There are exactly two ways to have an advantage in blackjack. First, you can play a game with ultra-favorable rules. An example would be a game with 2:1 payouts for naturals, the option to triple-down, and early surrender. Sounds fab… but in the real world, blackjack rules like that doesn’t exist, except occasionally as weird promotions that last a millisecond. The second way to get an advantage is to count cards and raise your bets as the deck becomes more likely to deliver favorable hands.

That’s it. Unless you have a Harry Potter magic wand, all other betting systems are worthless because they can’t give you an edge. Typically, these other systems "work" by raising and lowering bets based on previous wins and losses (if x happens then bet y). Since past results have no effect on the future, the systems are not predictive. They raise bets arbitrarily. Worthless! Nevertheless, the schemes are tempting because they’re easy to follow and they do win most of the time. The downside is that, occasionally, you lose a lot… sometimes scary-big amounts. So counting cards is better.

Advantage players, when they’re learning to count, are consistently and sternly warned by mentors to stay away from gambling systems. The implication is that only fools use them, except as methods of camouflage to make yourself look like a fool to casino employees.

However, let’s be realistic. Some games are uncountable. Moreover, not everyone counts cards. Unless you play only beatable games, and never ever wager anything other than a profitable situation, is there harm in using a gambling system when playing for pleasure and not counting?

It turns out the answer is… gambling systems are ok. They’re benign when used responsibly. Mathematically, they’re no better or worse than flat betting. Really. For example…

It’s the granddaddy of all gambling systems. The martingale is one of the cool math tricks of the universe. In any series of bets that pay 1:1, if you double up after losing a bet (1, 2, 4, 8, and so forth), then one win anywhere in the series wipes out all previous losses. Plus it nets one unit, the value of the base bet.

Consider this sequence of bets starting at $10: lose-lose-win. The results are -$10, -$20, and +$40. The net profit is $10. Pretty nifty, huh? It works with any pattern of losses and wins. Any pattern! The adjacent chart shows how the system progresses when it’s carried to five levels.

Nobody knows who discovered the martingale, but the first person to write about it was Giacomo Casanova. Yes, that Casanova. He was a famous lothario who gambled and slept his way across Europe in the eighteenth century. We know about his gambling exploits because he meticulously recorded everything in his autobiography, The Story of My Life.

Casanova used the martingale in 1754 to win (and later lose) a small fortune. He wrote:

Casanova was playing faro, but the martingale can be used with any game that has 1:1 payoffs, such as baccarat, roulette, pai gow poker, and blackjack.

Notice that Casanova mentioned luck in his winning streak. The martingale is hardly a sure bet. If you lose five consecutive decisions, then you’re down $310 (though your net loss probably will be less, depending on your previous winnings). What’s the probability of losing five consecutive decisions? In blackjack, it’s about 4.4%, not including ties. In other words, 95.6% of trials win $10 (not including extra money for naturals, doubles, and splits) during a series of decisions that stretch from one to five hands. The other 4.4% of cycles lose five consecutive hands and lose $310 (not including doubles and splits).

When all the winning and losing is put together over time, guess what… The house edge is unchanged! No difference! The system does change your average bet, but the net effect depends on what your average bet was prior to using the system. In the above example, if the average bet was $40 prior to using the system, and the casino has an advantage, then the martingale will actually save you money!

To be very clear, I’m not promoting the martingale or any gambling system. Rather, I’m saying that betting schemes can be harmless fun when a player isn’t counting. They’re ok, a pleasant distraction, like chewing gum.

The danger comes when someone follows a gambling system beyond the limits of his bankroll. For example, the system presented above tells you to stop if you lose five straight. Start again at bet #1 or walk away. Going further, playing an open-ended martingale to stratospheric levels, is an invitation for disaster.

About 51% of players will finish 15 five-limit cycles (approximately 30 hands) with an absolute profit of $150. The other 49% will lose anywhere from $310 to $170. Compare this to flat betting $30, which is approximately the average bet for this system. Only about 9% of flat-bet players will be ahead by more than $150 after 30 hands. On the other hand, only about 11% will lose $300 or more. About 19% will be up from $60 to $120. Another 13% will break even, and 48% will be down about $60 to $240 (not including naturals, splits, and doubles).

So, the martingale squeezes everything to the extremes. Hardly anyone breaks even or loses just a little bit. You either win a lot or lose a lot. Hey, it’s gambling!

Counting is preferable. However, if you can’t count, then raising and lowering your bet for other reasons, just to have fun, is in my opinion perfectly okay.

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(c) copyright 2012 Basil Nestor