Kasey: Something I don't understand about DI

[Kasey]

One thing I have learned above all others from BJA, it that EV alone is not the most important factor in evaluating a game or method of play. Rather, it is the relationship between risk and EV, in this case stated as DI.

Since DI increases as standard deviation decreases, it seems to me that any method of play with a positive EV and a standard deviation of 0 would be a very good game!

If this is true (big if!), why is Insuring a natural not the preferred play? Insuring a natural has a positive EV with a standard deviation of zero. My simulator is too simple to calculate the standard deviations, but I'm sure never Insuring (as in BS) or Insuring according to the count must have a standard deviation of greater than zero.

So it seems to me the DI for Insuring a natural must be much greater than the alternatives.

What have I missed?

Thank you!

[Don Schlesinger]

> What have I missed?

Automatically insuring a natural (assuring "blindly," irrespective of the count) makes no more sense than making any incorrect play that forfeits too much EV for the variance reduction it gains. The tradeoff is always between the EV sacrificed by making the apparently "wrong" play, and the commensurate reduction of variance that accompanies the "departure."

So, we examine the certainty equivalent to discover how much we can change an index, in the name of risk aversion. This, in turn, is a function of the spread we're using and the "volatility" of the play -- that is, how much the EV changes for each true count. That volatility is linear for insurance, and is rather large, so insuring at any index appreciably below the correct one just doesn't make sense.

Don

[Kasey]

> Automatically insuring a natural (assuring
> "blindly," irrespective of the
> count) makes no more sense than making any
> incorrect play that forfeits too much EV for
> the variance reduction it gains.

I'm going to make it a project to work out the math by hand. It'll be fun!