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Introducing Error Into Kelly Question
Hypothetical scenario:
I have found a baseball line of +155, and I believe the true value of that line to be +145 (+/-2) (from +143 to +147). (By "true value" I mean the odds corresponding to the actual probability the team will win.)
How would I introduce that error range into the Kelly Criterion to find optimal bet size?
Just use the most conservative number, which in your case is +147.
Originally Posted by LT Profits
But, I don't want the answer to be that easy.
If you know the probability of each probability, then the average probability of the game is the probability of the game, since life doesn't care about anything but the outcome. If you know it's +145 +/- 2 (and I defy anyone to nail an MLB game anywhere near that close with the kind of confidence that Kelly asks for) then that implies that over all games of this type it'll be +145. I would use that, but if I was actually using full Kelly I would ask how confident you really are in this edge.
I think the right answer is somewhere in between the two answers given. I agree with what Arilou is saying about averages when it comes to calculating probabilities. However, given this scenario and once you plug in Kelly, thinking in terms of averages is no longer valid. The reason being that it is much worse to overbet using Kelly than to underbet.
Phrase the question differently- You're trying to roll a 1 on a die. If you do, you get paid 4:1. Now, the catch is: You have to choose a die at random- 50% chance you get a standard 6-sided die to roll, and 50% chance you get a 4-sided die to roll (numbered 1-4).
Your odds, overall, are 5 in 24 of rolling a 1. Is your optimal stake different, given that you arrive at it as a combination of a "good" bet and a "bad" bet with the dice, than it would be if you simply chose a random number between 1 and 24 (and won on 1-5)?
I think the given scenario is more about "rounding" errors than probabilities.
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