Hello,

Plz excuse if this is a bit noobish, but I'm trying to get my head around this

Let's say we have a situation where multiple +ev situations exist

Take this hypothetical soccer game.

The win pays $1.5 (i believe that's 1:2) and the probability of the event is 80%.
The draw pays $102(101:1) and the probability is 5%
And the loss pays nothing, and would be 15%.

WhAts the best strategy here? And what's the maths involved? I have tried to add together multiple +Ev before but I'm not sure if I'm right.

I think the answer is going to be "it depends" because it seems to me that you could dutch book both those odds so that 85% of the time you're winning money at the expense of the higher ev but higher variance you would have if you only bet the draw?
Tia

This calls for the Kelly Criterion. The growth-optimal portfolio will be some combination of the two wagers. Your problem is probably similar to Example 6.2 of Thorp's chapter (pdf), since the wagers are correlated.

We had a simultaneous Kelly Criterion thread awhile ago. It dealt with two independent wagers. Here's a link to that thread:

https://forumserver.twoplustwo.com/2...-math-1644034/

Your case deals with dependent wagers (events), but I imagine that the same approach applies. Mathematically, the Kelly criterion prescribes that a bettor bet amounts on the two wagers that maximizes the expected logarithm of the bettor's ending bankroll.