On the whole I agree with Raemon’s review, particularly the first paragraph.
A further thing I would want to add (which would be relatively easy to fix) is that the description and math of the Kelly criterion is misleading / wrong.
The post states that you should:
bet a percentage of your bankroll equivalent to your expected edge
bet such that you are trying to win a percentage of your bankroll equal to your percent edge.
(emphasis added)
The 2 definitions give the same results for 1:1 bets but will give strongly diverging results with other odds.
In addition the post gives a method of calculating one’s edge which gives correct results for 1:1 bets. It is not entirely clear how one would use the formula for non 1:1 bets but it doesn’t seem to indicate a calculation which would give one’s edge correctly. (55%-45%=10% doesn’t seem to readily generalise correctly in the same way that (55%-50%)/50%=10% does).
The post never states that the definition is only for 1:1 bets so the impression given by the post is that these formulae can be used in the cases given in the post. However there are no guarantees that any of the examples in the post are 1:1 bets.
(The post does mention that the example is based on 1:1 bets but it doesn’t imply that the calculation as given only works for such bets.)
As a result the post effectively ends up recommending making incorrectly sized bets. For non 1:1 bets it is possible to calculate recommended bet sizes which have an expected negative impact on the logarithm of ones bankroll and as such actively makes one’s life worse.
(e.g. the bet odds are at 25% but you believe there’s a 50% chance that it will resolve true then your edge is 100% (calculated properly, not using the method in the post as I’m not sure how to use that) and the post would suggest betting your entire bankroll. The correct Kelly calculation gives 1⁄3rd of your bankroll)
Without this correction I would strongly recommend against including this post in the review.
This is a useful clarification. I use “edge” normally to include both the difference in probability of winning and losing and the different payout ratios. I think this usage is intuitive: if you’re betting 5:1 on rolls of a six-sided die, no one would say they have a 66.7% “edge” in guessing that a particular number will NOT come up 5⁄6 of the time — it’s clear that the payout ratio offsets the probability ratio.
Anyway, I don’t want to clunk up the explanation so I just added a link to the precise formula on Wikipedia. If this essay gets selected on condition that I clarify the math, I’ll make whatever edits are needed.
So there’s a technical definition of edge which is your expected gain for every unit that you bet, given your own probability and the bet odds.
I agree that not clumping up the post is probably best but to make the post correct I suggest adding the underlined text into the definition in case people don’t click the link.
bet such that you are trying to win a percentage of your bankroll equal to your percent edge.
On the whole I agree with Raemon’s review, particularly the first paragraph.
A further thing I would want to add (which would be relatively easy to fix) is that the description and math of the Kelly criterion is misleading / wrong.
The post states that you should:
However the correct rule is:
(emphasis added)
The 2 definitions give the same results for 1:1 bets but will give strongly diverging results with other odds.
In addition the post gives a method of calculating one’s edge which gives correct results for 1:1 bets. It is not entirely clear how one would use the formula for non 1:1 bets but it doesn’t seem to indicate a calculation which would give one’s edge correctly. (55%-45%=10% doesn’t seem to readily generalise correctly in the same way that (55%-50%)/50%=10% does).
The post never states that the definition is only for 1:1 bets so the impression given by the post is that these formulae can be used in the cases given in the post. However there are no guarantees that any of the examples in the post are 1:1 bets.
(The post does mention that the example is based on 1:1 bets but it doesn’t imply that the calculation as given only works for such bets.)
As a result the post effectively ends up recommending making incorrectly sized bets. For non 1:1 bets it is possible to calculate recommended bet sizes which have an expected negative impact on the logarithm of ones bankroll and as such actively makes one’s life worse.
(e.g. the bet odds are at 25% but you believe there’s a 50% chance that it will resolve true then your edge is 100% (calculated properly, not using the method in the post as I’m not sure how to use that) and the post would suggest betting your entire bankroll. The correct Kelly calculation gives 1⁄3rd of your bankroll)
Without this correction I would strongly recommend against including this post in the review.
This is a useful clarification. I use “edge” normally to include both the difference in probability of winning and losing and the different payout ratios. I think this usage is intuitive: if you’re betting 5:1 on rolls of a six-sided die, no one would say they have a 66.7% “edge” in guessing that a particular number will NOT come up 5⁄6 of the time — it’s clear that the payout ratio offsets the probability ratio.
Anyway, I don’t want to clunk up the explanation so I just added a link to the precise formula on Wikipedia. If this essay gets selected on condition that I clarify the math, I’ll make whatever edits are needed.
So there’s a technical definition of edge which is your expected gain for every unit that you bet, given your own probability and the bet odds.
I agree that not clumping up the post is probably best but to make the post correct I suggest adding the underlined text into the definition in case people don’t click the link.