As I mentioned in a previous column, the martingale is a negative-progression gambling system (it raises bets after losses), and it is typically used when bets pay 1:1, as in roulette, baccarat, or craps. The player bets one unit after every win, and doubles the bet after every loss…two, four, eight, sixteen, until a win. The result is always a one-unit profit, assuming the series ends with a win.
Clearly, you've discovered that the martingale works very well when a table is choppy. For example, if you could guarantee no more than four losses in a row...ever, then a bankroll of 31 units always would be sufficient, and you could earn a steady income playing roulette, baccarat, craps, or most other casino gambling games. If you rarely or never "hit the wall," the martingale is almost always more profitable than flat betting. Let's say you have four losses followed by four wins:
-10 -10 -10 -10 +10 +10 +10 +10 = 0
-10 -20 -40 -80 +160 +10 +10 +10 = 40
Flat-betting $10 wins nothing. The martingale wins $40 on the same sequence. Very nice, but remember that the flat bettor wagers $80, and the martingale bettor wagers $340. The extra action may not seem risky when we know that the fifth decision will be a win, but unfortunately, that advance knowledge is not available to us in a casino. We simply cannot say how long a streak will last. Five, seven or even ten consecutive losses are relatively common.
What about limiting the progression (as you did) to a particular number of steps? Won't that solve the problem? Yes, it will save you some money if the table produces a long series of losses, but it also increases the chance that you'll quickly hit the loss-limit and be forced to start from scratch. For example, you have about an 83% chance of losing five consecutive times in a typical hour of gambling (depending on the game), but only about a 35% chance of experiencing seven consecutive losses. Either way, it's always more likely that you will hit the limit before you win enough to recoup a loss. Remember, one loss at level five requires 31 wins to recover...unless you push to level six. That's always a dangerous temptation.
And don't get me started on table limits.
But you won money!
Hey, this is gambling, and luck happens. Maybe you gambled for four hours and hit the five-loss limit only once or twice. This occurs about 3% of the time (depending on the game). It's not too amazing. Then again 97% of players aren't so fortunate.
Besides, if we could predict streaks like the ones above, then the martingale would not be the best gambling system. Rather, a positive progression (raising the bet after wins) would be preferable. Using the exact same sequence of four losses and then four wins, a simple 1-2-3 positive progression yields a $60 profit. It works like this:
Positive 1-2-3 progression
-10 -10 -10 -10 +10 +20 +30 +40 = 60
The above progression raises the bet by one unit after each win and returns to the base unit after each loss. Total action is $140. Again, very nice when we know in advance how the decisions will come. But in the real world we cannot predict the future with accuracy. Unfortunately, positive and negative progressions aren't at all "predictive." They don't help us to make better choices, they simply raise the average bet. For example, I can scramble the order of the above sequence...
bet 40, bet 10, bet 10, bet 30, bet 20, bet 10, bet, 10, bet 10
...and if the cards or wheel oblige me, it's entirely possible that I can still win $60. Four consecutive wins and four losses are as likely as eight alternating wins and losses, or any other possible combination of four and four. And who can say that it will be exactly four and four? I could lose them all or win them all.
Keep in mind that raising bets after wins (or losses) isn't necessarily a bad thing or a mistake. A bet is a bet. It's just more money on the table. However, it IS a mistake to believe that a particular bet is more likely to win simply because it is further down the line in an arbitrary system. And overbetting a bankroll to follow a progression is potentially a catastrophic mistake.
Remember, the last decision does not affect the next one. Four, five, or ten consecutive losses does not mean that a win is "due." Indeed, in most casino games, the probability is always greater that you'll have another loss rather than a win.
Thus the problem with the martingale is that tables are not always choppy. Sometimes we see streaks. Conversely, the problem with positive progressions is that sometimes tables are choppy. Here's a lose-win-lose-win-lose sequence that demonstrates how positive progressions sometimes fail:
-10 +20 -10 +20 -10 +20 = 30
Positive 1-2-3 progression
-10 +10 -20 +10 -20 +10 = -20
And this takes us right back to the classic yin-yang gambling choice... What's going to happen next? I have a friend who says, "You tell me how the dice will roll, and I'll tell you the best system to use."
Some people will advise you to "follow the shoe," or "follow the wheel" and thus "hook into a trend," but streaks come and go. There is really no practical way to predict or prevent a long string of losses in games like roulette, craps, blackjack, or baccarat. That's why we call it gambling.
The gambling gods smiled on you during your last session, and I applaud your good fortune. But it would be unrealistic for you to expect the martingale (or any progression) to steadily generate profits day in and day out. In fact, the martingale will inevitably consume your recent windfall if you continue using the system.
I apologize if this makes me sound like the "voice of doom." On the contrary, consistent winning and long-term profits can be achieved when playing gambling games. But progressions are not the way to go. Instead, we must change the odds and bet with an advantage. That's how casinos earn their money, and that's how players can win, too.
Enjoy the game!
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