Why You Need a $10,000 Bankroll to Win $10/hour Card Counting Blackjack

The Kelly criterion says that to get the fastest rate of money growth without the risk of losing your bankroll, bet a fraction of the bankroll equal to your advantage in the gambling game. With blackjack card counting, your advantage or disadvantage varies with the count. How much should you bet at each count level?

Typical good blackjack games have return of -0.5% for a freshly shuffled deck (true count of zero), and the return improves by 1% for each +2 change in true count. That means you need a true count of +1 just to cancel the house edge, and +2 or more to gain an advantage. The count is just as likely to go negative as positive, so you'll be playing most of your hands with a negative return.

When the count gets to +2 and better, you need to bet quite a bit more to cancel out your losses while playing at a disadvantage. But you mustn't bet too much, or else losing streaks will drive your bankroll to zero.

By setting up a spreadsheet, you can estimate the opportunities for increasing your bets and how much to bet to get the maximum growth rate, under realistic conditions. You will find that a $10,000 bankroll will support a long-term win rate of only about $10 to $20 per 100-hand session, assuming perfect card-counting and perfect play.

When your expected win rate is $10 per hour, your long-term bankroll growth rate is even less that that because downward fluctuations in your bankroll will require you to make smaller bets. If you are betting one-half of the Kelly optimum bet size, your expected bankroll growth rate is 3/4 of your expected win rate.

For more insight into the Kelly criterion, see Part I of this presentation:

https://youtu.be/BJx3I8ygMSk

No advanced math is needed, not even algebra. If you understand multiplication, fractions, and decimals, you can follow the explanation.

In the video, I mention an excellent free online book on blackjack: Modern Blackjack, An Illustrated Guide to Blackjack Advantage Play, by Norman Wattenberger, available here:

https://www.qfit.com/book/ModernBlackjackPage-10.htm

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