I have a Kelly staking question that I can't figure out on my own. Let's say you are betting an over/under in football and you find value in the over. You calculate that the over is a 55% winner at -110 odds so you bet 5.5% of your total bankroll on it. Just prior to game time you get an updated weather report that shows a big storm coming in which changes everything for you. You now calculate the under to be a big winner, expecting it to hit 55% of the time at -110 odds (which you can still get at the same total you originally placed your over wager on). You already have 5.5% of your bankroll tied up in a bad bet with the over... how much of your bankroll should you bet on the under now and what is the calculation used to figure it out?
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Looks like what I need, I can't get it to work for me though. Anyone know the formula?Comment -
I'm pretty sure I've gone over this in numerous other posts but:
Let y = under position (variable of interest)
Let x = initial position on over (5.5%)
Let o = current decimal odds on over ()
Let u = current decimal odds on under ()
Let p = current win prob on under (55%)
Max wrt. y, st 0 ≤ y ≤ 1 - x:E(U(y)) = p * ln(1 + (u-1)*y) - x) + (1-p) * ln(1 - y + (o-1)*x)So inserting your #'s we get
FOC:Ey = 0 = -((1 - p)/(1 + (o-1)*x - y)) + (p*(u-1))/(1 - x + (u-1)*y)
y' = (x + p*(u - o*x + (o-1)*u*x) - 1)/(u-1)
y' = 10.9725%
Verifying 2nd order conditions are left as an exercise to the interested/bored reader.Comment
