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The Mini-Max Blackjack Betting Method
by Stanley Roberts

This rule assumes that you play your system repeatedly without error in the casino.

This month, we will deal with the Kelly Criterion. In this issue of Gambling Times, you may read two discussions of the Kelly Criterion; one by Edward 0. Thorp, the other by Lance Humble in the reprint of a portion of his book, Blackjack Gold. If you haven't done it already, you should read those two articles before continuing further. On this subject, I tend to disagree with my distinguished colleagues. I believe that as a practical matter, the Kelly Criterion should NOT be applied to blackjack play.

Now this does not mean that in a mathematical sense, the Kelly Criterion and its application is not a proper exercise in the determination of bet size. As a method, it is better than any other mathematical formula you may apply. Further, anyone who would do battle with Dr. Thorp on the subject of mathematics or related applications will more than likely find himself tilting at a skyscraper with a toothpick. Nonetheless, we shall venture forth with our opinions and the rationale behind them.

First, let me introduce the Roberts' mini-max betting concept, which, although not unique, was first expressed in writing by me in 1971. The blackjack player has but two bets to make: the table minimum or the table maximum, hence the name mini-max. The decision as to when to play the table maximum is based upon the moment the deck favors the player. The principle herein is that the incremental increase is a multiple of the favorable percentage, be it just a tiny fraction or a percentage point. The theory is that you will win more of these hands, and the more money in play, the more the playerwill eventually win. In practice, however, the table maximum is replaced by "the most you can get away with."

Of course, you must be properly bankrolled for a "table maximum" in order for this course to be feasible. Since blackjack is a game of probability as opposed to certainty, it is possible to lose, even when you have the edge in the short run. To overcome this, you must have an adequate bankroll.

One way to determine that bankroll figure is to use the Kelly Criterion, which will then involve a varying bet. Another way is to average these esoteric formulations to arrive at an operating rule of thumb. One that seems to work for the overwhelming majority of players is to keep the maximum bet within one to two percent of the starting bankroll. This will provide a sufficient wager for all but the most extraordinary of improbable occurrences. This rule assumes, however, that you play your system repeatedly without error in the casinos and that you are using a winning system which has received extensive computer testing, not one of your own derivation.

Now, as a practical matter, no casino will let you get away with a minimum-maximum betting pattern. In fact, if you would like the "thrill" (???) of getting barred, all you need to do is vary your bet from. the table minimum to the table maximum, and in short order, you will be approached by a floorman who will ask you to stop playing blackjack. If, by chance, you are one of those diehard skeptics who still does not believe that casinos bar skilled blackjack players, I recommend the experience.

So it became necessary to find a pattern which you can use. Here is the solution: Divide your total bankroll by either 50, or 100. If your time is short, say a weekend, use the 50 figure. The result is your maximum bet. It should be at least four times the table minimum. If you don't have this much money, you are in the wrong casino at the wrong table, or you should not be playing at all. Your minimum bet should be 20 to 25 percent of your maximum in a single-deck game. In a four-deck game, you should have a minimum bet of 10 to 15 percent of your maximum.

There is nothing else to consider in this matter, the Kelly Criterion notwithstanding, except that you should make your first bet off the top of the new deck twice the amount of the minimum. And if the number of chips you are betting as a minimum is two chips or more, you can experiment with both your minimum and maximum bets by varying them one chip in either direction on a random basis. However, your average bet should equal the standard you have set for the minimum and the maximum. The variations of betting are used to avoid the image of systematic betting which might make pit personnel think you are a card counter.*

I fully realize that many others will also disagree with the above commentary, not the least of which is my good friend, Kenny Uston. We have discussed this subject before. Further, if you have the skills of a player like Uston, the Kelly Criterion makes more sense. But to the overwhelming majority of average to good card counters, the Kelly Criterion is a needless burden that further complicates a difficult task. Again, remember the KISS rule: Keep it simple, stupid.




*As an example of this, assume that you have a $2,000 bankroll and you are in Nevada for a short trip. One-fiftieth of your bankroll is $40- that would be your maximum bet. Your minimum bet would be $10. You would probably play at a $5 minimum table. Your initial bet off a newly-shuffled deck would be $20. You could then vary your minimum bet from $5 to $10 to $15, and your maximum could be either $35, $40 or $45. When making the larger bet, you should use a $24 chip plus the required $5 chips. The fewer the chips, the less apparent is the jump in bets.

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