The Kelly Criterion [0] tells what strategy to employ if you're given fair odds on an unfair coin.
For example, if a bet can be made where you get 1:1 payout for a coin that's weighted heads with probability 0.8 and tails with probability 0.2, how much should you bet to maximize wins, under a suitable formulation, if you're allowed to play repeatedly. Betting all your wealth at each round nearly guarantees you'll lose everything the more you play, so it's not as straight forward as one might think.
If you decide to bet a fixed amount of your current wealth at every turn, that's the condition that the Kelly criterion tells you to bet:
K = (bp - q) / b
Where p=1-q is the probability of heads and b is the odds of winning (that is, the coin gives b:1 odds).
There's some SO posts about it [1] and I've also made a short blog post, with minimal explanation, which derives it [2].
Note that this has wider applicability than just "how to bet on a horse race you know is fixed". If you believe the stock market is not zero sum and is increasing by a certain amount, how do you bet part of your fortune to maximize your returns? If you have a cohort of people founding startups with a certain failure rate and return, how much of your funds wealth do you invest in these ventures?
The real world is complex but the Kelly criterion gives a starting point to talk about these things.
I heard somewhere that Warren Buffet uses a factor of 0.9 on top of the Kelly criterion calculation to account for increased risk.
For example, if a bet can be made where you get 1:1 payout for a coin that's weighted heads with probability 0.8 and tails with probability 0.2, how much should you bet to maximize wins, under a suitable formulation, if you're allowed to play repeatedly. Betting all your wealth at each round nearly guarantees you'll lose everything the more you play, so it's not as straight forward as one might think.
If you decide to bet a fixed amount of your current wealth at every turn, that's the condition that the Kelly criterion tells you to bet:
Where p=1-q is the probability of heads and b is the odds of winning (that is, the coin gives b:1 odds).There's some SO posts about it [1] and I've also made a short blog post, with minimal explanation, which derives it [2].
Note that this has wider applicability than just "how to bet on a horse race you know is fixed". If you believe the stock market is not zero sum and is increasing by a certain amount, how do you bet part of your fortune to maximize your returns? If you have a cohort of people founding startups with a certain failure rate and return, how much of your funds wealth do you invest in these ventures?
The real world is complex but the Kelly criterion gives a starting point to talk about these things.
I heard somewhere that Warren Buffet uses a factor of 0.9 on top of the Kelly criterion calculation to account for increased risk.
[0] https://en.wikipedia.org/wiki/Kelly_criterion
[1] https://math.stackexchange.com/questions/4384904/geometric-g...
[2] https://mechaelephant.com/dev/Kelly-Criterion.html