# Each Way bets - Optimization

Hi guys I use 0.1 Kelly on majority of bets

Really struggling to figure out how much I should bet on each way bets

For example how much should I bet on Tyrell Hatton @ 33/1 1/5 odds 7 places with a €60000 bankroll

Any help appreciated

10% Kelly says €22 on win part and €470 on top 6

Assuming the optimal bet is in between this …

My estimate is €120 Each way ( 60 and 60 )

Please help me have no clue what units to put on Cantlay EW @21 1/5 5 places

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Honestly I need to think about this one for a moment. In general, it is useful to (at least conceptual) split the bets into independent events, calculate kelly for each independent event, and then try to avoid overbetting.

However, in this scenario, due to the nature of the each way bet, you basically are trying to figure out how much you want to overbet the outright in order to get enough exposure to the top 5.

I am trying to think of a rule of thumb that is helpful (and not wrong in a way that can get you trouble), and I honestly need to think about it a little more.

3 Likes

Ok so I was looking at the sizing to try to get a rule of thumb for you, but here is what I can say for you, under the following three assumptions:

1. You are not placing any other outright or top 5 bets on Cantlay
2. Ignoring other matchup bets you are placing on Cantlay (which you shouldn’t, but for simplicity)
3. The assumption that the DG probability is the true probability

Using DG’s outright odds and Top 5 odds, you need a fair price for the each way, then you can just directly do a Kelly calc on the each way bet. I will describe how to do that below. In what follows,

the DG probability of a top 5 = p5
the DG probability of a win = p1
the DG probabilty of finishing places 2,3,4, or 5 = p5-p1 = p25
The each way odds offered = O

Now we write down the expected value of an each way bet in terms of these probabilities and the offered each way odds, set it to zero, and solve for the breakeven odds.

Expected Value of \$1 Each Way Bet = - (1-p5)+ (p25)((0.5)O/4) + p1O*(0.5)

0 = -+ (p25)((0.5)O/4) + p1O*(0.5)

(1-p5) /((p25/8)+(p1)/2) = Fair Odds For EW bet, 5 places

(Here I am assuming the odds of the place bet are the offered odds divided by 4, not sure if this is the case where you are playing or not)

5 Likes

The best rule of thumb is if it doesn’t make your heart race, its too low.

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