Forum Archive : Terminology


From:   Michael J. Zehr
Address:   michaelz@michaelz.com
Date:   15 June 1998
Subject:   Re: JellyFish "equity" and "volatility" evaluations: explain please.
Forum:   rec.games.backgammon
Google:   3585CFF4.89731E4@michaelz.com

Leo Bueno wrote:
> Could someone please explain the meaning and use of JellyFish's
> "volatility" and "equity" evaluations, particularly with respect to
> cube decisions?
> Thanks.

Tom Keith's glossary covers equity
(http://www.bkgm.com/gloss/lookup.cgi?equity) as pointed out by Claes
Thornburg, but it doesn't give a rigorous definition volatility.

JF uses the variance of equity as volatility.  For each of the 36 rolls
(21 unique rolls, but the non-doubles count twice in the equation) find
the equity resulting from the making the best move.  Find the equity
change for each move, square that, and add them all up, divide by 36 and
take the square root of that.

This is similar to the concept of market losers.  When you count market
losers you count the number of rolls with a positive equity swing
greater than some constant (the difference between the cash point and
your current equity).  For those that exceed this value you count 1, for
those that don't you count 0.

Volatility is similar except that every roll contributes something to
the variance with the ones that cause the greatest equity swing
contributing the most.

It's useful because for some positions one can get an approximate
double/no-double decision by calculating aE + bV (where E and V are
Equity and Volatility, a and b are factors) and doubling if the result
is greater than some constant.  (a, b, and the constant are left as
exercises for the reader.... though E+V > .60 means an almost certain
double in non-gammon, non-contact races.)

It's been written that if you're close to your cash point, a few market
losers is enough to make it a double; if you're farther away, you need
more market loser (see, among other sources Bell, "Winning with the
Doubling Cube," Gammon Press).

The formula above is mathematical way of saying that.  The more market
losers you have ("cashers" in the references source) and the bigger they
are, the greater V.  So if you're close to your cash point (E is .55)
then a few market losers (V >= .05) is enough to make it a double.  If
you're far from your cash point (E is .40) then you need many big market
losers (V >= .20) to make it a double.

[E + V > .6 is a simplified version of a more accurate formula.  But
there is no linear function of E and V that says whether or not to
double with 100% accuracy, even for very simple races.  Remember that
while neural nets might get V accurate, they don't do so well a job on E
(Snowie and JF sometimes disagree by .2 on equity, even if they both
agree on the best play in a position).  Furthermore, many doubles based
on this formula are easy takes, so while in theory it might be correct,
in practice it might be better to wait and give your opponent a tougher
decision to make.]

-Michael J. Zehr
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