[pzhon]

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here is a post i made a while back on the topic, with some discussion that went on.

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Would you care to summarize what you think that discussion accomplished? I don't think it made the progress you think it made.

You mentioned,
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this is nowhere close to the suggested 100 buy-ins: definitely RoR has plenty to do with that.

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No, it doesn't. Risk of ruin is not a separate consideration. It's easy to translate a proportional guideline to a ROR value if you stay at a fixed level, e.g., Kelly corresponds to a ROR of about e^-2 ~ 14%, and half-Kelly is about e^-4 ~ 2%. You can't blame the the tremendous discrepancy on a rational consideration of ROR.

100 buy-ins is a figure used out of context. Similarly, it is grotesquely inaccurate for the SSNL FAQ to suggest that you should have $100 to play NL $0.01-$0.02 on PokerStars just because there is a $5 buy-in. This ignores the fact that it is much harder to lose a 250 BB buy-in than a 100 BB buy-in, and that most penny-ante players hate money so serious players' win rates are ridiculously high compared with other stake levels. When people apply the 20 buy-ins rule out of context, they sit out until grossly overbankrolled for soft games, and but play while dangerously underbankrolled for tough games.

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scroll down to the revision i made a few posts down.

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Was the revision particularly concise and accurate? How does it compare with c * SD^2/ROI?

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there is also some good discussion there from some folks overseas on using exact finish distributions to better understand the variance involved.

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Do you mean the comment that the exact finish distribution has a very small effect? Paxinor wrote, "the difference is really really small so it won't matter." So, why bring it up?

With very skewed distributions, like +EV video poker with a large jackpot, the normal approximation is not good. You need a slightly smaller bankroll when the positive tail is thick, such as when you can win a jackpot. You need a slightly larger bankroll when the negative tail is thick, such as when you may have to pay out a jackpot. This isn't particularly relevant to SNGs.

To worry you that the recommended bankroll level might be too high by a few percent, you should have astoundingly accurate estimates elsewhere, particularly of your ROI (which should be known more accurately than 1%) and know exactly which Kelly fraction you are using (within a few percent). Others are worrying about getting the right bankroll within a factor of 2.

You also wrote,
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yes of course, roi is not constant. you don't need a more complex formula.

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You need to think about that more. Of course you need a more complicated formula when the ROI is level-dependent. In general, this says that you should play at levels where the fractional Kelly system you prefer would say that you are overbankrolled.

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it's good to see in the article the author used finish distributions, as this gives a little bit more info than using just ROI & ITM.

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The article failed to use the finish distribution properly, as mentioned in the note at the bottom. So, what was the point?

You get very little from using the finish distribution, ROI, and ITM that you don't get from the far simpler ROI + a simple estimate of 1.7 buy-ins for the standard deviation. The latter gives you a simple, applicable formula. The former is an invitation to make many types of errors.

Some people find complicated formulas and page-filling tables of values aesthetically pleasing. As a mathematician and theoretician, I don't, and I maintain that you aren't getting an increase in accuracy from the additional factors you want to include that can justify a huge increase in complexity over Kelly's c * SD^2/WR.