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Old 09-29-2017, 08:17 AM   #1
ajikavix
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Kelly Criterion question

If the win probability is 55% and the odds are +900.00 kelly says to bet $500, but if you enter odds of +2000.00 with the same probability of 55%, kelly says to only bet a extra $28 ($528). Why does kelly only increase the bet by $28 when the odds have doubled?

I would assume it takes into account some game day variables, but this seems weird if we are entering the correct true probabilities into the kelly calculator.
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Old 09-29-2017, 08:26 PM   #2
RustyBrooks
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Re: Kelly Criterion question

A kelly calculator should tell you what fraction of your bankroll to bet, not a dollar amount

I don't do sports betting, but does "+900" mean "If I bet 100 I profit 900"? i.e. the payout is 9:1?

f = (bp - q) / b
p is the probability of winning, here 0.55
q is the probability of losing, here 0.45
b is the payout in b:1 odds, here, if I understand properly, it's 9 in one case and 20 in the other

f1 = (9*.55 - .45) / 9 = 0.5
f2 = (20*.55 - .45) / 20 = .528

So yeah, it goes from suggesting you bet half your bankroll to 52.8% of your bankroll. I guess the deal here is that the payout is so astounding that the results get somewhat skewed. The most it will ever recommend you bet is 55% of your bankroll in this case, when b tends to infinity.

It should be kind of clear why - as b gets very large, you basically get
f = .55b / b
because q is very small compared to .55b
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Old 09-29-2017, 11:39 PM   #3
ajikavix
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Re: Kelly Criterion question

Quote:
Originally Posted by RustyBrooks View Post
A kelly calculator should tell you what fraction of your bankroll to bet, not a dollar amount
This calculator allows you to enter bankroll amount hence the dollar amount.

https://www.sportsbookreview.com/pic...ly-calculator/


Quote:
Originally Posted by RustyBrooks View Post
I don't do sports betting, but does "+900" mean "If I bet 100 I profit 900"? i.e. the payout is 9:1?
Yes


Quote:
Originally Posted by RustyBrooks View Post
The most it will ever recommend you bet is 55% of your bankroll in this case, when b tends to infinity.
OK, because that's weird as I read some articles where they said one could lose nearly their whole bankroll on a single bet, hmm.

Actually if I enter +100 or $2.0 decimal odds into all the online kelly calculators with a 99% probability of the bet winning, kelly says to bet 98% of your bankroll. Are these calculators over betting? Also why I posted the thread.
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Old 09-30-2017, 01:41 PM   #4
RustyBrooks
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Re: Kelly Criterion question

Sorry, to be clear, I mean that the highest fraction you can get is going to be your odds of winning, and that happens when the payout is extremely large. It's not 55% in general, it's 55% in your initial case because that were your odds of winning.

With 9:1 payout, you were already really close to 55%, which sort of "explains" why getting a bigger payout doesn't move the fraction much. It approach 55% asymptotically so the closer you are already to the max, the less an increase in payout moves the kelly fraction.

The calculators are doing no more, surely, than the formula I have given above, and as such are probably not very useful.

Lots of people consider using the full kelly fraction to be a bit of a roller coaster ride and will use a fractional kelly bet - like, whatever value of "f" you get, they might use f/2 or 2f/3 or something. This also helps a bit to compensate for when your estimate of your win chances is wrong - overbetting is worse than underbetting, so intentionally underbetting can keep you from accidentally overbetting.
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Old 09-30-2017, 02:01 PM   #5
ajikavix
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Re: Kelly Criterion question

thanks for explaining.
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