it impossible by instituting a table limit. Drat those pesky casinos. End of thread.
Quote: niczoneWhy are so many so enamored with these betting systems. They don't work. The math does not work out. Exactly right on asking pointless questions. The proof isnt on the person trying to refute a betting system. The proof ought to be on the person who makes the system.
The math was done by mathamaticians Martingale and D'Almbert.
A group of individuals scored big by reversing D'Almbert so the bets increased with wins vs. losses.
Read "Eight against the Bank" if I remember the title correctly. Refute that!
I agree that given any system the house holds a mathmatical advantage but who has the advantage if in a fifty/fifty prop bet where the bettor needs win only 35% of the time to beat the house. No math can overcome a 30% advantage over the house.
It's not to say you will never loose, because you will run into the table limit at which time you have been defeated, of course with a team of say six, you could expand the table limit by 500%
The idea is to win more than you loose if you can do that a system works.
Quote: Whiskeyjack
The idea is to win more than you loose if you can do that a system works.
In the short run you will probably come out ahead. You are subbing a lot of tiny gains while trying to avoid the one that breaks you. Make no mistake though, there will be a loss that will break you and takes all of your bankroll with it.
There is an amazing thing about house edge. If, in theory, you could play a game where the edge was in favor of the player, you could in theory make an infinite amount of money as trials approaches infinity. If the house has an edge of ANY size, the house will in theory make an infinite amount of money as trials approach infinity. If the game had no edge, neither you nor the house would make money as trials approach infinity.
The system has nothing to do with the house edge. The house edge has to do with the composition of the game itself. The "tie" in baccrat is a sucker bet because its house edge is much higher then betting player or banker. Card counters make money because they bet more when the deck is in such a condition that has an edge toward the player than when it does not.
They impose table limits to manage their risks and variance and to some extent to be able to segment their market.
Truth is that since no one can beat the tables why gamble at all.
In the short run, useing systems, I have faired well often winning the entire amount of my bankroll two or three times before running into my limit. Ofetn times getting nice comps in return. All in all I have some fun. I have studied BJ and in the old days was tossed from the El Cortez, Flamingo and 4Q for winning not as large of sums one would imagine. The fact that I could play hour after hour and not loose my shirt brought attention. In one case I was up a lousy $2800 and got asked to cease and desist from the BJ tables.
My point is be tough, have a plan, stick to it and most of all enjoy your time at the casinos.
The title above is wrong read the following about systems. People will forever scheme to beat the odds..that is what makes us human!
Thirteen Against the Bank:
The True Story of How a Roulette Team Broke the Bank with an Unbeatable System
by Norman Leigh
In my opinion, the toughest player is a craps player who presses very heavily on the odds (ideally at an 100x odds house), while keeping his pass line bets at the minimum.Quote: WhiskeyjackExactly, so the question is is a system player tougher than a non system player? I think that casinos fear system players more than uneducated gamblers. After all if you really understand any game your outcome is likley to improve.
The second toughest would be a very skilled high limit video poker player with a very large bankroll.
Casinos aren't really afraid of blackjack or baccarat players because they know they can grind you down eventually. If you are counting, they will boot you.
Edit: That guy on 60 minutes who bet sports for insane amounts is pretty scary, but he's probably an exception.
Quote: thecesspitThe house doesn't post table limits to avoid being Martingaled and D'alemberted out of existence.
They impose table limits to manage their risks and variance and to some extent to be able to segment their market.
Perhaps so, but my reading of the historical reasons for limits was they were imposed in France and Monaco to counter the Martingals and D'Alembert long before Las Vegas existed.
Quote: teddysIn my opinion, the toughest player is a craps player who presses very heavily on the odds (ideally at an 100x odds house), while keeping his pass line bets at the minimum.
The second toughest would be a very skilled high limit video poker player with a very large bankroll.
Casinos aren't really afraid of blackjack or baccarat players because they know they can grind you down eventually. If you are counting, they will boot you.
Edit: That guy on 60 minutes who bet sports for insane amounts is pretty scary, but he's probably an exception.
Right on all tough, planned and educated itr makes sense they would have the higher chance of winning.
Quote: WhiskeyjackPerhaps so, but my reading of the historical reasons for limits was they were imposed in France and Monaco to counter the Martingals and D'Alembert long before Las Vegas existed.
They were imposed in France and Monaco for the same reason they were imposed in Las Vegas: the house doesn't have an unlimited amount of money. If you break it down, there's no obvious reason why the Martingale or D'Alembert systems should "work" at all -- each system is just some combination of different bet amounts. If you had a different player making each bet amount (that is, flat betting), you wouldn't expect any of them to beat the house. If none of them individually is winning, then they clearly aren't winning as a group either.
Quote: Whiskeyjack... I think that casinos fear system players more than uneducated gamblers. ...
I suspect those two look a whole lot alike.
Quote: TheNightflyOk, you're right. Now go and win money using the system. Oh, you say you can't win because the casinos have made it impossible by instituting a table limit. Drat those pesky casinos. End of thread.
Well I have indeed done just that, what I said about limits is that if they were not tight one could win and win and win.
So did these Thirteen!
Thirteen Against the Bank: The True Story of How a Roulette Team Broke the Bank with an Unbeatable System
by Norman Leigh
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Quote: WhiskeyjackWell I have indeed done just that, what I said about limits is that if they were not tight one could win and win and win.
So did these Thirteen!
Thirteen Against the Bank: The True Story of How a Roulette Team Broke the Bank with an Unbeatable System
by Norman Leigh
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You mean this unbeatable system?
From ME's linked article, I'm not sure whether the book would have been more properly titled "How to sell a book like this one by pretending that you beat the casino" or "How to make some money by scamming your backers".Quote: MathExtremistYou mean this unbeatable system?
This is a widely held belief, but it is not true.
Unlimited bankrolls, and unlimited maximum bets do not matter. Please read the thread.
Quote: WhiskeyjackExactly, so the question is is a system player tougher than a non system player? I think that casinos fear system players more than uneducated gamblers.
There is no "more" or "less", they are the exact same people.
Quote: WhiskeyjackAfter all if you really understand any game your outcome is likley to improve.
Of course, understanding how exactly Baccarat is played gives you massive advantage over the house.
Quote: WhiskeyjackWhat I am saying is simple, D'Almbert took millions from french wheels because his system worked until the house limits were calculated to stop a further bet from winning. His system worked so well he forced the houses to change their game.
No, he won (assuming that he was even telling the truth) because he was LUCKY. Lucky as in, lucky enough not to experience a losing streak that EITHER a) busted him outright or b) required him to make a bet larger than his remaining bankroll.
He didn't win because he had a wonderful foolproof method. And the casinos were extremely stupid to put in table limts if the reason for doing so was to stop system bettors--but I doubt very, very, very, very much that they actually did so because they were afraid of people like D'Alembert.
Quote: MathExtremistYou mean this unbeatable system?
I did not write the book I just read it. One can debunk any book by simply casting dispersions that does not make the critic right or for that matter the writer of the book. One thing I would do if I were a party to a winning scheme. Keep my mouth shut as to the extent of the winnings. Who would want to pay the taxes.
If you have been in Vegas long you know that people can find ways to win. Phoenix dog racing operation. Blackjack teams and more.
Remember long ago they had electric crap games in local bars. They actually had dice in them that rolled like on a table. They are no longer in service because someone close to me figured out how to beat the program. Too bad at the time he did not realize all the games had one owner. In a drunk stupor he won 2k and the bartender called the qwner to pay off. Blitzed he promptly went to a high stakes poker game and lost the 2k. No worries there were six different bars he knew of with the crap games so he hit the next bar for 2k. The same owner came tp pay and realized the chances were nil so the next day the games were removed never to return.
For over a year he had been making a few hundie off each game each week but greed and booze ruined his source of income. After seeing my friend do this I gave up drinking myself.
Quote: WhiskeyjackFor over a year he had been making a few hundie off each game each week but greed and booze ruined his source of income. After seeing my friend do this I gave up drinking myself.
That's a good first step. Give up systems betting too and you'll be golden.
Quote: WhiskeyjackWell I have indeed done just that, what I said about limits is that if they were not tight one could win and win and win.
So did these Thirteen!
Thirteen Against the Bank: The True Story of How a Roulette Team Broke the Bank with an Unbeatable System
by Norman Leigh
Share | .Be the first to review this item | Be the first to post a discussion
I've read the book. It is a nice story that includes some basis in fact and a lot of fiction. Here's another good story (albeit a much shorter one) from the Quatloos website.
Parity Hedge System
The point is that until you or anyone can show that a system DOES work, no intelligent person who knows anything about math and odds will give any system any merit. So, as I said before, go and use your system (or any system) and break the bank. You'd better be prepared for two things though... ridicule and an empty bank account. Say what you want about a sysytem, a book about a system, a friend who told you about a system or a website that promotes a system... they're all worthless unless you can prove they're not... and you can't do that because it's not possible, regardless of what you read in a book.
Given an infinite bankroll on both sides, and infinite time, then everything falls away from the equation except the house edge. Regardless of the game. 00 Roulette? There is a 105.26% chance you will go infinitely bankrupt before you will infinitely bankrupt the house.
One infinity is larger than the other. That's all there is to it. (Yes, there are different sizes of infinities.)
Quote: Mosca
One infinity is larger than the other. That's all there is to it. (Yes, there are different sizes of infinities.)
Not really. There are indeed different "sizes" of infinities in some sense, but it is not the case here. Both infinities in this case are exactly the same.
The complicating issue with martingale is indeed that the probabilities grow similarly, in a coin flip scenario.
Overall house edge, however, does not remain a constant. In a 52.6% house win scenario, for instance, the probability of losing 8 hands in a row is 1/170, while the reward to risk ratio is 1:255. This means the effective house edge for an 8-step martingale sequence becomes 33.3%, up from a mere 5.2% for flat-betting. Player's expected loss on that sequence is $0.506 (255*1/170-1*169/170), up from $0.416 (0.052*8) from flat-betting eight times. The average win of a martingale sequence is $1, down from $2.67 if flat-betting 8 times.
I can't do the math for martingale with all possible sequences, and it's not worth simulating, but overall one can see the house advantage increasing, particularly it simultaneously produces an increased hold percentage and a reduced potential reward. Without long streaks, as martingale becomes closer to flat-betting, the difference becomes less dramatic, but it still is there. It becomes dramatic again, however, when doing a risk to reward comparison.
Quote: MoscaThanks for the correction. I'm not sure how to express it, that the edge holds regardless of the number of chances or size of bankrolls, even when applied to infinities. (Are infinities sized in integer values?)
There is a special set of numbers (called infinite cardinals) that are used to "measure the size" of infinities. All countable infinities are the same "size", that is referred to as "aleph-null". A "larger" kind of infinity is known as continuum (an example is the set of all numbers, including irrational), and denoted as aleph-one. If you consider a set of all subsets of the set of all irrational numbers, you'll get a yet "larger" infinity - aleph-two. Etc. The relationship between between two neighboring alephs is that apleph-N is 2 to the power of aleph-(N-1).
One interesting fact, related to this is that there are as many integer numbers as there are rational ones.
The way this relates to house edge is that 94.4% of aleph-0 is still aleph-0, thus, if you have infinite amount of money, it won't decrease even when you are playing with the house edge.
Quote: P90
Overall house edge, however, does not remain a constant. In a 52.6% house win scenario, for instance, the probability of losing 8 hands in a row is 1/170, while the reward to risk ratio is 1:255. This means the effective house edge for an 8-step martingale sequence becomes 33.3%, up from a mere 5.2% for flat-betting.
What is "effective house edge"? Are you referring to hold?
I think Whiskeyjack is also off when he says unlimited bankroll and unlimited trials. Because as soon as he picks a place to stop and call a win, he has violated his own conditions; he limits the trials. Since it is unlimited it can never stop, and thus it must always lose at the same rate as the house edge.
Quote: weaselmanWhat is "effective house edge"? Are you referring to hold?
House edge if you regard the entire sequence as a single bet.
Quote: MoscaThanks.
I think Whiskeyjack is also off when he says unlimited bankroll and unlimited trials. Because as soon as he picks a place to stop and call a win, he has violated his own conditions; he limits the trials. Since it is unlimited it can never stop, and thus it must always lose at the same rate as the house edge.
Yes. I think, the correct formulation of the problem is that you can make a bet of any amount at any time, and play as long as necessary without a limit, until, the total amount of your wins exceeds the amount of losses.
Under these conditions, you will always "win".
Quote: weaselmanThis is actually correct, in a way
What is correct is that your upper bound grows linearly while your lower bound grows exponentially and your bankroll oscillates between the two growth curves. If you plot the oscillating curve and find it center of gravity, you get a line corresponding to the house edge.
--Ms. D.
Quote: DorothyGaleWhat is correct is that your upper bound grows linearly while your lower bound grows exponentially and your bankroll oscillates between the two growth curves. If you plot the oscillating curve and find it center of gravity, you get a line corresponding to the house edge.
I wanted to ask why you think it grew exponentially, but a more urgent question is how do plot the growth (and oscillation) of infinity? :)
Quote: P90House edge if you regard the entire sequence as a single bet.
Hmmm. If you lose 8 hands in a raw, with a probability of 1/170, you will have wagered and lost 511 units.
So, the "effective house edge" should be (511/170 - 169/170)/511 = 0.39%. No?
Also, these people are clearly trolls who like to pull your collective legs.
Quote: weaselmanHmmm. If you lose 8 hands in a raw, with a probability of 1/170, you will have wagered and lost 511 units.
So, the "effective house edge" should be (511/170 - 169/170)/511 = 0.39%. No?
255 units - it's 1+2+..., so only 2^n-1. I'm calculating edge from the initial bet (as such one unit), because the idea is that followup bets just compensate for it.
House edge can be calculated in multiple ways, of course, so it becomes somewhat moot to figure out the baseline when the amount bet is variable. Since most times you won't be betting all 255 units, that's not a good baseline. Mine probably wasn't either, though.
It's more practical to use EV as a common denominator. That way, it's an EV of -0.506 units. Overall expectation can be compared to the potential win for calculating performance, and the potential win is the same 1 unit for a single bet (paid for by -0.052 in EV) and martingale (paid for by -0.506 in EV).
Quote: weaselmanYes. I think, the correct formulation of the problem is that you can make a bet of any amount at any time, and play as long as necessary without a limit, until, the total amount of your wins exceeds the amount of losses.
Under these conditions, you will always "win".
Right. And even still; he is proposing that one side be allowed to say when to stop, but not the other. I could reduce the proposal to, "If I am allowed to play until I win, and then stop, then I will always win." Well, yeah, if the other player is not allowed the same condition.
Quote: P90255 units - it's 1+2+..., so only 2^n-1.
2^(n+1)-1 actually. 2^n is the size of the last bet. The total is 2^(n+1)-1 = 511
Quote:I'm calculating edge from the initial bet (as such one unit), because the idea is that followup bets just compensate for it.
Then it should be 199.29% (0.39*511), not 33% as you suggested.
But I have never seen the term "house edge" used this way ...
Quote: weaselman2^(n+1)-1 actually. 2^n is the size of the last bet. The total is 2^(n+1)-1 = 511
The first bet is 1, the second bet is 2, the third is 4, so on till 128 as the last bet (1,2,4,8,16,32,64,128). It's [1..n]Sum(2^(n-1))=2^n-1.
