Advantage Play with John May

11 March 2001

By John May

Advantage players typically want to know how favourable a particular game or technique is. A variety of methods have been used to try to determine the worth of a game or system.

When card counting, the advantage player's staple, was first developed, the measure used was percent advantage. This is simply defined as your expectation divided by your average bet.

Unfortunately percent advantage isn't of much use in explaining how much money you will win from a given opportunity. The reason is a little complicated and has to do with correct betting. The higher the ratio of a winning wager to a losing wager, the lower your bet needs to be in order for you to minimize the chances of being wiped out by an adverse streak of luck.

For example, would you prefer a 10% advantage on a wager with a 10 to 1 payoff or a 5% advantage on a wager with an even payoff? The pro gambler prefers the latter opportunity. Why? Professional gamblers bet the percent of their bankroll according to their percent advantage divided by the ratio of a winning wager to a losing wager. This is known as the Kelly criterion, and it ensures that your bankroll grows at the fastest possible rate. All serious gamblers use something close to the Kelly criterion.

Let's say we have a bankroll of $1000. The Kelly bettor would bet 1% of his bankroll, or $10, on a wager with a 10% advantage and a 10 to 1 payoff, winning $1 on average. The Kelly bettor would bet 5% of his bankroll, or $50, on a wager with a 5% advantage and an even payoff, winning $2.50.

Clearly the amount of risk involved is very important in determining how favourable a wager is.

Modern blackjack theory acknowledges this and uses a combination of advantage and risk. Pioneering work was done in this area in the early 90s by Abdul Jalib M'hall. It was only in the last couple of years that formal systems have emerged to replace percent advantage as the yardstick of favourability. Brett Harris developed an intriguingly simple method that he describes as NO, which is simply the number of rounds or trials that a player takes to double his bankroll. Don Schlesinger followed up in his revised edition of Blackjack Attack with a measure known as SCORE, which rates a game or system based on the bankroll growth per hour with a given bankroll.

Substantial room for development in this area still exists, particularly in the relationship between time and a player's bankroll growth (similar to the "compound interest" effect, which has been much discussed in investment circles recently).

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For more information about blackjack, we recommend:

Get the Edge at Blackjack by John May
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
Twenty-First Century Blackjack: New Strategies for a New Millennium by Walter Thomason
Blackjack: Take the Money and Run by Henry Tamburin
Blackjack Bluebook: The Right Stuff for the Serious Player by Fred Renzey