BlackJack- Card Counting + Optimum Martingale = Proven Effectiveness

First off, the Martingale system does not work. I intend to prove to you, however, that by tweaking the strategy a bit, the "optimum martingale" as I call it can be used to mask card-counting detectors employed by the casinos.

The Martingale Betting System- A failure by itself. It requires the player to double his/her bet every time she looses, covering previous loses incurred on the losing streak and returning to the player an amount equal to their lowest common bet. It is not efficient because when you inevitable hit a major loosing streak, you risk running your bankroll dry or reaching the maximum bet and not being able to double anymore, all for one measly lowest bet in return.

I documented over 1,000 hands using this technique, taking into consideration every variable, playing with basic strategy, shuffling after each hand, and purposely leaving out the variable of card counting to ensure there was only one variable. I ran the losing streaks out until I had either won, or ran my bankroll dry. Then, I went back and calculated what would have happened had I decided to cut my loses, reset my bet to the original, and continued playing after loosing 8 hands in a row, 7 hands in a row, 6 hands in a row, and so on until I was theoretically flat betting every hand. Most losing streaks did not exceed beyond 8 hands, but if they did, I calculated for that too.

I found that, beyond a shadow of a doubt, reseting your bet to the original low was most effective when you reset after a three-hand losing streak. Whereas reseting after any other number of lost hands either lost money in the scenario, or gained very little for the amount of time it took, reseting at three consistently wielded a positive average of roughly $41 per 70 hands played, using a $1 lowest common bet. At the same time, my bankroll never went more than $23 below it's original value, and steadily increased after that. After testing over 1,000 hands, this is quite definitely the optimum time to reset your bet using the martingale system.

This is a major bonus to Card-Counters, because it fools computer technology commonly employed to catch counters, and it also masks your efforts to the dealer (the most direct link between you and the pit-boss). Most card counters will flat-bet a small amount when the count is low, and then slam their bets up high when the count is in their favor. This is easily noticed by dealers and by computers, which use RFID sensors to keep track of the bets on the table, and another technology to keep count in the game using almost every count system imaginable. If your bet or cardplay matches what the computer has analyzed as close enough to consider counting, you got a one-way ticket to the next casino. If you employ the optimum martingale system instead of flat-betting when the count is low, it will mask your efforts to the dealer especially, and to an extent with the computers. It allows the counter to not risk much money, while also making the swings in his bets not as noticeable. I find it most effective to use the Optimum Martingale, even as the count climbs, but instead of reseting my bet at three, I will continue to climb my bets up, win or loose, until the count begins to decline. By sticking to the style of doubling your bets when the count is high, even if you win or lose, you stray from the average card counter which the computers are looking for while also retaining the ability to place large bets when the count is high and decrease them as it recedes.






I did this all by hand, using ledger paper, taking into consideration these variables: L.C.D. bet, starting bankroll, ending bankroll, starting time, ending time, Bank Roll amount, Hand number, Players Cards, Dealers Up Card, Suggested strategy action, actual action, win/loss/push/bust/dealer busts. If you have a computer to simulate this, with special attention to when to reset your bets on a losing streak, and would like to add on, please do! Otherwise, try it out! Even if you can't count cards it is a fun system and is slightly more effective than it's predecessor. However, I wouldn't play it for money if you intend on using it by itself. After all, betting strategies are not useless, but they're not reccomended by themselves.

Very interesting post - Thanks!

One thousand hands in nowhere near a robust enough sample to draw the sweeping conclusions you are making. Hint: calculate your standard error.

>This is easily noticed by dealers and by computers, which use RFID sensors to keep track of the bets on the table ...
I would think that extreme bet variation would indeed bring instant attention even before anyone in the casino started to verify the count when it was taking place.

I think those RFID tags inside the chips with sensors at the table's betting circles do actually exist but I doubt it exists in anywhere near as many casinos as people seem to assume. Its a bit pricey to have such systems and I rather doubt it catches all that much in the way of bet capping or card counting.

If you go from one green chip to three black chips, you are going to be noticed. If surveillance plays back the tape and counts down the deck to the time at which you suddenly started betting big they will be able to confirm their worst, but still foolish, fears: there is a card counter in their midst.

I don't see how any other aspects to the play are going to disabuse them of this notion. If you revert to a lower level of play after three losses, you are still a card counter who has come to their attention.

I agree about the chips, they are rare outside of Vegas. Also, not a lot of casinos keep track of card play electronically. It basically boils down to fooling the dealer. Think of it like you're an entire blackjack team and you're 'Wonging' your own table, the benefit being there is no obvious flat-betters keeping count or some 'big better' stepping in only when the count is high. Externally you appear to be relying on a betting system, in reality you are not.

As far as the 'reset' aspect, the three-loss rule doesn't use any information from the count; it's played using solely basic strategy while keeping track of the count, so you're still not playing your hands like a counter, just someone with a strategy chart. Only when the count is extremely high or low do you begin to change your gameplay according to the count, and double your bets even if you win. I didn't explain that very well :p

I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.

I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.

Quote: Thunk

I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.

I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.

I've always wondered, when using the Martingale (which I haven't before), what does one do when he has lost several hands in a row, has much more money out on the table, and then is faced with a double-down or split situation. In other words, after you've lost several hands and have doubled and then redoubled your bet accordingly, what is the proper action when faced with a double-down or split hand? Do you double-down or split per basic strategy and risk additional monies (and gains), or should you simply hit or remain with one hand?

This is a tricky question, and also why it is a good idea to stop at three. That way, you can never loose too much even if you do double down your third bet and lose again. As a rule of thumb, I don't deviate from basic strategy until the count is high or low enough to make a profound impact. However, if I am faced with a double down or split situation, and I have a lot of my bankroll on the table, I'll use information from the count to impact my decision. Don't do anything stupid, like not splitting eights against a six, or not doubling an eleven against a six, but for instance I would not double a 9 against an 8 if I was on my third loss, only on the first or second hand. There's simply not a high enough potential loss/potential gain ratio once you factor in the act of reseting your bets.

Remember: If you bet $10, lose, bet $20, then double and lose, you've lost $50 and your next bet has to be $60 to keep in pace. Some might prefer, once they get to that point, to just bet $50 and hope to merely cover loses before reseting.

Quote: Thunk

I used maximum likelihood to figure this out. Without knowing the true value of the standard deviation, which is impossible to predict, standard error is impossible to calculate and will only be an estimate, nothing I would take into consideration at the table. Standard Error in a game like blackjack, to me, is a fallacy.

I am a Statistical Analyst which is what got me into BlackJack in the first place, and I am very confident in my accuracy. I have taken this strategy to Biloxi on six occasions now and have banked $3,420 in those six trips.

1. You used maximum likiihood to figure what out? What are you estimating?

2. Of course you would estimate the standard deviation, if you do not know it--this is basic statistical inference.

3. I do not wish to get too personal, but from you have written it is clear that you do not know basic, elementary statistics and yet you claim to be a "statistical analyst".

4. It appears that your conclusions are based on a sample of six and you have not used any statistical inference to reach your conclusions.

I used maximum likelihood to figure out when to reset the losing streak, which is why I shuffled the deck after each hand to ensure an unbiased pool. The sample mean is of course the number of and values of the cards themselves, and is not an estimate. The estimate in this case was the sample variance like you said. I used this equation to determine maximum likelihood, only after I had proved it in principle to myself first. I chose not to use average log-likelihood and opted for the equation below, which is more geared towards statistic probabilities (statistics I had already gathered in my principle-proving session)

...............................................n..........
L(0|x1,...,xn)=f(x1,x2,...,xn|0)= II f(xi|0). (I apologize for my lack of accurate characters but you get the equation)
..............................................i+1.........


If it appears there is no statistical inference, it's because the average blackjack player doesn't need to know all this and I don't really want to type it out. I don't feel the need to prove my understanding of statistics to anyone by confusing them into submission. This is a forum, not a classroom, and egos don't belong in mathematics. We're dorks.

Quote: Thunk

I intend to prove to you, however, that by tweaking the strategy a bit, the "optimum martingale" as I call it can be used to mask card-counting detectors employed by the casinos.


I found that, beyond a shadow of a doubt, reseting(sic) your bet to the original low was most effective when you reset after a three-hand losing streak.

Just show the proof, if you have one.

I just reread the original post. The poster just went through over a 1000 hands playing the martingale, and then figured out with the SMALL sample size, what would have been the optimal reset point. Explicitly leaving out counting.

Um... 1st) you can't go through past results and prove that a useless strategy is optimized by setting a certain parameter. a) that's not how you prove things. b) The martingale is ultimately useless regardless of your reset point.

2nd) how did you make the leap to counting? How does martingale + counting = money? Your 'experiment' specifically left out counting!

Quote: dwheatley

I just reread the original post. The poster just went through over a 1000 hands playing the martingale, and then figured out with the SMALL sample size, what would have been the optimal reset point. Explicitly leaving out counting.

Um... 1st) you can't go through past results and prove that a useless strategy is optimized by setting a certain parameter. a) that's not how you prove things. b) The martingale is ultimately useless regardless of your reset point.

2nd) how did you make the leap to counting? How does martingale + counting = money? Your 'experiment' specifically left out counting!

I agree about the total lack of any actual proof at all, but I'm kind of intrigued by the premise. I think a 1-8 unit martingale would be a fairly effective way to mask a 16 or 32 unit jump bet when counting.

Betting systems are all equally worthless, unless of course you have the advantage.

It's not your martingale that's making you win, it's the counting. Any simulation or real hands played w/ the martingale that shows a profit on a -EV game simply means it's not a large enough sample size. Placing -EV bets results in a loss no matter what betting system you use (unless you're martingaling with no table limits and an infinite bankroll)

You're just using the "betting system" as cover for increasing your bets, which isn't a bad idea.

Nothing like doubling your bets if you're losing as the count's skyrocketing. When you finally win, if the pit boss is around, breathe a deep sigh of relief and say something like "good old martingale, never fails!" and maybe start talking about all the money you win at roulette doing it :D

I just reread the original post. The poster just went through over a 1000 hands playing the martingale, and then figured out with the SMALL sample size, what would have been the optimal reset point. Explicitly leaving out counting.

Um... 1st) you can't go through past results and prove that a useless strategy is optimized by setting a certain parameter. a) that's not how you prove things. b) The martingale is ultimately useless regardless of your reset point.

2nd) how did you make the leap to counting? How does martingale + counting = money? Your 'experiment' specifically left out counting!
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Surely, you did not read the post. I go into great detail about when to employ counting, and the answer is constantly. You keep a running total of the count without adjusting your bet to the count. That is how you set the card-counting detectors off, if you play like a computer. You will, however, let the count effect your gameplay. Only when the count is extremely high or low will you let it effect your betting, i.e. continuing to double after a win (no reset), doubling past three loses if the count justifies it, or halving your bets per hand when the count is incredibly low. (this is tricky because you need experience to know when to actually let the count effect your bet)

Other than that, the only goal of my experiment was to optimize the martingale system as an undercount. I cannot test two variables in the same experiment, let alone three (those three variables being optimum reset, when to employ counting per gameplay, and when to employ counting per betting). I mean, do I really have to run yet another test on how much card counting improves your game? I aimed to eliminate play most counters employ in order to separate myself from most counters, and I do so by gearing count information towards cardplay in a low-risk environment, and sparsely gearing count information towards the bet on the table.

Um... 1st) How else am I supposed to prove the optimum reset point without reseting parameters from past results. a) You can't complain about a theory until you read it with an open mind. b) That's not how you get taken seriously. c) the martingale is useless, as I discussed in the first sentence.

2nd) I'm not looking to write a book, I'm looking to optimize an undercount that isn't completely pedestrian.

f2d understands.

"You're just using the "betting system" as cover for increasing your bets, which isn't a bad idea."

Most card counters flat-bet until the count is high or low enough to make an impact, some have a continuously exponential or linear relationship with the count or their bet. I have neither :)

Quote: Thunk

f2d understands.

"You're just using the "betting system" as cover for increasing your bets, which isn't a bad idea."

Most card counters flat-bet until the count is high or low enough to make an impact, some have a continuously exponential or linear relationship with the count or their bet. I have neither :)

What exactly does your betting look like? Does the Martingale pattern hold most of the time? Or does the count disrupt the Martingale enough that your bets appear random?

Quote: rdw4potus

What exactly does your betting look like? Does the Martingale pattern hold most of the time? Or does the count disrupt the Martingale enough that your bets appear random?

He says he'll martingale up to 4 units (3 times = 1, 2, 4) if the count's even or negative, and unlimited if the count's positive.

This way he just looks like another idiot trying a dumb betting system instead of a counter.

While betting this way surely isn't optimal for RoR, it may actually have a larger overall EV if it allows you to spread say, 1 - 20 instead of 1 - 8

I think a willingness to act a little would help the situation a good bit. What youd do is play "scared" to bet more than 4 or 8 units in the martingale when the count is negative, then "get the guts" to bet big and "pay yourself back" when the count is high.

I still reject the premise that 1000 is enough trials to prove a theory, but I think there might be some promise here to deflect attention from card counting. Especially in a big corporate casino where it can all be done on one table. Where I run into trouble is that around here, limits are $5 to $200 or $25 to $500. I'd need to go find a $5-$1000 (closest is in northern IA) or $25-$10k (closest is in northern IN) table to really make it work. Oh, and I'd need to find $10k, too...:-)

Quote: rdw4potus

I think a willingness to act a little would help the situation a good bit. What youd do is play "scared" to bet more than 4 or 8 units in the martingale when the count is negative, then "get the guts" to bet big and "pay yourself back" when the count is high.

I still reject the premise that 1000 is enough trials to prove a theory, but I think there might be some promise here to deflect attention from card counting. Especially in a big corporate casino where it can all be done on one table. Where I run into trouble is that around here, limits are $5 to $200 or $25 to $500. I'd need to go find a $5-$1000 (closest is in northern IA) or $25-$10k (closest is in northern IN) table to really make it work. Oh, and I'd need to find $10k, too...:-)

It'll also help if you buy in for EXACTLY like 6 bets or something.

Example:

Your smallest bet is 25

Buy in for 1575 and stack your chips in front of you in the following stacks:

25
50
100
200
400
800

I dont think anything could possibly scream sucker louder then that.

Plus if/when you actually USE those 400 or 800 bets (which would be a whopping 32-1 spread) it'll draw a lot less heat if it's prestacked since the pit boss knows you'll be doing it sooner or later. You won't be the first person to try martingaling at the blackjack table. Im sure plenty of people have done this and busted out in short order.

Sheeesh, so much wrong with this:

If a counter; the double small martingale vs. the advantage martingale cuts into a rather thin top possible advantage of roughly 2%. Any computer system is rather easy to decipher and works like this: total bet x advantage, vs. total bet x disadvantage.. no system will ever miss this and IF it does.. DUH you didnt play with an edge to begin with!!! Cant count in one sitting the total number of wannabe advantage players who thought they could beat the game but didnt understand the first step in true advantage play.... instead they sat there gambling it up at a disadvantage thinking they were the smartest player on the planet and laughing it up when promo chips were sent their way instead of comps blaming variance on their 200 max bet downswings.

Now, for clarity, a martingale is a good cover play, it cuts into your overall advantage (which as a card counter is unbelievably thin)the card counters usual maximum advantage is the equivalent to QQ vs. AK in poker, which is deemed a "coin flip". So now instead of the previously planned 2% advantage we are more likely facing a 0.75% advantage and wondering why our Risk Of Ruin numbers were so skewed? If you bet an aggregate total of $1k in the negative and $10k in the positive even the "special" kid taking your order at McDonald's will spot it, nevermind a computer designed for that sole specific purpose.

There are plenty of viable materials to study on this exact scheme as well as similar ones.. I suggest: Blackjack attack by Schlessinger, Burning the Tables In Las Vegas and then Beyond Counting Exhibit CAA which debunks it all.. there flat out is no easy way to sit back and play an advantage game heat free while raking in the cash, instead it is an artform of balancing on a razors edge knowing all the while the welcome mat for you has a time limit....

Like f2d says. The only time I will ever bet more than four times my lowest common bet is if the count is very high and I am still winning, although... you really pocket the cash when you opt to simply let it ride if the count is still high. Or even reset when you're comfortable with the amount I've taken in during that heater. Knowing when to do that has been imperitive to my success, and not doing it effectively can crush you. Conversely, if the count is very low, I might not double my bet even if I continue to lose. I'll just flat-bet until the count evens out. This is tricky though because if you make it too obvious, it blows your cover.

Another thing to consider.. if spreading 1-4 in negatives you have an average negative bet of roughly 2.3 units.. a 1-8 no longer cuts it in gaining an edge. Your new unit it 2.5 as 1 and 15 as six...