Joined: Sep 24, 2011
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June 11th, 2019 at 2:00:23 PM permalink
Quote: Wizard

You're absolutely right. Thank you for the correction.


You're missing the second right parenthesis just before the caret in this term:

(1 + (0.01*1)^(14/36)

Dog Hand
Joined: Oct 2, 2017
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June 13th, 2019 at 12:40:35 AM permalink
From the Kelly page:

“Example 2: A casino in town is offering a 5X points promotion in video poker. Normally the slot club pays 2/9 of 1% in free play. So at 5X, the slot club pays 1.11%. The best game is 9/6 Jacks or Better at a return of 99.54%. After the slot club points, the return is 99.54% + 1.11% = 100.65%, or a 0.65% advantage. The Game Comparison Guide shows the standard deviation of 9/6 Jacks or Better is 4.42, so the variance is 19.5364. The portion of bankroll to bet is 0.0065 / 19.5364 = 0.033%”

I got a slightly different answer using the simple Kelly formula.

Take (100.65 / 99.54)^2 * 19.5364 to get 19.8520 which is the variance (V) of the game including the promotion. Its return (R) is 1.0065. Its imaginary payoff on a “to 1” basis is V/R + R - 1 = 19.73034. So the optimal Kelly bet is the advantage of R - 1 divided by the payoff equals 0.000327422 of bankroll.
Last edited by: Ace2 on Jun 13, 2019
Joined: Jun 28, 2011
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June 20th, 2019 at 7:47:51 AM permalink
The whole reasoning behind the Kelly formula is based on three assumptions :
- independent trials.
- same game repeatedly.
- Infinite repetition .

If the repetition is finite, the formula includes a N factor (N=nb of repeats).
The calculus takes advantage of infinity, but also exact similaritiy of the trials, in order to progress towards the formula. In other cases, there is no demonstration. Only some unfounded confidence that it is « more or less » valid.

In the situation described here, it looks like a one-shot opportunity (if you consider the individual bets, each but the last have negative EV, so Kelly says Don’t Play). The Kelly criterion is designed to optimize long-term growth of your bankroll over time. Definitely not your objective: your goal is to not bankrupt before the last bet. So, better forget that formula and develop an optimization that is relevant to your objective.
Reperiet qui quaesiverit

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