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A comment on Kelly Criterion. Parent comment

Re:Kelly Criterion by jfengel on Friday April 16, 2021 @12:31PM (#26835970)
Did they know that it was biased towards heads? With only a 60-40 split I probably wouldn't notice it unless I was actually keeping track, which could take a while. A 6-4 split on 10 tosses doesn't tell you anything. If you told me it was a fair coin and I thought the experiment was about something else, it might take a very long time before it occurred to me to test the hypothesis that the coin wasn't fair.

If they knew it was biased... I'm sure there's an optimal strategy, but a simple strategy would be "bet half of what you have on heads every time". Any idea how much worse that is than the optimal strategy?

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Re:Kelly Criterion by kqr on Friday April 16, 2021 @12:36PM (#26836038)
You can plot

g = 0.6 log (1 + 2f) + 0.4 log (1 - f)

And locate f=0.5 and compare to the maximum g.

Edit: I wanted to check my intuition so I did: https://www.wolframalpha.com/input/?i=plot++0.6+log+%281+%2B...

Looks like 0.5 is a slight overbet, but still very, very good.

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Re:Kelly Criterion by seoaeu on Friday April 16, 2021 @01:48PM (#26836984)
> Did they know that it was biased towards heads?

"Prior to starting the game, participants read a detailed description of the game, which included a clear statement, in bold, indicating that the simulated coin had a 60% chance of coming up heads and a 40% chance of coming up tails."

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Re:Kelly Criterion by tedunangst on Friday April 16, 2021 @01:13PM (#26836557)
If only there was a link to the study so we could see how it was setup.
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