by the Green Baize Vampire

More hysteria and misinformation about the subject of progression betting has been written than any other gambling subject.

Gamblers with an intellectual interest in gambling fall into two basic categories:- players who follow scientific methods, based on mathematical models and computer simulation.

The other category involves gamblers who use scientifically unproven methods. There is often a rational basis for these ideas, and they may involve pseudo-scientific concepts but their justification depends on argument rather than data.

The biggest class forming this latter category use progression systems. I get at least one e-mail a week from the user of some form of progression system. Generally I do not comment on such methods, except to point such individuals in the direction of works by Thorp, Epstein and Levinson which prove the futility of using betting systems to overcome a negative expectation.

However, the game of single-deck explaination is an exception to the general rule. There is a small but significant correlation between advantage and the results of the previous hands before the last shuffle.

The effects, calculated by John Gwynn and published in a 1986 edition of Blackjack Forum, revealed that:-

a) Following a win, player advantage decreases by .10%

b) Following a loss, player advantage increases by .12%

c) Following a push, player advantage decreases by .15%

Moreover, these effects are cumulative. They depend on the number of cards played. At the half deck level for example, a win causes a .20% reduction in player advantage.

It is the opinion of the experts that these effects are statistically negligible. It is my assertion that they are not. After five successive losses the player has an advantage of 1% over his basic strategy expectation.

This phenomena tends to embarass blackjack experts because technically it makes the argument that progression systems do not change the house edge correct.

Unfortunately, the popular progression systems do not exploit the win/loss correlation properly. None of the popular systems increases expectation by more than 0.05% even in single-deck. The reasons for this are several:-

1) The effects of the win/loss correlation are quite small. The effects are far weaker than even the simplest counting systems.

2) They do not take into consideration the number of unplayed cards remaining.

3) Crucially, the progression is not reset at the shuffle.

4) Wins at the minimum bet are ignored.

It is technically possible to design a progressive system that can win at blackjack, but in practice the gain would be so small that it would hardly be worth bothering with.

John Gwynn tried to design such a system. Leon Dubey expanded on Gwynn's ideas in his "No need to count" (1981), which includes a number of other "situational" effects, such as the increase in advantage following hard double-downs and non-ace pair splits. Commenting on Dubey's system in his "Blackjack Wisdom" Arnold Snyder stated in the most favourable single -deck games Dubey's system might win a dollar or two per hour if the player were to spread his bets from $1-$20. Snyder was writing for an audience that knew there would be horrible and frequent losing sessions associated with the use of such a system. Snyder mentions that such wild bet variation would frequently get the player barred, as apparently happened to Dubey.

Nevertheless, there are perhaps a few angles that have not been exploited.

If you were to try to create a winning system, here are some ideas which may help:

1) Find a single-deck game with rules that give you a break-even edge off the the top with basic strategy. If you do not know how to calculate your basic strategy disadvantage from the posted rules you will find out from a good blackjack book or by looking up www.conjelco.com.

2) Look for games that deal a great deal of cards, +75% is excellent. You must play alone with the dealer or the system will not work.

3) Keep a count of wins and losses, for the deck you are playing only ie only count wins and losses since the shuffle. Have one pile of chips record wins, another losses, another pushes. Simply add a chip to the relevant pile each hand.

4) By looking at your pile of chips you can work out your edge/disadvantage which is your basic strategy disadvantage - .15% * the number chips in the push pile, -.10% * the number of chips in the win pile and +.12% * the number of chips in the loss pile. You can improve your results by doubling these figures when half the deck has been dealt out, or five rounds have been dealt. 5) When you know you have the edge bet more chips. If you jump your bet too much the dealer will shuffle, so you may have to stick to doubling your bet. You would preferably spread up to the table maximum, if you can afford to.

6) Leave the table after three successive losses or pushes. You have quite a large disadvantage now. Ideally you would leave the table every time there were more wins and pushes than losses, but you would leave the table so often this would be impractical.

7) You can change your playing strategy with knowledge about wins and losses.

Stand 16 vs 10 when losses outnumber pushes and wins. Also hit 13 vs 2 and 12 vs 4.

There are other simple ideas you could add based on "situational" information. You could leave the table after an ace-split for example. But there are dangers to adding too much information to a system whose chief value is its simplicity.

Of course such a system would require very large bankroll for very small return on investment. But, it would almost certainly produce a positive expectation even in quite bad games. Unfortunately it is currently impossible to simulate this system with any commercial software, so it is difficult to quantify exactly how much gain it brings.