The Martingale: Progression to Depression
Aug 30, 2019 It’s just a more fun experience and maybe a system will help you enjoy blackjack games even more. Martingale – The Martingale is a regressive betting system. What you do is double your bet after each loss. For example, if you made a $5 bet and lose, your next bet would be $10. Lose that one and your next bet would be $20.
By Arnold Snyder(From Card Player, April 1995)
© 1995 Arnold Snyder
(Note from Arnold Snyder: To learn how to win at blackjack over the long run, with or without card counting, start with our Intro to Winning Blackjack.)
Question from a Reader regarding the Martingale Betting System: I lost a substantial amount of my savings playing blackjack at [casino name deleted] in Atlantic City — almost $30,000. I admit that I was using a progressive betting system — a straight martingale, and I know that won’t give me any advantage — but even so, I feel pretty certain that I was cheated.
I was winning steadily for quite a few hours using this betting system (a simple double-up after a loss), then in a short series of hands that lasted only about 30 minutes — they totally cleaned me out. I was playing perfect basic strategy.
I have enclosed a chart which shows the series of bets I made, and the win/loss results that eventually bankrupted me. I would like to know your expert opinion on whether or not this could have happened in an honest game.
Can I take any kind of legal action against the casino if this series of hands is indicative of cheating? I have a friend who witnessed the debacle who can attest to the truth of what happened.
Answer: I have studied your results, and although anyone would acknowledge that you suffered an unusually unlucky series of hands — and an especially devastatingly unlucky series for any martingale player — the series of hands in and of itself would not be indicative of cheating. I highly doubt you were cheated.
The straight martingale is one of the riskiest betting systems any gambler could use. Any gambler who ever has used it with any regularity could tell you his own hair-raising “impossibly unlucky” tale of why he gave it up for more conservative betting methods.
Here is what happened to you: Cruise ship casino slot odds.
1) You bet $10, and lost.
2) You bet $20, and lost.
3) You bet $40, and lost.
4) You bet $80, and lost. Leaf green slot machine odds.
5) You bet $160, and doubled down on your 11 vs. the dealer 8, and you lost.
6) This double loss required you to place a next bet of $480, which you then lost.
7) You placed a bet of $960, and split your 8s vs. a dealer 10, and you lost both hands.
8) This double loss required you to place a bet of $2880, which was higher than the $2000 table max. So you bet the max, and lost.
9) On your next hand, you bet the max again, and insured your 20 vs. the dealer ace. You lost both the insurance bet, and your hand when the dealer hit to 21. This put you behind by a total of $7880.
10) You then bet the max, and pushed.
11) You then bet the max and won!
Blackjack Double Bet When Losing
You say that the above series of results took about 10 minutes, and that you do not recall the exact series of wins and losses in the approximately two dozen hands that you played over the next 20 minutes. You note there were a few wins interspersed with the mostly losses, but you had to have had 12 more max bet losses than wins (perhaps 18 losses and 6 wins?), as you left the table a $29,980 loser.
How “impossible” is this?
Unfortunately, not very.
You must realize that you were required to start placing max bets after only 7 consecutive losses. Once you are actually placing $2000 bets, a loss of $30,000 is not at all unusual. This would be equivalent to a $5 bettor losing $75 — which any experienced $5 bettor could tell you would not be uncommon. If you count your double loss on your split pair as two hands, you actually began your unfortunate series of losses by losing 10 hands in a row. How unusual is this?
If I were flipping a coin, with heads being a win, and tails a loss, the odds against me coming up tails 10 times in a row would be about 1000-to-1. That’s pretty unlikely, though far from impossible.
Blackjack, however, is less advantageous than a coin flip. In 100 hands, a basic strategy player will experience, on average, 43 wins, 48 losses and 9 pushes. Since a martingale bettor ignores pushes and lets his bet ride, we can ignore them in our analysis. For every 100 win/loss decisions, a basic strategy player will see about 53 losses and 47 wins.
With these win/loss proportions, the odds against losing 10 consecutive decisions are only about 500-to-1. Now 500-to-1 may seem nearly impossible to many people, but realistically, at any given time, a series of losses equivalent to yours is happening to dozens of players in Atlantic City, and to hundreds of people every day of the year in U.S. casinos. It’s happening right now to one out of every 500 people who are playing. How many tens of thousands of people are playing blackjack right now in U.S. casinos?
You must realize that if you had been flat-betting $10, instead of “doubling-up” to try to recapture your previous losses, you would only have lost $110 (and this includes both your pair split and your double down loss!), instead of being behind by $7,880 at the end of that first unfortunate string of losses. Dragon lord slot machine download. And your total loss at the end of the debacle would only have been $230, not $29,980.
The martingale is a systematic method of chasing your losses. There’s no other way to describe it. This is about the most foolish way to gamble. You violated the single most important rule for gamblers: If you can’t afford to lose it, don’t bet it. ♠
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I had a look at the web site and also found what little he says about the theory behind his system makes it sound like card counting. However I'm deeply skeptical of anything that claims to 'blow old fashioned card counting away.' I think we can file this under 'If it sounds too good to be true is probably is.'
Update: The web site in question vanished sometime after the publication of this question.
I don't put a lot of emphasis on betting systems. In the long run you will lose the same percentage of money bet no matter what system you use. So my advice is use a system that maximizes the fun of the game.
The simple answer is no, it neither helps you nor hurts you. However, you will have less bankroll variance by betting two hands of x as opposed to one of 2x. Card counters are an exception to the simple no, they may play multiple hands to draw more cards out of a deck rich in good cards, thus improving their odds.
Second question, does the number of hits one takes effect the outcome? For example, if I have five cards that total 15 against a dealer's 10, am I pressing my luck by taking a sixth card? In other words, are the odds of busting on a 5-card 15 the same as busting on a 2-card 15?
Thank for the compliment and I'm happy to help your bankroll last longer. When I gamble for fun I keep playing until it isn't fun any longer. Usually the fun ends when I have lost too much or have played too long. With the ups and downs of blackjack it takes hundreds of hours before regression toward the mean will cause actual results to look like expected results. Furthermore, the player who puts a conservative cap on their winnings is never going to experience the fun of a long hot winning streak. Keep in mind this is just what works for me. You should do what you are comfortable with. Everything I have to say about money management can be summarized by the following two rules (1) don't gamble with money you can't afford to lose, and (2) don't gamble if it isn't fun.
Regarding your second question, there is something to be said about the composition of a hand. The fewer the decks the more this is true. My blackjack appendix 3A and appendix 3B show the exceptions to single- and double-deck blackjack, based on the composition of the hand. These appendices show that the more cards that are in your hand the more inclined you should be to stand. Regarding your 15 against a 10 example, there are two situations in single deck blackjack where you should stand when the 15 is composed of 5 cards, A+A+A+6+6 and A+A+3+5+5. Note that in both of these situations either two fives or two sixes have left the deck which are the two most helpful cards for the player. The two situations where you should be the most inclined to stand if you have a multiple card hand are 16 against a 10 and a 12 against a 3.
I have said numerous times that there is no long-term way to beat a game with a house edge. If there were a true 50/50 game with no house edge it would be impossible to guarantee beating or losing to it under real world conditions. The results always approach the house edge in the long-term. It is not just computer simulations that back this up but the fundamental laws of probability.
About video blackjack, that may be the way of the future. I have seen fully electronic tables with video display at the World Gaming Expo. I have also seen tables that with cameras can track every bet and every play each player makes. This enables the house to accurately comp players and alert them to card counters. These tables look and feel like any other blackjack table, so you card counters may be out of business if these tables are successful.
I’m not familiar with it. Ken Fuchs co-wrote Knock-Out Blackjack so he can’t be all bad. However I just hear the word progression and I’m immediately skeptical.
Progressive betting systems, like yours, will turn a good session into a great one without the risk of catastrophic loss as with regressive systems like the Martingale. However progressive systems will turn a choppy neutral session into a bad one. Consider what would happen if you alternated between a win and a loss the entire session. The wins would all be at $15 and the losses at $30. Funny you should mention the ’Weakest Link.’ I tried out for that show during the summer and didn’t make it. It is probably just as well because I’m not that witty in real life and doubt I could come up with a good rejoinder to one of Ann’s jabs.
The name for this system is the Martingale. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is .52518 = 1 in 173.
If you can’t double or split that adds 1.9% to whatever the house edge is otherwise. This just goes to show that you should always have double or split money available if you need it.
I’ve been playing blackjack for quite awhile using basic strategy, mostly betting an even unit each hand. Occasionally I will increase the bet because I 'feel' like I am going to win the next one. I would think that just about all recreational players bet on feel once in a while at least. I was reading through some of your past Ask the Wizard columns and saw your calculation of the probability of a string of losses in the August 4, 2002 Column. You know those emotional thoughts that pop in head while gambling (well maybe not your head), 'I’m due for a win!'Blackjack Bet Spread
That column seemed to put the mathematics to that 'feeling' a player can get. In that columns’ example of a player losing 8 consecutive hands of blackjack the odds were (.5251^8 or about 1 in 173). My question though is what does that really mean? Is it that when I sit down at the table, 1 out of my next 173 playing sessions I can expect to have an 8 hand losing streak? Or does it mean that on any given loss it is a 1 in 173 chance that it was the first of 8 losses coming my way?
I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. I’m still curious though. Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if you have lost a string of hands you are 'due' for a win.
I have no problem with increasing your bet when you get a lucky feeling. What is important is that you play your cards right. Unless you are counting cards you have the free will to bet as much as you want. As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good as flat betting over the long term. When I said the probability of losing 8 hands in a row is 1 in 173 I meant that starting with the next hand the probability of losing 8 in a row is 1 in 173. The chances of 8 losses in a row over a session are greater the longer the session. I hope this answers your question.
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Blackjack tournaments are not my strong subject. For advice on that I would highly recommend Casino Tournament Strategy by Stanford Wong. Wong says that if you are behind to bet opposite of the leader, small when he bets big, and big when he bets small. If you are in the lead then you should bet with the second highest player. The book gets into much more detail. Speaking of supporting my site, it helps to click through my Amazon links when buying books there.
Your expected loss of this play is 0.005*20*$1000=$100. The betting system will not affect the expected loss, but will affect the volatility.
Without knowing anything else, if you lost the last hand in blackjack then it is slightly more likely that more small cards than large just left the deck. This would make the remaining deck more large card rich and thus lower the house edge. However I speculate this is an extremely small effect. Yet it does go to show that if you must use a betting system one that increases the bet after a loss is better than one that increases after a win. I hesitate to put this in writing at all because again the effect is probably very small and I fear system sellers will misquote me and imply I endorse any system, which I DO NOT.
You didn’t say how many rounds there were. However, I would bet $10 in all five hands every hand, or go bust trying. With 1,000 players and a relatively low max bet you’ll need all the variance you can get.
I’ve been wondering this myself for years. In 2004 somebody accepted my betting system challenge, claiming he could beat blackjack without counting. The details are in my page on the Daniel Rainsong challenge. After I posted it, I received a message from a blackjack genius, who goes by the handle 'Cacarulo.' He challenged me under the same conditions and blackjack rules set forth in the Rainsong challenge.
Knowing how knowledgeable he is about blackjack, I felt that he was probably right, so I declined the challenge. I asked anyway how he would have gone about his strategy, but he wouldn’t tell me. I tend to think that he would have bet the minimum most of the time, except if it was late in the shoe, and the ratio of losses to wins was very high since the last shuffle, he would have bet the maximum. The reason is that losing is positively correlated to small cards being played, and winning to large cards. In other words, a benefit of losing is that it tends to make the count better. However, this is a weak correlation. My challenge allowed the player a bet range of 1 to 1,000, which is probably enough to overcome the house edge, but it will be hard to find a real casino okay with a jump in bet size by a factor of 1,000.
The short answer to your question is, no, tracking wins and losses will not help enough to warrant the bother of doing it.