Thread: Risk of Ruin
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Old 07-24-2005, 11:04 PM
jason1990 jason1990 is offline
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Join Date: Sep 2004
Posts: 205
Default Re: Risk of Ruin

I voted for the fifth option, but it probably should have been worded differently. No one can know their RoR exactly because (1) the formulas for RoR are based on models that incorporate simplifying assumptions, and (2) no one can "exactly" know their true winrate and standard deviation (SD).

I've brought this up before, but it's been a while, so I'll bring it up again. We all are well-versed in sample size requirements for winrate. But what about SD? In Mason's essay, Computing Your Standard Deviation, he says

[ QUOTE ]
A good rule of thumb is to have at least 30 observations (playing sessions) for the estimate to be reasonably accurate.

[/ QUOTE ]
It's true that 30 observations are going to give you a pretty accurate confidence interval for your winrate. (I don't mean a small interval, just one whose size accurately corresponds to the given degree of confidence.) The confidence interval for your winrate should ideally be built using your true SD. But in practice, you must use your estimated SD, which is going to have an error. How different is the confidence interval which uses the estimated SD from the confidence interval which uses the true SD? Well, with 30 observations, it's not going to be much different. But it is not because your estimated SD is close to your true SD.

When I started in nano-limits, I did some analysis of my SD. After about 40 sessions, I had an estimated SD of 21 BB/100, but a 95%-confidence interval for my SD was [17,29].

So 30 sessions is plenty if all you want to do is build a confidence interval about your winrate. But it is not enough if you want to get close to your true SD. And accurately estimating your true SD is what you need to do to compute RoR. (Of course, it may be harder to get close to your true winrate, which you also need for RoR, but at least you can try to get one statistic nailed down.)
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