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Systems are great, when the games cooperate!

Jul 22, 2003 3:13 AM

It is amazing how many otherwise intelligent people, some of them even in the gaming industry, believe that money management systems can overcome house percentage.

And why is it, when they are about to explain the strengths of their system, they always tell how it was checked against a computer simulation or recorded rolls of the dice or spins of a roulette wheel.

That’s fine, as long as every dice or roulette table agrees to "follow the script" as laid out by its program or recorded results. Mathematics is the only true test of a betting system and you don’t have to have a PhD from M.I.T. to know that no matter how you add negative numbers together (the negative numbers in this case being the negative expectation of each bet made) the sum will always be another negative number.

A common misconception is based on what the layman calls "the law of averages," which is a way of saying "the doctrine of the maturity of chances." It is miss-interpretation of that law is what mathematicians call the "gambler’s fallacy" ”” that "the longer the time between events (such as the pass line winning or red showing on roulette) the greater the chance that it will happen." Gamblers seem to think that the fact that the last 10 spins on a roulette table have been black, red is "overdue." They will even quote you the odds of 11 black numbers in a row, as though that were some kind of proof that red is the superior choice.

The chances of throwing heads five times in a row are: ½ x ½ x ½ x ½ x ½ = 1/32. This means if I want to bet a friend that I will throw five heads in a row, he should be willing to pay me 31-to-1 odds on that proposition. However, if he watched me throw four heads in a row and I said, "I bet you $1 against 31 that I will throw heads again" he would be a fool to accept this wager; the chances of heads again is exactly ½. So why do people think that past results are evidence of future occurrences?

I know "The dice have no memory" is a very trite expression; it is however, true. No matter how much our human nature wants to fight this particular truth: "every chance event is absolutely independent of all preceding or following events." While it is true that 50 percent of coin tosses will be heads and one sixth of rolls using two dice will come up seven, that is only in the long term, in the short term anything can happen.

I would place all betting systems into one of four categories:

1. Bet your whole damn bankroll on one bet that has the smallest house percentage that you can find, such as player or banker in baccarat or the pass line or don’t pass in craps. Yes, I know the penalty for failure would be swift and most horrible, but at least you wouldn’t be exposing yourself to the accumulative effect of house percentage for decision after decision.

2. Bet the same amount every time. While us so called gambling experts may scoff at this betting style, it certainly has one advantage over the next two: if there are an equal number of winning and losing bets, the bettor will always be even.

3. Negative progressions. The granddaddy of all negative progression betting systems is the dreaded "martingale." Using the martingale, the gambler starts with a one-unit bet and continues to bet one unit as long as he wins. When he loses he doubles his bet until he wins. When he does finally win, he wins one unit. The good news is that the martingale will win one unit almost all the time. The bad news is the martingale bettor has two very potent adversaries: the size of his bankroll and the table limit. Martingale advocates like to trivialize the effect of the table limit as though it will never come into play. The fact is, that is why casinos employ table limits is so a gambler can only double a bet eight times or so before hitting it. It is also why the table limits are usually smaller on small minimum tables. When the martingale bettor finally reaches the point when he can no longer win that one unit he has been chasing, he will lost all of those one unit bets he has accumulated and more.


The D’Alembert is an example of a variation of the martingale where the bettor increases his bet one unit after a loss and reduces it one unit after a win. It would seem as long as there are an equal number of winners and losers, the bettor is guaranteed to win one unit for every bet won.


Bet $5 Lose -$5

Bet $10 Win +$5

Bet $5 Lose even

Bet $10 Lose -$10

Bet $15 Win +$5

Bet $10 Win +$15


There were three winners (and three losers) and the bettor is winning $15, instead of being even if he was betting $5 each time. Where this system fails is when your session begins with a long winning streak followed by a protracted losing streak.


Bet $5 Win +$5

Bet $5 Win +$10

Bet $5 Win +$15

Bet $5 Lose +$10

Bet $10 Lose even

Bet $15 Lose -$15


Starting the session by betting more than one unit will not significantly alter the results in the long run.

4. Positive progressions. The reverse martingale is a system where the bettor doubles his bet after a win and reverts to a one unit bet after a loss. Now while I have to admire the manly spirit of the kamikazes that employ this system, it dooms the bettor to losing one unit almost every time. While I use a more moderate version of the reverse martingale, such as parlaying a winning bet four or five times before taking "same bet," I would never promote this style of play as a method of overcoming the odds. A friend of mine once pointed out that succeeding in parlaying a one unit bet five times would give the gambler a thirty-two unit advantage for the house to overcome. Yes that’s true, but if you did that every time, think of all the 1, 2, 3 and 4 winning runs that you would have squandered just to get to that point.

The Contra-D’Alembert is a system (you guessed it) where the bettor increases his bet one unit after each win and reduces it one unit after each loss. Which may make you wonder why if all these systems are so great, why do they all have opposites? Which brings me to something I was told a long time ago: All systems are great, when the dice co-operate." The main drawback to the contra-D’Alembert is that the user suffers worse in a short losing streak than if he had just returned to a one unit bet as with the reverse martingale.

Promoters of gambling systems advocate the maturity of chances doctrine whether they are aware of it or not. I could write out a different series containing an equal number of winning bets and losing bets for all negative and positive progressions that would end in the bettor having less money than he started with. Of course, at this point the huckster would tell me that if the next decision were a winner the gambler would be ahead. But if the next bet were to be say $180, does that mean he has a better chance of winning than the player that just walked up to the game and made an $180 bet?

(Dale S. Yeazel is the author of "Precision Crap Dealing" and "Dealing Mini-Baccarat." They are E-books on CD-Rom available for only $20 each (plus tax) at Gamblers Book Shop and Gamblers General Store in Las Vegas.