RE: [Bug-gnubg] Bearoff dB position, few questions

[Alain Redlinger]

Thank you for your answers Misja and Massimiliano. 
I'll answer Misja whose point is more developed.
Although not an advanced player, I am aware of Gammon Go / Gammon Save 
strategies, a GG move for example being a move of higher
equity, but not of highest GWC. 
My question was whether the "Win, Wg, Wbg, Loose, Lg, Lbg" figures in the hint 
box were independent of the score, and what were they
exactly?

If I take your position Misja, having Gnubg at the predefined settings supremo 
for checker and worlclass for cube decision
(evaluation). If I ask for a Hint at both scores, I get these.

-1c, -2

 GNU Backgammon  Position ID: 23YHAEC/AQAAAA
                 Match ID   : 8AllACAACAAA

1. Cubeful 0-ply    2/1 2/off                    Eq.:  +1,579
       0,993 0,297 0,001 - 0,007 0,000 0,000
        0-ply cubeful prune [expert]
    2. Cubeful 0-ply    2/off 1/off                  Eq.:  +1,257 ( -0,322)
       0,872 0,256 0,002 - 0,128 0,000 0,000
        0-ply cubeful prune [expert]

-2, -2

 GNU Backgammon  Position ID: 23YHAEC/AQAAAA
                 Match ID   : cAllABAACAAA

    1. Cubeful 2-ply    2/off 1/off                  Eq.:  +1,367
       0,867 0,323 0,003 - 0,133 0,000 0,000
        2-ply cubeful prune [world class]
    2. Cubeful 2-ply    2/1 2/off                    Eq.:  +1,330 ( -0,037)
       1,000 0,188 0,001 - 0,000 0,000 0,000
        2-ply cubeful prune [world class]


These figures are hard to compare, because one is 0-ply, the other 2-ply.
So I made rollouts. 

***  Rollouts  ***
__________________________

-1c, -2

 GNU Backgammon  Position ID: 23YHAEC/AQAAAA
                 Match ID   : 8AllACAACAAA

    1. Rollout          2/off 1/off                  Eq.:  +1,384
       0,875 0,317 0,006 - 0,125 0,000 0,000 CL  +1,384 CF  +1,384
      [0,001 0,001 0,001 - 0,001 0,000 0,000 CL   0,002 CF   0,002]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 862030641 and 
quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
    2. Rollout          2/1 2/off                    Eq.:  +1,362 ( -0,021)
       1,000 0,181 0,001 - 0,000 0,000 0,000 CL  +1,362 CF  +1,362
      [0,002 0,002 0,000 - 0,002 0,000 0,000 CL   0,004 CF   0,004]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 862030641 and 
quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]



-2, -2

 GNU Backgammon  Position ID: 23YHAEC/AQAAAA
                 Match ID   : cAllABAACAAA

1. Rollout          2/off 1/off                  Eq.:  +1,404
       0,875 0,317 0,006 - 0,125 0,000 0,000 CL  +1,306 CF  +1,404
      [0,001 0,001 0,001 - 0,001 0,000 0,000 CL   0,002 CF   0,004]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 862049290 and 
quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
    2. Rollout          2/1 2/off                    Eq.:  +1,319 ( -0,085)
       1,000 0,182 0,001 - 0,000 0,000 0,000 CL  +1,319 CF  +1,319
      [0,001 0,002 0,000 - 0,001 0,000 0,000 CL   0,003 CF   0,003]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 862049290 and 
quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]


You see that the "Win, Wg, Wbg, Loose, Lg, Lbg" figures given for each move are 
the *same* for the same moves, *independently* of
the score, (-1c, -2) or (-2,-2)!

So what are the "Win, Wg, Wbg, Loose, Lg, Lbg" figures given for each move? 
Are they Money Game Winning chances?
Is match winning chance / Match equity computed from these by some formula such 
as: 
MWC = Win*T(i-1,j) + Wg*T(i-2,j) + Wbg*T(i-3,j-3) + Loose*T(i,j-1) + 
Lg*T(i,j-2) + Lbg*T(i,j-3), at score i-away, j-away, with T the
MET ?

Best regards
Alain


-----Message d'origine-----
De : Misja Alma [mailto:address@hidden 
Envoyé : samedi 27 juin 2009 12:41
À : Massimiliano Maini
Cc : address@hidden; address@hidden; address@hidden
Objet : Re: [Bug-gnubg] Bearoff dB position, few questions

Here's an example of a position that has different GWC depending on
the matchscore:

 GNU Backgammon  Position ID: 23YHAEC/AQAAAA
                 Match ID   : 8AllACAACAAA
 +13-14-15-16-17-18------19-20-21-22-23-24-+     O: gnubg
 |                  | O | O  O  O  O  O  O |     2 points
 |                  |   | O  O  O  O  O  O |
 |                  |   | O  O             |
 |                  |   |                  |
 |                  |   |                  |
v|                  |BAR|                  |     3 point match (Cube: 1)
 |                  |   |                6 | X
 |                  |   |                X | X
 |                  |   |                X | X
 |                  |   |             X  X | XX  Rolled 21
 |                  |   |             X  X | XX  1 point
 +12-11-10--9--8--7-------6--5--4--3--2--1-+     X: misja

I hope it is still readable :)
The point is that O is on the bar and X is bearing off:
At the given score, trailing 1-2 crawford, X should sacrifice about
13% winning chances to win 14% extra gammons and play 2/off 1/off.
Would the score have been 2-2 then X should of course play safe, for 100% GWC

Misja

On Fri, Jun 26, 2009 at 4:35 PM, Massimiliano
Maini<address@hidden> wrote:
>
> address@hidden wrote on 26/06/2009
> 15:34:56:
>
>> About the side question (purely theoretical)
>>
>> I think that there are many different equities and winning chances
>> implied in match play. If we want to keep things clear, the GWC
>> ***should *** not depend on the score. What has the match score to
>> do with the possibilities that a given position leads or not to
>> winning the game where it occurs? Clearly nothing.
>> It is absolutely necessary here to distinguish between Match Winning
>> Chance (win or loose) and Game Winning Chances (win/loose
>> simple, gammon, backgammon).
>
> Win/lose may be the same across different scores, but for sure gammon
> and backgammon percentages are not.
>
>> I would find it ***very*** helpful, at least for a beginner like
>> myself that would also like to have a theoretical perspective on
>> the game and/or software, if in the different dialog boxes of GnuBG,
>> it had been made explicit whether, in match play, the term
>> “equity” refers to match equity or the current game equity (as if it
>> were a money game). Currently my understanding is that money
>> game equity is completely irrelevant to match play, and that in a
>> match situation, in every window, the term equity refers to match
>> equity (even if expressed as NEMG), except when explicitly otherwise
>> mentioned.  Am I wrong about this?
>
> For match, the real thing is MWC.
> Conversion of MWC into EMG equities is done only for the purpose of
> providing an estimation of the magnitude of the gap betwen two plays
> in a manner that it is as independent as possible from the match score.
>
> A 1% MWC error at 0-0 to 15 could easily be a 10% error at double match
> point. On the other hand, the normalization to EMG equities will make
> the two errors similar in magnitude.
>
> MaX.
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