Search BlackjackInfo

 Blackjack and Card Counting Forums - BlackjackInfo.com Optimal betting of multiple hands
 FAQ Members List Social Groups Search Today's Posts Mark Forums Read

#1
April 7th, 2005, 11:15 PM
 Eric Member Join Date: Mar 2005 Posts: 1
Optimal betting of multiple hands

I've been trying to figure out the optimal bet for blackjack, given a certain number of hands and my advantage. I think my math is wrong, because I'm getting some funky results. Does anyone know the correct math for this? Read on for my attempt.

I'm using the kelly function:
bet = advantage * bankroll / variance

Assume my bankroll is 1000, my advantage is 0.05, and the variance of 1 hand is 1.32.

bet = 0.05 * 1000 / 1.32 = 38

Now, you would assume that it would be be better to spread those 38 bets to 5 hands, rather than have them all on the same hand.

Computing the bet again, for 5 hands this time, I get some weird results. The variance of 5 hands of blackjack is 16.20. (using the function 1.32*n + 0.48*n*(n-1) )

bet = 0.05 * 1000 / 16.20 = 3.09

3.09*5 hands = 15. Shouldn't this number be greater than 38?

Should I be dividing by standard deviation instead of variance?
#2
April 8th, 2005, 02:28 PM
 KenSmith Administrator Join Date: Mar 2005 Posts: 2,118
Explained

The variance you calculated for all 5 hands is fine, but you then need to divide it by 5 before using it in your bet-sizing formula, which expects the variance per bet.

So, the average variance per bet for each of your five bets is 16.20 / 5 = 3.24.

Your optimal bet on each hand is 0.05 * 1000 / 3.24 = 15.43.

Your overall action of 15.43 * 5 = 77.15, which is as expected, quite a bit larger than the 38 units you should bet on a single hand.

P.S. For anyone following along, the magic numbers in the equation are variance=1.32, covariance=0.48.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Welcome to the BlackjackInfo Forums     Site Announcements Blackjack Forums     Blackjack - General     Blackjack - Voodoo Betting Strategies     Blackjack - Card Counting     Blackjack - Advanced Strategies     Blackjack - Variations     Blackjack - Theory and Math     Blackjack - Online Casinos     Blackjack - Stories Land Based Casinos     Las Vegas     Nevada - Outside Vegas     Eastern US     Southern US     Midwest US     Western US     Canada     Australia     Europe     Asia, Africa & Far East     Caribbean & Latin America Online Casinos     Reputable Casinos     Problem Casinos     Latest Promotions Miscellaneous     Other Games     Gambling Law     Blackjack in the Media     Site Discussion     News     Sports Betting     Investing and Financial     Anything Else

All times are GMT -6. The time now is 06:41 AM.