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From time to time every blackjack expert gets asked the question "What are the odds of me losing X number of hands in a row at the blackjack tables?" And it's one that causes a great deal of frustration because it's not about odds and more about probability and leaves out the important answer of how the person posing it plays the game.
It also generally means that the player in question is planning on using the infamous Martingale betting system or some other negative progression betting system they've found online.
For those not familiar with the Martingale betting system, in essence it is a strategy where you double your wager after losing any hand in order to recoup your losses in those that follow until you win. At which point you will supposedly have recovered all that you have lost and earned a profit equal to your original wager.
The literature on the Martingale system makes it sound like a reliable strategy, and in practice it may even seem to work well, that is until it doesn't. The main flaw in this approach is that the majority of players underestimate how likely the chances of encountering losing streaks really is. Of course, as the number of losses increases, the probability of them occurring decreases, but the probabilities are not small enough to make them inconsequential.
While the Martingale system does give you a high percentage chance of winning a relatively small amount (ie. the equivalent to the value of your original wager), it does require a huge amount of luck. For any blackjack player that should be the end of contemplating using it, because after all, we play blackjack because it is a game of skill that can be played strategically to increase our odds of winning, as opposed to a random, chance based game that is ultimately determined by luck.
If we look at a practical example, let's consider a player who wagers $10 per hand in a standard game of blackjack. If he/she needs to be able to "carry" up to 7 consecutive losing hands while employing the Martingale betting strategy, doubling after every loss, he/she will require a bankroll of $2550 and be willing to wager $1280 on the eighth hand to win just $10.
If it doesn't seem ludicrous enough to you already, consider that a loss on the eighth hand occurs on average, once in every 170 hands. Again, all of this to be up by a mere $10.
Blackjack is also by far the worst game to play according to the Martingale system due to the fact that it often involves splits and doubles, occasionally on the same hand, which increase the size of your wager and mean that you will need a considerably larger bankroll than mentioned above if you are going to play according to sound basic blackjack strategy.
If you elect to ignore basic strategy on doubles and splits then the bankroll mentioned above will be adequate but you will incur a significantly higher loss rate on all of your wagers.
The same outcomes are applicable to any other progressive betting systems in blackjack - all of which are doomed to fail. If you are serious about playing blackjack for profit, then do so at land based casinos and learn to count cards. If you are just playing for fun, you'll make more money simply flat betting and you'll require a significantly smaller bankroll.
So if Martingale is crossing your mind as a blackjack player - think again. You will lose more than you win.