Please Explain Equity
Craig Yannuzzi
moves. Why are the numbers negative with the highest number best?
Thanks in advance!
Gary Wong
> Can someone please explain how to interpret Equity numbers for various
> moves.
There is a precise definition of equity and some discussion on Backgammon
Galore at:
http://www.bkgm.com/gloss/lookup.cgi?equity
Another good description is this one by Robertie (_Advanced Backgammon_
vol 2, position 357):
"_Equity_ is a fundamental concept of backgammon, indeed of any game which
is a mixture of skill and chance. The equity of a position is the
average profit (or loss) that one would net, per game, by playing the
position to conclusion an infinite number of times. It is the `value'
of the position."
Equity may appear somewhat obscure at first, but it really is a very natural
way of measuring the strength of a position. The unit of measure is
"points per game" (ppg) which has a very intuitive interpretation: suppose
the cubeless equity in a particular position is estimated at -0.247. That
means we expect to lose 0.247 points per game -- if we played 1000 games
for $1 a point with no cube starting from that position, we would expect to
lose $247.
> Why are the numbers negative...
We all try very hard _not_ to make the numbers negative :-) Since one
player loses exactly as much as the other player wins (backgammon is a
"zero sum" game), if the equity is positive for one player then it will
be negative for the other. If the equity is positive then you're winning;
if it's negative then you're losing.
> ...with the highest number best?
The higher number is best simply because you expect to win more! Sometimes
I've seen posts arguing "a move isn't better because the equity is greater;
the equity is greater because the move is better", but I think it's pointless
trying to impose any cause and effect here. That would be like saying "You're
not taller than me because your height is greater; your height is greater
because you're taller than me." They are exactly equivalent; you can't
have one without the other; and if you try to separate the two then you're not
doing justice to either. As Robertie writes:
"...You are not, of course, mentally comparing two numbers; you are choosing
whichever position looks better. The process of your backgammon education
is properly linking `looking better' with `higher equity'."
Cheers,
Gary.
--
Gary Wong, Department of Computer Science, University of Arizona
ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/
bob100...@pacbell.net
> Craig Yannuzzi <clyan...@home.com> writes:
> > Can someone please explain how to interpret Equity numbers for various
> > moves.
>
> There is a precise definition of equity and some discussion on Backgammon
> Galore at:
>
> http://www.bkgm.com/gloss/lookup.cgi?equity
>
> Another good description is this one by Robertie (_Advanced Backgammon_
> vol 2, position 357):
>
> "_Equity_ is a fundamental concept of backgammon, indeed of any game which
> is a mixture of skill and chance. The equity of a position is the
> average profit (or loss) that one would net, per game, by playing the
> position to conclusion an infinite number of times. It is the `value'
> of the position."
[Remainder snipped]
I understand the concept of equity, but as a relative newcomer to the game, it's
not clear to me how in complicated, difficult positions you can determine equity
with any precision. Also -- a related issue in my mind -- exactly how does a
"rollout" determine which is the best move in a position? The answers would be
straight-forward if every position had only one obviously correct move, but then
there wouldn't be any need for rollouts.
To illustrate what I'm not understanding here: say I'm trying to determine
whether move A or move B is better in a given position. A couple moves later,
depending on the numbers that are rolled, I may then be confronted with another
difficult position where I have to choose between move C and move D. And still
later I may have to decide between move E and move F. All of this is in just one
sequence of rolls, and to do a rollout, I assume there will be numerous sequences
of rolls, each presenting a number of decisions to be made. How does all of this
get evaluated in order to determine equity? And how do you do a rollout without
being confronted with numerous judgment calls on what moves to play as the rollout
proceeds?
I hope I'm not being dense here. What am I missing?
--
Regards,
Bob Stringer
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