zoomie: Question for Math / Stat Experts

[zoomie]

It seems to me that all of our probabilistic analysis involving std dev, variance, RoR etc. presumes that BJ (or SP21) outcomes follow a normal distribution. Has that been confirmed? I ask because back when I was a finance student a U of Chicago professor published a paper arguing that stock price changes are not distributed normally, that instead that distribution has thicker tails than normal. Sometimes the high variance of BJ/SP21 makes me think of that paper . . . TIA for the answer to this one.

[Norm Wattenberger]

First, I believe BJ is far less prone to outside forces than the stock market. I've programmed 62 different financial market technical analyses methods and find them wildly contradictory. But this certainly does not mean that risk of ruin methodologies don?t fit financial markets.

Probabilistic analyses are always estimates. And I agree that they tend to ignore particular exact circumstances. That is, they are not exact models. But the confirmation you are looking for is in Blackjack Attack. Chapter 8 of Blackjack Attack provides several tables giving risk results based on both equations and simulation. The conclusion is that in most circumstances they are reasonably close. The more extreme the situation the less accurate. But for the common cases, the formulae give quite acceptable results.

> It seems to me that all of our probabilistic analysis
> involving std dev, variance, RoR etc. presumes that BJ
> (or SP21) outcomes follow a normal distribution. Has
> that been confirmed? I ask because back when I was a
> finance student a U of Chicago professor published a
> paper arguing that stock price changes are not
> distributed normally, that instead that distribution
> has thicker tails than normal. Sometimes the high
> variance of BJ/SP21 makes me think of that paper . . .
> TIA for the answer to this one.

[Don Schlesinger]

The question you ask involves whether, in addition to the mean and the standard deviation, we need to concern ourselves with the third and fourth moments of a distribution -- that is with skew and kurtosis. And, the simple answer for blackjack is no.

The financnial markets are, indeed, different, where stock prices are lognomally distributed, not normally distributed, and where, in addition, the phenomenon of leptokurtosis, or fat tails, is indeed found.

Don