Progressive Betting Versus Counting Cards

6 October 1999

By John May

Walter Thomason appears to have kick-started an age-old argument with his interesting new work 21st Century Blackjack: New Strategies for a New Millennium --the old progressions versus counting warhorse. I can hear the damning criticisms from those who will never read the book.

Naturally, as a player who believes in the math, I am going to come down on the side of...well, dammit, I am going to come down on my own side, because I am not really happy with the arguments from either camp.

It might be of interest to know that there are precedents for Walter's work on progressions.

In the Theory of Blackjack, Peter Griffin reports briefly on the results of extensive simulations that showed a win/loss correlation between hands equivalent to 0.2 hi/lo points (0.1% of the top of the deck). The reason is simple: winning hands are likely to contain high cards, resulting in a depression of advantage and vice versa. It is important to understand this is cumulative not additive; it behaves exactly as a count system would, becoming more important the more cards that are seen. So, five losses would give you a 1% edge.

Leon Dubey expanded on "situational" blackjack systems in his (out-of-print) classic No Need to Count in 1981.

Technically, the argument that progressions do not change the house edge is incorrect for blackjack. In practice, however, the classic progressions do not change advantage by more than 0.05%, usually less. This is largely because a) the negative correlation between hands is rather weak, b) the shuffle dilutes this already insignificant effect, and c) the classic progressions themselves do not exploit the negative correlation very well.

Interestingly, this has not always been the case. These systems would have been more effective in the pre-war days of single-deck blackjack dealt down to the last card. It is even possible that the systems may have given some pre-war players a small advantage over the casinos, though this is unlikely. None of the classic progression systems give the player more than 0.3%, even with 100% penetration. The pre-war player would need to have played pretty close to basic strategy and had a huge bankroll to profit in the long run.

It is also interesting to note that players who use a Martingale system in handheld games will be making maximum bets in what on average will be a positive count. Do these players get barred, mistaken for card-counters? How much have casinos lost by confusing the two classes of players?

At this point, some statistically-minded players scratch their heads and say, Why is he encouraging people to take an interest in this stuff? Does May not know how dangerous this is?

"Encourage" is a little strong. My book, Baccarat for the Clueless, contains a chapter devoted to debunking progressive systems, virtually the only book on the subject that attacks the misinformation concerning that particular game. I have spent a lot of time talking individuals out of parting with their life-savings for some huckster system, usually with success. My conscience is completely clear.

I have repeatedly explained my beliefs on the subject. The fundamental theory of card-counting is based on the dependence of trials. You cannot say that expectation is unaffected by the negative correlation between hands, nor that expectation is divorced from "situational data", because that would, by implication, invalidate card-counting. This is not a minor point of theory.

I have repeatedly qualified everything I write on this subject with caveats about the impracticality of applying this as a method for playing with a positive expectation and highlighted fraudulent salesmen for what they are. I fully believe in giving people the truth and letting them do what they will with it.

You can design a progression system that would change the house edge significantly. Something like a 1,1,1,1,5000 sequence will give you an edge. I don't think its practical, however.

I looked at creating a progression system to limit losses, but I couldn't find anything as powerful as the simple blackjack systems such as ace-five.

One thing of interest I learned is that using a progressive system while also using a count system to vary the play of your hands is mathematically superior to flat-betting. Theorists often point out the increased risk arising from combining both progression and count systems, but this depends on the progression. The D'Alembert system, for example, used with the Advanced Omega II system increases expectation by about 0.2% over flat-betting without any increase in fluctuation.

Progressive systems are not going to make you a millionaire. They may give you a little entertainment, if that is how you like to play. But they do also have useful mathematical properties which are worthy of discussion.

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For more information about blackjack, we recommend:

Best Blackjack by Frank Scoblete
The Morons of Blackjack and Other Monsters! by Frank Scoblete
Winning Strategies at Blackjack! Video tape hosted by Academy Award Winner James Coburn, Written by Frank Scoblete
Blackjack: Take the Money and Run by Henry Tamburin
Twenty-First Century Blackjack: New Strategies for a New Millennium by Walter Thomason