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## [Bug-gnubg] EMG article

 From: Jeremy Bagai Subject: [Bug-gnubg] EMG article Date: Thu, 06 Dec 2007 10:35:13 -0800

Hi all;
Hi Max,

Thanks for providing the link to my paper:

Hi all,
you can find here an interesting article on EMG (Equivalent to Money Game) equities.

http://www.fortuitouspress.com/emg.html

I had posted to GammonU and was about to post here but you beat me to it.  Thanks also for your introduction and summary of the issue.  I hope people on this list get interested in the problem.

I've made a suggestion which wouldn't be too complicate to put in place:

1- let's call W1/2/3 (L1/2/3) the MWC at the scores of a single/gammon/backgammon win (loss)
respectively. They are associated to NE (Normalized Equities)of +1/2/3 (-1/2/3) respectively.
The six points [L3,-3], [L2,-2], ... , [W3,+3] form a poly-line with 5 segments (at most,
at some scores two point may be identical because gammons/backgammons may not count).

2- draw the poly-line, then use it to convert MWC to NE.

It's like having a different interpolation depending on the magnitude of the error you're
trying to normalize.

Three examples:

- I'm leading 3-0 to 5 cube at 1, what can happen ? With a simple/gammon/backgammon win I go
to 4-0/5-0/5-0 while with a simple/gammon/backgammon loss I go to 3-1/3-2/3-3.

- I'm leading 4-1 to 5 post-Crawford (I owe the cube at 2), what can happen ? With a simple/
gammon/backgammon win I go to 5-1/5-1/5-1 while with a simple/gammon/backgammon loss I go to
4-3/4-5/4-5.

- I'm leading 3-0 to 5 owing the cube at 2, what can happen ? With a simple/gammon/backgammon
win I go to 5-0/5-0/5-0 while with a simple/gammon/backgammon loss I go to 3-2/3-4/3-5.

In any of the above situation, just associate the w/wg/wb scores with NNE +1/+2/+3 and the
l/lg/lb scores with NNE -1/-2/-3, reads the MWC of the different scores from your favourite
MET, put the points on a graph and draw the poly-line (attention: in some cases you have to
use post-Crawford METs).

Upside:
- it solves the issue above: all the 3 errors wil have the same normalized equity
- for "small errors" (leading to MWC that are in the interval [single loss, single win]),
my suggestion would return the good old EMG.

Can you please provide a full numerical example of your proposal?  You say that "it solves the issue above:  all the 3 errors wil have the same normalized equity," but you don't say what that equity will be.  Can you show the calculation?

Thanks very much,

Jeremy Bagai

____________________________________

Jeremy Bagai

415 308 5958