Mythological Moment: Progression systems – part 1

A "progression system" is a method of attempting to gain the advantage by varying bet size in a predetermined fashion, according to the result of the hand just played. For example, a well known progression system is the martingale, in which you start out betting the table minimum, then after each loss, double your bet, until you finally win, then start over again at the table minimum. With a push, keep the same size bet. This seems to be a sure thing. For example, if the sequence is lose, lose, win then you will bet \$5, \$10, \$20. You lost the \$5 and \$10 bets for a net loss of \$15, but you then won \$20 for an overall gain of \$5. For a longer sequence, consider

LPLWPWLLWWLLLLLLLLLLW

You can figure out your profit very simply: it is your minimum bet times the total number of wins in the sequence, in this case \$5 ´ 5 = \$25.

How can there be anything wrong with this logic? Just leave on a win and you walk away with profit in your pocket every time.

However, for many reasons, you can’t always leave on a win. So, for example, in the previous sequence, the hand before the final win you were actually down \$5100. Very few people can sustain this type of loss and keep on playing. The wager you placed on your final hand was \$10,240. Did you bring \$15,340 along on the trip, just in case you needed to make such a bet? What if the hand required two splits and a double down, did you bring \$61,360? What if you lost it all? The situation of losing 10 hands in a row is not rare: it occurs about once every 1540 hands, or 15 hours of play.

Based on that last hand, either you leave winning \$25, or you leave losing \$15,340 (you’re ruined). Would you risk \$15,340 (or more) on a return of \$25? A decent mutual fund will return about \$2000 per year on the same investment, with much less risk.

The net result, using a martingale (or any betting sequence) averaged over all possible sequences of hands that can occur, is that they have no effect whatsoever on your long term expectation, but they do create a much larger variance in terms of their effect on your bankroll.

However, progression systems do change certain odds. They increase the odds you will have a winning session, since most of the time you will not have a long sequence of losses and will be able to leave on a win. This can give the appearance that they are winning systems. You may find that suddenly you are winning nine out of ten sessions. The flip side is that your losing sessions will be much larger than your winning sessions. Sometimes catastrophically large.

Here is a soliloquy from a progression system player that tells the story. This is taken verbatim from Standford Wong’s public blackjack bulletin board, at www.bj21.com.

Since the beginning of the year I’ve been going to the casino 5 days a week. I keep a log of my losses/winnings and number of times I played. So here are the numbers: I played 100 times, I’ve won 72 and lost 28, and I am down \$290,000. My average bet is \$1,000 and the largest one day winning was \$22,000, and my largest one day loss was \$69,000. I can also tell you that out of the 100 times I played, at some point I was up about 99 times. The last money that I have is \$70,000, and I am willing to put the time and effort to get my money back even if it takes a year. I am not a card counter, and I need some help on a betting system or other way of risking \$10,000 per trip to win \$2,000 to \$3,000. I’ve read many books about money management. My mistake is that I lost about \$200,000 in four trips. I am in a very difficult financial situation and I hope someone can help.