Why systems fail

A reader who picked up on something I'd written about the Martingale wagering system e-mailed for a little clarification.

"You said that the Martingale runs up against maximum bets," he wrote. "Does that mean a system that doesn't rely on increasing wagers can work?

"What if I'm playing craps? A 12 should come up once per 36 rolls, right? So what if I've counted 18 or so rolls without a 12? On the average, it'll show up sometime in the next 18, right? I understand that it's not going to work every time, but with 30-1 payoffs, you have to have an edge, right?"

Wrong.

It's a common enough misconception that long streaks have to end soon, that the streaks somehow change the odds of the game. They don't.

A craps shooter has a 1 in 36 chance of rolling a 12 on every roll. Whether he's gone one, two, 18, 30 or 100 rolls in a row without rolling a 12, he still has a 1 in 36 chance of a 12 turning up on the next roll.

If you start betting on 12 after 18 rolls without the dice landing on those double-sixes, the house still has its 13.89% edge. The system described will lose money in the long run.

The bigger point is that nearly all systems fail because they don't change the odds of the game. My e-mailer mentioned the Martingale, in which bettors double their bets after each loss in the expectation that a win will wipe out all losses and leave a profit equal to the original bet.

On a table with a $5 minimum, that can mean bets of $5, $10, $20, $40, $80, $160, $320 and so on. If the maximum bet at the table is $500, a seven-loss streak would mean the player can't make the $640 wager called for by the Martingale system.

Even if there was no table maximum, having already lost $635, I wouldn't want to have an additional $640 at risk for a chance to show a $5 profit, would you? Especially since you know that a loss on the next play is no more and no less likely if you've lost seven times in a row than if you were starting fresh.

Whether you're playing craps, roulette, baccarat or just about any other game, systems don't work because they can't change the odds of the game. You're still at a disadvantage on every bet.

The exceptions come in games where the odds do change. Card counting works in blackjack because the odds of the game change as cards are removed from the deck, leaving the opportunity to bet big when the odds favor the player and small when they favor the house. Dice control works at craps for the few skilled enough to do it because they can depress the frequency of loser sevens and increase the frequency of winning rolls, thereby changing the odds of the game.

But mere betting schemes don't change the odds. Counting trials between wins doesn't change the odds. The house retains its mathematical edge no matter how much money you have on the table. And that's why systems fail.

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I'm sometimes asked if other card games are like blackjack, with odds changing with every card dealt. As a woman at a seminar once put it, "I can see why odds don't change at roulette or craps (except for dice controllers). But what about baccarat or Caribbean Stud?"

Most casino card games, including Caribbean Stud, Let It Ride and Three Card Poker, are dealt from a freshly shuffled deck on every hand. With a new shuffle, any potential for the odds to change from hand to hand is eliminated. You can't count cards and adjust bets accordingly.

The exception is baccarat, which is usually dealt from an eight-deck shoe. As cards are dealt out, the odds DO change, just not enough to help us.

Game analysts and mathematicians worked on baccarat, just as they worked on blackjack, trying to develop a workable system for counting cards. Nothing turned out to be practical. The late Peter Griffin wrote in The Theory of Blackjack that a baccarat player who doesn't bet unless he has an advantage can squeeze an edge of about 0.7% of his maximum bets on banker and player. However, that player might play only about three hands per eight hours. That's watching, not playing.

For bets on ties, it's theoretically possible to count down to a 24% edge with six cards remaining, provided all the cards are dealt out. Problem is that no casino actually deals out all the cards, and with one-half deck cut out of play, the bettor's potential edge on the last hand shrinks to just .08%.

And that's the LAST hand, meaning you're watching all the way to the end of an eight-deck shoe, dealt out two hands at a time, for a potential one-hand edge of less than a tenth of a percent.

The odds may not be as unchanging in baccarat as they are in other non-blackjack table games, but it's close enough.