I get 1500 * .382 = 573
When contemplating hedges, I consider their value ex ante. Below is an example.
Suppose one can get +200 future on KC to win SB midseason. An estimate of their chances is 36%, so one concludes this is a +EV bet.
Without considering any possible hedge, one should bet $400 on KC future SB bet. This yields an expected growth of 0.158%.
Let's assume one will be able to get a 0EV hedge on KC's SB opponent. Assume one has $10,000 bankroll. How much should one bet on KC future @ +200?
The answer is uncertain, because we do not know the forward odds of KC winning the SB. This is because we do not know their opponent. (and even if we did, odds change over time) We also don't know what KC's chances are of reaching the SB, which is a required condition to make the SB hedge bet.
To make it simple, let's assume KC is 60% to reach the SB, and their fair value odds will be -150 to win SB. This means their opponent will be +150 fair value.
The optimal bet sizes are $2,000 on KC future, and $3,200 on SB opponent +150. Expected growth is 2.63%. Below are the possible outcomes, and the resulting log of expected growth:
Code:
KC out of SB 0.4 -0.089257421
KC wins SB 0.36 0.027705975
KC loses SB 0.24 0.087514347
Sum 1.0 0.025962902
Instead of -150, assume KC is -122.2 (55% win equity) fair value odds to win SB. This means their opponent will be +122.2 fair value.
The optimal bet sizes are $2,000 on KC future, and $4,100 on SB opponent +122.2. Expected growth goes up to 3.84%%. Below are the possible outcomes, and the resulting log of expected growth:
Code:
KC out of SB 0.4 -0.089257421
KC wins SB 0.33 -0.003316611
KC loses SB 0.27 0.13025506
Sum 1.0 0.037681029
Below is a chart of bet sizes and expected growth for varying KC SB win equities:
Code:
KC W/E Future Hedge Exp. Growth
0.5 $2,000 $5,000 5.704%
0.525 $2,000 $4,550 4.689%
0.55 $2,000 $4,100 3.840%
0.575 $2,000 $3,650 3.151%
0.6 $2,000 $3,200 2.630%
0.625 $2,000 $2,750 2.269%
0.65 $2,000 $2,300 2.072%
0.675 $2,000 $1,850 2.044%
0.7 $2,000 $1,400 2.190%
0.725 $2,000 $950 2.519%
0.75 $2,000 $500 3.044%
0.775 $2,000 $50 3.779%
0.8 $2,200 $0 4.690%
Now, these are significantly higher than if you simply placed an optimal EG future bet on KC without considering a hedge. Needless to say, a $2,000 future bet implies one has a 40% chance to lose $2,000. (20% of one's bankroll) So, there is obviously large exposure if KC does not make it to the SB. If KC makes it though, one is essentially in a no-lose situation with the hedge. This fact yields the opportunity to significantly increase EG. Hedging after the fact misses this opportunity.
Last edited by PokerHero77; 02-03-2021 at 08:20 PM.