## Saturday, April 12, 2014

### the kelly number

the kelly criterion is a number between -1 and +1 that tells you the maximum percentage of your account to allocate to a defined risk trade in order to have positive expectancy without blowing out your account. a positive kelly number is a green-light, a negative kelly number says that the edge lies with the opposite side of the trade. by positive expectancy i mean that there is a theoretical chance of gain, over time, once all the wins and losses have been totalled.

here is the formula:
f = (p * (b+1)-1)/b
• f is the kelly number
• p is the probability of success
• b is the return/risk ratio (sometimes called the odds.)
so consider the fate of coin flippers. p is obviously .5 and in the typical example b is 1 i.e. risk 1 to make 1. in this situation the kelly number, f, is 0 (=(.5*(1+1)-1)/1). this is a mistake for either side to play this game.

now suppose you are jeff ma (the real-life protagonist of the movie 21, the big-player for the infamous mit blackjack team, and the author of the house advantage in my brane fud section) and you sit down at a blackjack table for which your confederate has signalled that the count favors players 51:49. how much do you bet? the kelly number is .02 (=.51*2-1). if you have 50K in your bankroll then you bet \$1000 a hand.

next i apply kelly to vertical-option spreads ...