The intent of a progressive betting system is to vary the size of your bets in a predetermined manner, according to whether or not the previous bet won or lost. With some progressive betting systems, you increase your bet following a losing hand (so-called negative betting progressions), while in others you increase your bet following a winning hand (positive betting progressions). In this article, I’ll focus on one of the most famous and widely used progressive betting systems, the Martingale, or double-up, system.

The Martingale betting system is easy to understand and use: you just double your bet after every loss until you finally win, at which point you will be ahead by one betting unit. For example, suppose you wager $10 and the results of the next three hands are loss, loss, and win (L-L-W). Using the Martingale system, you lost $10 on the first hand, $20 on the second hand, and won $40 on the third hand. You wind up with a net win of $10, which is the goal of the progression, to win an amount equal to your starting wager.

How can there be anything wrong with the logic of the Martingale? Just leave the table after a win and you always walk away with a profit. Right? Well, yes and no. Long streaks of consecutive losses will doom the Martingale player, but pundits will always counter with "the chance that this will happen is slim." Really? Let’s take a look.

(Note: The math involved in calculating the percentages of streaks is rather complex (e.g., in this instance, it involves 100 x 100 matrices). I’d like to thank the Wizard of Odds, Michael Shackelford, for providing the following percentages.)

You have about a 52 percent chance of losing a hand in blackjack (excluding ties). The chance that you will lose, say, ten consecutive (resolved) hands followed by a win is 0.069 percent, meaning you will average one sequence of ten losing hands (excluding ties) followed by a win in about every 1441 hands, and so, this losing streak will occur about once in roughly fourteen hours of play (assuming you play 100 resolved hands per hour). And get this ... you don’t know when that string of ten consecutive losses followed by a win will occur in the fourteen hours (of course, it may not occur at all). The math says that you have roughly a 3 percent chance of losing ten in a row in the first hour; a 6 percent in the first two hours; and a sixteen percent chance after five hours. Sadly for Martingale bettors, a streak of ten consecutive losses is not such a rare event after all.

What about all those frequent winning sessions that Martingale players (and system sellers) always tout about this system? The fact is this: although most players will walk away a small winner most of the time, the money you will lose in that one catastrophic losing session will more than completely wipe out all the money that you will win in your more frequent winning sessions. In the long run, your wins and losses will add up to the casino’s edge, and the amount of money that you will lose using the Martingale betting system will be close to the casino’s theoretical edge in the game times the total amount of money that you wagered, the same as it is for every other player who plays blackjack (except card counters). In other words, mathematically speaking, you can’t, and you won’t, gain the advantage over the casino using a Martingale betting system.

There is another more practical issue with the Martingale that also dooms most players who use it, and it’s this: on an extended losing streak, you may not be able to double-up your bets because you will bump up against the maximum betting limit imposed by casinos. For example, suppose you are a $5 bettor and you lose eight (resolved) hands in a row. Your losses at this point total $1,275 (gulp!). Assuming you have the bankroll (and the guts) to double up again, your next wager according to the Martingale is $1,280, which exceeds the $1,000 table-betting limit (that you’ll find in most casinos on low-limit tables). Unfortunately, there is no way for the progressive bettor to bet enough to recoup his losses when this occurs (other than to move to a higher-limit table).

What about betting progressions where you increase your bet following a win (known as positive progression systems, where you are hoping for a long streak of wins)? The bottom line on them is this: most of the time a player will wind up his playing session with a small loss, and rarely will he experience a big winning session. Just as in the negative betting progressions, the wins and losses in the long run will add up to the house edge.

If you remember anything,remember this absolute fact about the game of blackjack: the odds of winning any hand in blackjack are not dependent on whether you won or lost the previous hand (which is why betting progressives don’t work), but rather the odds of winning are dependent on the ratio of high cards to low cards in the unplayed cards (which is why card counting works).

(Note: My thanks to Donald Schlesinger for his help with some of the calculations in this article.)

In 1986, blackjack statistician John Gwynn published an article in Blackjack Forum that embarrassed many blackjack experts (including me) who argued that "progressive betting systems do not change the house edge." Gwynn conducted extensive computer simulation studies and discovered that certain situations, like losing a hand, will increase the player’s expectation of winning the next hand. Leon Dubey Jr., in fact, wrote a book about this and other situational advantage indicators. However, blackjack guru Arnold Snyder later showed that "no individual situational indicator is worth more than a few hundredths of a percent, and all of them combined are not worth more than a few tenths of a percent in a deeply dealt one-deck game with a big bet spread." However, you could earn $1-$2 per hour using situational indicators but here’s the catch: you’d have to make your small bets $5 and your high bets $100. There are two major issues with this: first, deeply dealt single-deck games have gone the way of the horse and buggy, and second, even if you found this game, using a $5 to $100 bet spread smacks of card counting and you would, most likely, be tossed out of the casino.