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3 outcome answered question

Hi all,

I've been having trouble finding the Kelly Criterion bet size for an each-way bet.

The above link shows the solution to a problem with 3 distinct and mutually exclusive outcomes. In an each-way bet there are three distinct outcomes (Lose all bets, horse places but doesn't win, horse places and does win).

An each way bet is a matched bet of one bet on the outright win and one on the placing of the horse (1st or 2nd or 3rd for example). These bets are of an equal amount.

I have calculated the Kelly criterion decimal bet for the win only and place bets independently and these are: 0.06 and 0.23 respectively but since to place this each way bet, I must choose an equal stake for each bet, hence my problem.

One option is a simple average which brings us to 0.145

The problem to use the Kelly criterion method as linked is that I can not know the odds for the second possible outcome (places but doesn't win) as the odds for place (win or not) or outright win can only be known. Does anyone have any insights into this?

Thanks for reading and any forthcoming help!

Community
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enda1
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2 Answers2

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The question to which you link to, answers your question too, as you can treat these as 3 different outcomes. For example, if you back a horse E/W with x-x @5/1 odds with 1/5 E/W for places 1-2-3, then, in David Speyer's answer, you need to substitute for no place $b_1=-2$, for place 2-3 $b_2=1-1=0$, and for win $b_3=1+5=6$ (where the numbers are nice because I've chosen the parameters so).

domotorp
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In its simplest possible form, the Kelly Criterion states that, on an even money bet, the percentage of the bankroll to bet is:

(Win probability x 2) - 1

So if the chance of winning on a single bet is 80%, the bettor should wager 60% of one’s bankroll. Note that if the formula is absolutely strictly applied, one would literally never make an even money bet, because the equation results in a zero when 50% as the win probability. read more here if you want to apply to NFL betting

https://nflbets.com/2021/02/12/kelly-criterion-betting-system

Reemo
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  • Horserace betting is not even money betting, especially if you are taking account of the different payouts on win and place bets. – Henry Apr 08 '25 at 01:04