Re: [Bug-gnubg] Gnubg - Snowie error rate comparison

[jorma kala]

Hi,

I have been re-reading your  very clear mail about error calculation in gnubg.
If I  understand correctly, the total error is the sum of the EMG
equity difference of all suboptimal moves divided by the number of
unforced moves.
For instance, if you make 10 errors in a match, each error's equity
difference being 0.1, and the match contains 100 unforced moves, the
total error rate would be:
0.1 *10 / 100 = 0.01

But this seems a very small number,considering that 10 big errors have been commited.
Am I missing something, is this computation multiplied by some other factor?

Thanks  a lot.

On 11/14/07, jorma kala <address@hidden> wrote:

Thanks a lot for the very clear explanation.

On 11/13/07, Massimiliano Maini <address@hidden > wrote:

> On 11/13/07, jorma kala <address@hidden> wrote:
> Hi,
> how is the total error rate and the per move error rate exactly calculated?
> Is it just the average difference in MWC of each unforced move with
> respect to the MWC of the optimal move?
> Thanks.
> jorma

Hi Jorma,

I'll try to explain, somebody with better insight please correct if wrong.

Errors are measured in terms of equity difference of your move with respect
to the optimal move (according to the currelt level of play, e.g. world
class).

If you don't normalize the equities, the same error could have a different
magnitude depending on the cube value (for money sessions) or depending on
the cube value and the score (for matchplay).
Thsi is of course inconvenient, hence the normalization.
In money games, it's enought to ignore the value of the cube.
For matchplay it's a bit more complicate since you have to consider the
match equity table and EMG (Equivalent to Money Games) equities are used.
They are computed by linear interpolation (and extrapolation) against the
value of a simple win and the value of a simple loss (assumed to be +1 and
-1) at the current cube value. They are described here :
        http://www.bkgm.com/gloss/lookup.cgi?equivalent+to+money+game+equity

Example: at some point in a match you have exactly 50% mwc. A simple loss costs
you -15% mwc (this is a normalized equity of -1) for 35%mwc, and a simple win
gives you +15% mwc (this is a normalized equity of +1) for 65% mwc.
Now you can draw a line between the points (35%,-1) and (65%,+1) to obtain the
conversion between mwc and EMG equities.
An error that costs you 7.5%mwc will correspond to ((+1-(-1))/(65%-35%)) * 7.5% =
(2/30%) * 7.5% = 0.500: this means that this error was half bad as losing the
whole game.

In general, an error with an EMG equity of 0.100 (quite a big one) will
correspond to a small error in terms of mwc (e.g. 0.1%) in the very first
games of a long match (e.g. 0-0 to 21 pts) but the same EMG equity of 0.100
could well correspond to 5% or more in the last game of a match (e.g. double
match point).

The total error is just the sum of all the individual errors.
As explained by Christian then, the per move error (rate) is cumputed
dividing the total value by the number of unforced moves (this is specific
to gnubg, Snowie divides by the number of moves, forced and unforced).

Because of that, the gnubg error rate is more severe than the Snowie one
(i.e. higher).

MaX.