Wizard is wrong on his Martingale analysis

I understand the math that the wizard presents in slamming the Martingale system as a loser. However, his calculations assume a constant odds of winning each hand -- like Roulette. And that if you double your bet each time you lose, when you finally get a win, you have only won your minimum bet. Eventually you will hit a losing streak and lose everything.

The problem with this logic is that there are clear situations in Blackjack where you have a better than 49% odds of winning. This is when you face a favorable double down or split situation. In these cases, the chances that you will win are up to 80%. And when you win, you are winning a lot more than your original bet. This effect is not modeled into his mathematics of dissing the Martingale system, and is why Martingale is better played using Blackjack than Roulette.

For example, if you have a minimum bet of $10, then lose the $10 bet, the $20 bet, and the $40 bet, then when you win the $80 bet you only net $10. A long losing streak will kill you, and you cannot win enough of the minimums to make up for losing streaks beyond the table max or your own bankroll. However, what about when at the $80 bet level you have an 11 against a 6. You will win that almost 80% of the time. When you win a double down there, you win the $10 minimum bet PLUS the $80 you just wagered as the double. If you lose, you continue to double, and then bet $320, but if you win the $320 bet then you actually are winning $90 again, not just the original minimum bet.

Situations like favorable splits and double downs, and the occasional blackjack, actually do help the Martingale system look a lot better than the doomsday scenario he paints, when playing blackjack. It is not Roulette where all bets are the same. I think the Wizard is wrong in this one. I am not sure how you model it though? The chances of facing an occasional situation with better than 50% odds, with a big bet out, turns it in your favor. I would say that the Martingale system actually works best when you are floundering collecting your original minimum after every win, but hit it big after a big win in a favorable situation of doubling down or splitting 9s against a 6, etc.

I think that using the Martingale system, and employing card counting, is the best strategy. Wizard, you would be surprised how the occasional double down, split, or blackjack especially on a big bet turns the Martingale favorable for blackjack. Your anaysis is wrong, and lets see you model it with these facts in mind...

First, doubling an 11 against a 6 has a 67% expected return, not 80%. Beyond that, you're completely ignoring the negative possibilities at the higher levels of the Martingale. What happens when you get 8-8 against a 9, split, and lose both hands? Then you're much worse off for having raised your bet, right? Instead of losing $10, $20, or even $80, you've lost $160. To get back to even (or, I guess, +$10), you would have to increase your starting wager to $320 on the next hand...

While counting with martingale is probably good disguise, rdw is right: you are ignoring all the downsides. In the straight up game of blackjack, you don't win anywhere near 50% of your hands, so you will have deeper and longer losing streaks than one might expect. A double or split that goes wrong will kill the bankroll, as already mentionted. Very volatile, and very dangerous. It doesn't need to modeled, it won't work. I hear someone will bet you 10:1 it won't work, if you have the cajones.

Quote: andraaklly

I think that using the Martingale system, and employing card counting, is the best strategy. Wizard, you would be surprised how the occasional double down, split, or blackjack especially on a big bet turns the Martingale favorable for blackjack. Your anaysis is wrong, and lets see you model it with these facts in mind...

Six hundred years this has been debated, and there are still people who think that the Martingale system works.

Relative advantage doesn't matter. Give yourself a situation where you win 60 percent of your bets--a 50% advantage--and you will STILL inevitably go broke using a Martingale. It just takes longer.

I guess you, like the child who is told that the stovetop is hot, will have to learn through experience. It may amaze you to learn that OTHER PEOPLE HAVE TRIED the Martingale, and NONE has succeeded. If this were an infallible EZ-win method of amassing riches, do you think any casino in the world would still be operating? Oh, wait, they survive because the Secret Brotherhood of Martingale Wizards only shares its methods with a select few.

Quote: mkl654321

Oh, wait, they survive because the Secret Brotherhood of Martingale Wizards only shares its methods with a select few.

The select few who pay them for lessons or buy their books, no doubt.

Blackjacks (3:2) and other better than 1:1 payouts HURT you if you are doing a martingale, making you lose faster. Every time a casino is giving better than even money on any wager, that means they are beating you that many more times above 50%, which makes longer losing streaks and more martingale-busting hands in a row. If you were forced at gunpoint to Martingale for as long as you could, I'm guessing something like Bac with no bonus payouts on the Banker or Player wager (always 1:1 or 1:1 minus commission) would keep you in the game the longest.

Quote: mkl654321

... where you win 60 percent of your bets--a 50% advantage--and you will STILL inevitably go broke using a Martingale.

If win 60%, then lose 40%... a 20% advantage?

Anyway, there are many aspects to this topic... too many for any of us to hope to properly address now in a single reply. (Other than the rhetoric, one way or the other.)

Asfaras picking one's spot(s) to morph the standard ramping of bj-bets into some sort of martingale, rightly or wrongly, i have seen players try far-worse approaches just in the name of "cover".

The biggest problem with such questions is that too few of the supposed experts are ever really "in the field", or available as such. And beyond the "endless" talk, same-old refinements to the AP stuff, etc, found on most bj message-boards... oh yes, another book to buy.

Quote: Garnabby

If win 60%, then lose 40%... a 20% advantage?

No. 50% more wins than losses=50% advantage.

Quote: Garnabby

Anyway, there are many aspects to this topic... too many for any of us to hope to properly address now in a single reply. (Other than the rhetoric, one way or the other.)

Asfaras picking one's spot(s) to morph the standard ramping of bj-bets into some sort of martingale, rightly or wrongly, i have seen players try far-worse approaches just in the name of "cover".

The biggest problem with such questions is that too few of the supposed experts are ever really "in the field", or available as such. And beyond the "endless" talk, same-old refinements to the AP stuff, etc, found on most bj message-boards... oh yes, another book to buy.

It's sort of like a discussion on alchemy in the year 2010. If someone claims to be able to turn lead into gold, I don't actually need to see his experimental apparatus to know that it won't work. Similarly, we don't need to minutely examine a Martingale, nor pay attention to any new "twist" or variation thereon, to know that it's an exercise in futility.

Quote: Garnabby

If win 60%, then lose 40%... a 20% advantage?

60/40-1 = .50, or 50%

Quote: andraaklly

Your anaysis is wrong, and lets see you model it with these facts in mind...

You could stand to use a little more tact if you want to discuss this like gentlemen, rather than come out guns blazing and insulting me on my own site.

Show me specifically where I say that the Martingale would lose on any game with a player advantage. Basically, what I say that is that any betting system can't beat a game with a house edge, like roulette. Not only can't betting systems beat the house edge, they can't even dent it.

delete

Quote: Wizard

You could stand to use a little more tact if you want to discuss this like gentlemen, rather than come out guns blazing and insulting me on my own site.

Show me specifically where I say that the Martingale would lose on any game with a player advantage. Basically, what I say that is that any betting system can't beat a game with a house edge, like roulette. Not only can't betting systems beat the house edge, they can't even dent it.

Hey, Wiz, I think I know the problem with this type of guy. People seem to get lost in the math. When I was getting to undedrstand the finer points of gambling I thought you could dent the house advantage by say progressive betting (ie: increase a unit after wins but flat bet after losses.) I got it when someone said, "Look at it this way, if you win half the bets and win .95 and lose half and lose it all you will never come out ahead no matter if you bet $1 or $1MM--IT DOES NOT MATTER." Or the guy said something like that.

I'd suggest that as a math guy and a college professor you should be able to make people understand. But I have read every last "Ask the Wizard" on WoO and been here almost since the start. These martingale guys are the type that think the moon landing was faked but professional wrestling is real.

heres a way to look at it. if you bet $10 and lose, do you think it makes any difference to the casino if you bet $20 the next hand or leave the table and the next guy proceeds to bet $20? were you more likely to win than him? is he now more likely to win since you lost the last hand and hes taking your place?

Quote: rudeboyoi

heres a way to look at it. if you bet $10 and lose, do you think it makes any difference to the casino if you bet $20 the next hand or leave the table and the next guy proceeds to bet $20? were you more likely to win than him? is he now more likely to win since you lost the last hand and hes taking your place?

A spurious example at best. Are you trying to say that if I bet the $20 the next guy won't come up and play and bet his $20?

System believers are almost hopeless. They believe with a religious faith that if an event has not happened for a while, like red in roulette, it becomes overdue, and more likely. They abuse the Law of Large Numbers to make their point. What is difficult to make them understand is that regression to mean happens, even with every trial being independent. I can't count the number of e-mails I've received from people who finally saw the light after spending money on several betting systems, and seen all of them fail, with the so called "money back guarantees" rebuffed.

Not to say this is the case with the original poster. If you have a positive EV game, then a betting system couldn't lose over the long run.

I'm guessing the OP, who joined today and made his first (and only) post today, was just trying to start some bs. My $.02 lol

Quote: mkl654321

It's sort of like a discussion on alchemy in the year 2010. If someone claims to be able to turn lead into gold, I don't actually need to see his experimental apparatus to know that it won't work. Similarly, we don't need to minutely examine a Martingale, nor pay attention to any new "twist" or variation thereon, to know that it's an exercise in futility.

From http://answers.yahoo.com/question/index?qid=20080527073447AASdVm8 we have, "Best Answer - Chosen by Voters
Well, it can be done by nuclear reactions but it is much easier to convert Gold into Lead as the two elements are three protons apart.

Using neutron capture in the following reaction you can convert gold into lead. So any gold in a nuclear reactor would eventually become lead.

197Au + n �¨ 198Au (halflife 2.7 days) �¨ 198Hg + n �¨ 199Hg + n �¨ 200Hg + n �¨ 201Hg + n �¨ 202Hg + n �¨ 203Hg (halflife 47 days) �¨ 203Tl + n �¨ 204Tl (halflife 3.8 years) �¨ 204Pb (halflife 1.4x1017 years)

Of course you cannot convert lead into gold by any chemical reaction, which is what the alchemists wanted to do.
2 years ago"
______________________________________________________________________________________________

Unbelievable, how many of these posters, including the Wizard, are so quick to accept the "rhetoric"... even before others are allowed the chance to continue a worthwhile thread.

wiz 1, system believers 0...............game over.

Quote: Garnabby

Unbelievable, how many of these posters, including the Wizard, are so quick to accept the "rhetoric"... even before others are allowed the chance to continue a worthwhile thread.

I think most people would disagree, that it's not a worthwhile thread. It's a quick and easy disproof. And you just proved your own point -- you can't turn lead into gold!

Quote: Wizard

If you have a positive EV game, then a betting system couldn't lose over the long run.

The problem is, the original poster is confusing a positive EV game with a positive EV event.

He has taken a positive expectation event, (the occasional double down), applied it to a session running on a negative expectation game, and compounded it with a Martingale.

Quote: Wizard

Not to say this is the case with the original poster. If you have a positive EV game, then a betting system couldn't lose over the long run.

If I can assume a finite bankroll, I'll challenge this statement:-)

I disagree with you -- it is too simplistic to say that any overall house advantage would automatically mean that a betting system will lose, in a game with occasional variable odds. Remember, with Martingale you can lose 80% or more of your overall bets and still come out a winner. You just don't want negative streaks. You calculate the probability of a long negative streak (which will kill Martingale) based on the overall house advantage. However, that is not correct in blackjack where occasionally bets are made with better odds. Perhaps if the house advantage is big enough, you may still come out a loser, but you would rather have a game with variable odds than with consistent odds to break streaks. Lets say that you are in the 10-20-40-80-160 progression, the ability to place another 160 down with better than 50% odds (if you get 11 against a 6, for example) helps to break streaks. You can say, well that is factored into the overall odds of a 51-49 house advantage with perfect basic strategy, but I would say, that is correct when your bets are even each time, but not correct with a progressive betting system where you don't care how many wins you get you just care about not having long losing streaks.

Overall, practically you might hit the table limit or run out of money before you get enough "favorable" bets to make a difference, but theorectically I would like to see the math in a situation where there are variable odds (even occasionally) not consistent odds in a progressive betting system. That is my point.

I play Martingale because I walk into a casino about once a month with $1000 and don't care about losing it, and don't care about walking out with $700 or $1200 by playing straight bets, but care about occasionally hitting it big. Yes, I have busted many times with my $1000 after being up and then crashing. Then I walk out. But last month, I walked out with exactly $25,000 from my $1000 using Martingale. Many times, $3000 - $7000. Over time, if I played once a month for 10 years with my $1000, then added up all my winnings and losses, I would probably come out behind, unless you count. But it is a lot more fun -- playing straight Martingale 90% of the time you are up at some point (unless you hit a bad losing streak right at the beginning) and that is what is fun. According to you, no matter what in the long run, you will end up a loser with gambling. But would you want to win or lose $200-300 each time or lose your grand 75% of the time but almost always be up (before you crash, but that only takes 5 minutes) with a lot of chips on the table and occasionally walk out with LOTS of money? That is what gambling is about, entertainment. This is a lot more fun. And not as doomsday as you state -- for the reasons above.

By the way, I count too and quickly adjust my Martingale (keep high bets out) when the count is favorable and stop at only 3 progressions when the count sucks. The dealers can't figure out I am doing it, as I am always adjusting my bets and with a busy table they can't remember what progression I am on. That is probably the best way to play. Maybe that is why I am ahead, as I can get to 50% odds or perhaps more by counting...

Quote: andraaklly

However, that is not correct in blackjack where occasionally bets are made with better odds.

By the way, I count too and quickly adjust my Martingale (keep high bets out) when the count is favorable and stop at only 3 progressions when the count sucks.

1. You don't know in advance when the bets with better odds are coming (or when the bets with worse odds are coming), so the martingale does not help you.

2. Straight counting is better than the counting + martingale, because you'll have less money out in poor counts.

deleted

You are right that you don't know in advance, but it doesn't matter. Mathematically I believe (correct me if I am wrong) that with the same total house advantage of lets say 51-49, you would rather not have each bet be 51-49 like Roulette when betting progressively, but have some bets be 60-40 in your favor and some bets be 40-60 not in your favor or whatever inbetween (averaging to 51-49 house advantage). You can't beat the house advantage outright, so with straight betting you will always lose in end, but you are trying with betting systems to beat streaks, where you can win money even if you overall lose more times then you win, because you are winning the bigger bets. That, perhaps, can be done in a game with variable odds and progressive betting? I just want to see the math, but it is very complicated... that is why blackjack is a facinating game.

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Quote: andraaklly

That, perhaps, can be done in a game with variable odds and progressive betting?

As long as the mean odds are in the house's favor, you lose in the long run. The variability does not help you. Among other things, the way you can tell that's true is that everyone is not betting like you do. If it really worked, people would do it...

Quote: andraaklly

You are right that you don't know in advance, but it doesn't matter. Mathematically I believe (correct me if I am wrong) that with the same total house advantage of lets say 51-49, you would rather not have each bet be 51-49 like Roulette when betting progressively, but have some bets be 60-40 in your favor and some bets be 40-60 not in your favor or whatever inbetween (averaging to 51-49 house advantage). You can't beat the house advantage outright, so with straight betting you will always lose in end, but you are trying with betting systems to beat streaks, where you can win money even if you overall lose more times then you win, because you are winning the bigger bets. That, perhaps, can be done in a game with variable odds and progressive betting? I just want to see the math, but it is very complicated... that is why blackjack is a facinating game.

You don't know when you sit down if the next bet will be a 60/40 or 40/60 hand. You don't know if the advantage split will happen when you bet $5 or $600. It all wraps up after doing the mathematics the hard way that you'll lose about 0.5% of the total amount staked.

If you count, your better to play other systems than a martingale (progressive/parlay). If you can easily calculate the edge, you are best using the Kelly Criterion (proven to the highest rate of bank roll growth you can get).

Even with the 60/40 game, a Martingale is not the best method. A Martingale would work if there was a game with very dependent trials, but as it doesn't exist in the gambling world, it's not really that interesting in terms of this board.

You are coming from a position of positive experience rather than a mathematical, logical basis. That's fine, and it's a common mistake. The Martingale is not the most horrible thing in the world. You can win for long periods of time, and it's exciting. But in the long run you will lose slightly more than straight betting, and your variance will be higher. That's an established facts. I agree, blackjack is a fascinating game, and I'm sure there are people who are ahead over a long period of time even without counting because of where they fall on the expectation curve. (I'm down over the long run).
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If you read the first chapter of Richard Hoffer's Jackpot Nation you will find he continuously won over a period of a couple years just Martingaling and straight betting. He paid for his children's educations and his mortgage. Then he had an absolutely catastrophic loss and went six figures in the hole. So yeah, it can sometimes take place over a long period of time.

I disagree that it all averages out.

Lets say you have a 1/2 chance of winning any bet (coin flip), then the chance of losing two times in a row is 1 in 4. That would be the case with steady odds. But lets take blackjack -- say one bet you have a 1/4 chance of winning, and the next bet you have a 3/4 chance of winning (exaggerated, but just for example). The average chance of winning overall is the same -- 1/2 as the coin flip. However, the chance of losing two in a row is now 3/16, which is less than 1/4 with constant odds. So when you have variable odds on each bet, you are less likely to have a losing streak then with a constant odds game. It doesn't matter whether or not you know when you have the 1/4 chance or the 3/4 chance, the very fact that it is variable is in your favor when calculating chance of streaks. That's the math.

Once again, with constant betting it makes no difference -- an average is an average. But when you are interested in streaks (Martingale), you are less likely to have a streak with a variable odds game than constant odds, even if it averages the same overall chance of winning. Now of course it is less likely to have winning streaks as well, but you don't care about that in a progressive betting system -- you just care about not having any streaks at all.

So if the variability is high enough, you might be able to make up for the house advantage for all practical purposes when playing Martingale? Take an extreme example, where half the time the odds are 1/10 to win and another time 9/10. The average is 1/2. But the chances of losing 5 in a row that might kill Martingale are not 1 in 64 but actually 27 in 1,000,000,000. Not that you can find a game like that... but you get my point. The question is, what is the most variable odds game? Is there one? That's where a system based on streaks can be used best...

Quote: andraaklly

I disagree that it all averages out.

Lets say you have a 1/2 chance of winning any bet (coin flip), then the chance of losing two times in a row is 1 in 4. That would be the case with steady odds. But lets take blackjack -- say one bet you have a 1/4 chance of winning, and the next bet you have a 3/4 chance of winning (exaggerated, but just for example). The average chance of winning overall is the same -- 1/2 as the coin flip. However, the chance of losing two in a row is now 3/16, which is less than 1/4 with constant odds. So when you have variable odds on each bet, you are less likely to have a losing streak then with a constant odds game. It doesn't matter whether or not you know when you have the 1/4 chance or the 3/4 chance, the very fact that it is variable is in your favor when calculating chance of streaks. That's the math.

Only if you assume a 1/4 game is immediately followed by a 3/4 game. It isn't, and if you knew it was you'd min-bet the first hand and Kelly bet the second. No Martingale required.

A better example would be to model as follows :

When you play a game, you have 50% chance of playing a game where you win 25% of the time and 50% chance of playing a game where you win 75% of the time. You have no idea a priori which of the two games you are about to play.

What's the chance of losing two in a row in this case?

Chance of winning a single game :

1/2 * 1/4 (playing the bad game)
PLUS
1/2 * 3/4 (playing the good game)

=> 1/8 + 3/8 = 4/8 = 50%.
=> Two in a row = 1 in 4.

The EV is zero. If you assume these are NOT independent trials, then you need to start looking at Bayesian probabilities. Blackjack is non-independent, which is why you count, but in that case instead of martingaling you're better to bet with the cards rather than betting due to a previous loss.

I have no idea where you get your 27 in 1 billion number from. You'll have to show your working as I think you are making assumptions on the games being dependent.

In fact, I don't see if it matters if some of the games are more or less fair... the pattern of results will still look like coin flips.

Actually the chance of getting a long losing streak is greater in blackjack than in other games (e.g. Roulette, Craps). Somebody posted an interesting analysis of it: https://wizardofvegas.com/forum/gambling/blackjack/2456-streaks-in-blackjack-some-actual-data/ For example, the dealer will get three times as many 10 win streaks as the player will. Those are $5120 losses in your progression system, not counting any double downs or splits. You make up this sizable disadvantage in split and double down situations, but you will still lose a great majority of the hands in the game.
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I agree with the person who said baccarat is the best game for Martingaling. But nobody here will agree with your proposition that Martingaling will create a positive expectation in a negative expectation game, and trying to prove that point will be like trying to break a rock with your head.

Quote: teddys

I think most people would disagree, that it's not a worthwhile thread. It's a quick and easy disproof. And you just proved your own point -- you can't turn lead into gold!

Please speak for yourself, or show us all all the "quick and easy disproofs" involved. (Bet you can't even begin, lol.)

The only thing for sure so far... mkl654321 has backed off a pretty-stupid (for such a renowned so-called teacher) remark about "turning lead into gold". (And apparently you have carried it through to this topic, itself, double lol.)

Quote: Garnabby

Please speak for yourself, or show us all all the "quick and easy disproofs" involved. (Bet you can't even begin, lol.)

The only thing for sure so far... mkl654321 has backed off a pretty-stupid (for such a renowned so-called teacher) remark about "turning lead into gold". (And apparently you have carried it through to this topic, itself, double lol.)

Yo, Garnabby, dude. I'm not renowned, but I AM a teacher. And if you think that it's stupid to say that you can't turn lead into gold--well, I have news for you--you can't. (And before you bring up the nuclear reactor process that someone else mentioned, that isn't turning lead into gold, it's breaking down gold into its constituent atomic particles and rearranging them into lead, or vice versa--but in each case, some material is lost/discarded.)

I guess I have to presume that you don't get the point of the analogy--that in the same way a knowledgeable chemist would not bother to investigate the intricacies of a claim to be able to (chemically) turn lead into gold, a knowledgable gambler should not bother to examine in detail a claim for an effective Martingale system.

And far from "backing off"--I REITERATE that statement.

Quote: Garnabby

Please speak for yourself, or show us all all the "quick and easy disproofs" involved. (Bet you can't even begin, lol.)

Well, lol, there is a quick and easy, lol, disproof, lol, that can be easily stated, lol, thusly: it is impossible to add a series of negative numbers and end up with a positive number, lol, as a result.

Lol.

Quote: mkl654321

Well, lol, there is a quick and easy, lol, disproof, lol, that can be easily stated, lol, thusly: it is impossible to add a series of negative numbers and end up with a positive number, lol, as a result.

Lol.

Quote: mkl654321

Now, you're starting to babble.

And by the way, there's no such word as "there're" (it is indeed used quite a bit, but so are words like "anyways").

Quote: Garnabby

Nothing

Thanks for contributing.

Quote: andraaklly

I disagree that it all averages out.

https://wizardofvegas.com/forum/gambling/blackjack/2456-streaks-in-blackjack-some-actual-data/

There is some data here on streaks in blackjack. Look at dealer streaks for lets say 5. If your hypothesis is true, then the number of dealer streaks that end at 5 should be more than the sum of dealer streaks of 6, 7, 8, etc. More generally, streaks of n would be greater than the sum of all n+i streaks where i goes from 1 to infinity. This notion would imply that the dealer losing 5 and then giving a way a winner is more likely than the dealer continuing to win. If you add up the numbers here, you will find that that the number of streaks of lesses >5 are higher than the total number of 5 loss streaks.

It is now up to you to either refute this evidence through finding potential flaws of calculation or present your own statistical analysis that refutes these findings.

Quote: andraaklly

I disagree that it all averages out.
[snip]
So if the variability is high enough, you might be able to make up for the house advantage for all practical purposes when playing Martingale?

No, because increasing the variance (variability) of a series of bets doesn't change the mean (house edge). Consider two extremes:
A) You take $100,000 and make a single blackjack bet. The house edge (in dollars) is approximately $500. Variance is through the roof.
B) You take the same $100,000 and flat-bet $1 for months in a row until you've bet $100,000 in action. The house edge in dollars is still approximately $500, but variance is much, much lower.

If you play a Martingale with $100,000 in handle, your variance will be somewhere between A and B. It can't be greater than A, and it's certainly higher than B. The question you need to answer is "is the house edge still $500?" If it's $500 at both ends of the variance scale, then intuitively does it make sense that it would change somewhere in the middle?

Quote: andraaklly

I disagree with you -- it is too simplistic to say that any overall house advantage would automatically mean that a betting system will lose, in a game with occasional variable odds. Remember, with Martingale you can lose 80% or more of your overall bets and still come out a winner. You just don't want negative streaks. You calculate the probability of a long negative streak (which will kill Martingale) based on the overall house advantage. However, that is not correct in blackjack where occasionally bets are made with better odds. Perhaps if the house advantage is big enough, you may still come out a loser, but you would rather have a game with variable odds than with consistent odds to break streaks. Lets say that you are in the 10-20-40-80-160 progression, the ability to place another 160 down with better than 50% odds (if you get 11 against a 6, for example) helps to break streaks. You can say, well that is factored into the overall odds of a 51-49 house advantage with perfect basic strategy, but I would say, that is correct when your bets are even each time, but not correct with a progressive betting system where you don't care how many wins you get you just care about not having long losing streaks.

Overall, practically you might hit the table limit or run out of money before you get enough "favorable" bets to make a difference, but theorectically I would like to see the math in a situation where there are variable odds (even occasionally) not consistent odds in a progressive betting system. That is my point.

I play Martingale because I walk into a casino about once a month with $1000 and don't care about losing it, and don't care about walking out with $700 or $1200 by playing straight bets, but care about occasionally hitting it big. Yes, I have busted many times with my $1000 after being up and then crashing. Then I walk out. But last month, I walked out with exactly $25,000 from my $1000 using Martingale. Many times, $3000 - $7000. Over time, if I played once a month for 10 years with my $1000, then added up all my winnings and losses, I would probably come out behind, unless you count. But it is a lot more fun -- playing straight Martingale 90% of the time you are up at some point (unless you hit a bad losing streak right at the beginning) and that is what is fun. According to you, no matter what in the long run, you will end up a loser with gambling. But would you want to win or lose $200-300 each time or lose your grand 75% of the time but almost always be up (before you crash, but that only takes 5 minutes) with a lot of chips on the table and occasionally walk out with LOTS of money? That is what gambling is about, entertainment. This is a lot more fun. And not as doomsday as you state -- for the reasons above.

By the way, I count too and quickly adjust my Martingale (keep high bets out) when the count is favorable and stop at only 3 progressions when the count sucks. The dealers can't figure out I am doing it, as I am always adjusting my bets and with a busy table they can't remember what progression I am on. That is probably the best way to play. Maybe that is why I am ahead, as I can get to 50% odds or perhaps more by counting...

The above post is the "advantage" of the martingale system.
Shouldn't be surprising, the Wizard already produced a graph of this:


The benefit of the martingale system is that you walk away a big winner or a big loser. It gives the feeling of success or the "oh well, i lost it all" feeling. Hitting blackjack on your 1 unit bet is "meh" but hitting it after your 6th losing hand on the martingale system and BANG you feel fantastic...like a genius that cracked the game.

I am not completely on board about betting systems being phooey though. I do agree that all hands are stochastic instances and rely on nothing but chance (well, mostly...obviously BJ has a running count that could influence your net EV), but for games with more complicated dynamics it feels like you could exploit those dynamics via a betting system. Let It Ride comes to mind...I don't have a good strategy for this but I can see an opportunity for development there.

That's a -small- winner or big loser.. as the ratio is about 5:1 between wins and losses there...