## The Kelly Criterion – How Much To Bet

Posted by blackjackguru on July 17, 2009

Moving along the path towards becoming an Advantage Player, we must give consideration to an important aspect of the game: how much to bet. To begin, we must consider a brief history of the evolution of the math regarding this all important subject.

Edward Thorp’s famous book, *Beat the Dealer* applied a mathematical principle to blackjack regarding how much to wager. Professor J.L. Kelly originally suggested it and proved it mathematically in 1956. Computers later substantiated his claims.

**The optimal betting method is to bet a percentage of your total bankroll that corresponds exactly to the percent advantage you have at that time**.

This is known as the Kelly Criterion. It may seem intuitive and obvious but it was not always so. Early gamblers did not realize the precise relationship between the amount they should bet regarding their bankroll and their advantage. The Advantage Player makes the correct sized wager knowing the advantage she has at the time.

How Much Should I Bet?

To apply the Kelly Criterion, you would place for your next bet an equal percentage of your total Bankroll as the percent of your Advantage for the next round. If you have a bankroll of $10,000 and you have an advantage of 1%, your Kelly bet is $10,000 x 1% = $100. If the advantage is 1.5% you bet $150. If the advantage is negative, such as at the start of the shoe, you don’t bet anything, or you bet the minimum.

**How Do I Know My Advantage?**

Peter Griffin, one of the most revered analysts of the game of Blackjack, had calculated that a player’s advantage is the Basic Strategy edge plus one-half of the True Count as a percentage. For example, in a shoe game the player’s advantage with perfect Basic Strategy is -0.5% meaning the House has the Edge, no surprise there. But if the True Count reaches +4, half of the True Count as a percentage is 2%. The player’s advantage adds the two numbers: -0.5% plus 2% = 1.5% player’s advantage, which is positive, which means the player should bet more than the minimum. The Kelly bet here would be 1.5% of the total Bankroll. If the bankroll is $10,000 then the Kelly bet would be $150.

**Caution: Never Bet Full Kelly**

The risk of ruin playing full Kelly is significant. That is why professional players choose to bet less than full Kelly, because even though the Expected Value (EV) of Kelly betting is profitable in the long run, the Standard Deviation of Blackjack at full Kelly can result in losing the entire bankroll before getting to the long run. Even worse would be to bet more than full Kelly. It has been proven mathematically that betting as little as Double Kelly would eliminate all the advantage and making complete Ruin almost inevitable.

## Leave a Reply