Kelly criterion for EW bets

[slapdash]

If you are making simple win/lose bets and know the actual probability that each bet will win, then the Kelly criterion gives a simple formula, in terms of the odds and probability of winning, for the optimal proportion of your bank to stake on each bet, to make your bank grow as fast as possible in the long run. In a thread in At The Races Systems, akm asked for a similar formula for each-way bets. The answer is probably more on-topic here. There is a formula, but it's considerably more complicated. Let m be the profit you'd make on a 0.5 unit EW bet if the horse wins, and let n be the profit you'd make if it places (so, for example, if the odds are 10/1 and a place pays 1/5 the odds, then m = 6 and n = 0.5). Let p be the probability of the horse winning, and let q be the probability of it placing (but not winning). So 1-p-q is the probability that it is unplaced. Now let: A = mn B = (p+q)mn +pn +qm -m -n C = pm +qn -1 + p + q. Note that C is just your expected profit on a 0.5 unit EW bet. Then the optimal proportion of your bank to use as the unit stake (so the total stake is twice this) is [b + sqrt(B^2 + 4AC)]/4A sqrt means square root. Well, he did ask. :\ This also applies to other kinds of bet with two winning outcomes; e.g., an asian handicap bet with split handicap.

[DeepBlueDevilFish]

Re: Kelly criterion for EW bets Very interesting. Thanks. :clap