The Martingale: Progression to Depression
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:
1) You bet $10, and lost.
2) You bet $20, and lost.
3) You bet $40, and lost.
4) You bet $80, and lost.
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!
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. 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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