“But that can’t possibly happen,” you say, “because the probability of winning on an even-money prop is 47 percent!”—And believe us, man, we feel you.
But as we explained in Section IV, probability is hellova complex. For instance, it is relatively probable that a long string of losses will occur—which we know because we can calculate the likelihood of it happening by multiplying the probabilities for all the events together. So, going back to our even-money bet, all we have to do to find the probability of a two-loss streak is multiply 20/38 by 20/38. The two twenties equal 400, and the two thirty-eights equal 1444, so the fractional probability is 400/1444. Now, if we simplify that by dividing 1444 by 400, we find that the probability of a double loss is 1/3.61 or about once every four spins.
Really, deciding if you can play a system, then, is as easy as accounting for the amount of money you will probably lose and seeing if, over time, you can still come out ahead. No doubt, we don’t want you committing the “gambler’s fallacy” or falling into a “law of averages” pit trap, but it is a mathematical truth according to the “Law of Large Numbers” that, the more times a wheel is spun, the closer the average number for each occurrence will come to the ideal probability. Again, this doesn’t mean 10 spins or 100 spins. It means 1,000, 1 million, 1 billion spins over time.
Armed with this little bit of information, let’s go back to our example and see how it works out: For one thing, we know that Black is an even-money bet, and for an even-money bet, the probability of losing seven times in a row on an American wheel is 1/89 or once every 89 spins. As we mentioned in Section IV, there are about 105 spins per hour. So on a table with a $500 limit, you will probably lose $635 once every hour. Meanwhile, 105 spins aren’t nearly enough of a sample to get your average number of wins close to the ideal probability. And even if they were, each time you’d win, you’d only net $5 for 49 wins (i.e., a loss of about $400)!
Yet, this isn’t to say winning with the Martingale is entirely impossible. To get the odds in your favor, all you have to do is play a table with a 200-1 limit and “null bet.” Null betting—the practice of waiting out a couple spins until several consecutive losses have occurred—forces the house to produce an improbable string of losses over such a large number of spins that you can’t help but win. Also, because you aren’t actually betting anything on the first couple losses, null betting allows you to lose about the same number of times you would have for a more probable losing streak. In the case of our Black bet, probability states that it will have an 11-loss streak only once in about 1,164 spins. This is closing in on that large sampling we need to ensure that our ratio of wins to losses will average out to about what their ideal probability is. What’s more, we only need to wait out for three losses in a row, which happens every seven spins or so.
Over time, if we continue to wait until a three-loss streak occurs before betting, we should win more than we lose. Because the average number of spins per hour is 105, we can reasonably guestimate that an 11-streak will occur once in about eleven hours, with the house netting a total of $1,275. Meanwhile, because we’d be playing enough spins to get close to the ideal probability and because nothing but an 11-loss streak can hurt us, we’d rack up somewhere in the ball park of $2,500—that’s a profit of about $1,200, not counting the times you’ll lose only half your bet if you’re playing a wheel with Surrender.
So, yes, Virginia, you can use a Martingale to win, but probably not in the way you imagined. You can’t, after all, walk into a casino with a nickel and walk out a millionaire. That’s simply the stuff of fairy tales. In reality, you’ll need a large enough bankroll to hold you through that one big loss, plus play out the rest of a 1,164-spin series.
Finally, we can’t promise that you won’t have two or three—heck, even ten—eleven-loss streaks in one 1,164-spin session. Again probability is at best only a guestimate of what is likely to happen, not what will. The wheel itself has no clue that you’re playing it, let alone what numbers it should choose, and you can almost assuredly bet that you’ll eventually have a couple bad days. For this reason, we’re advising you to set a loss limit: if you reach 600 spins and are still in the hole by a 60 percent margin, scram.