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

[Alain Redlinger]

Hi Misja,

May be in the position you indicated:
        23YHAEC/AQAAAA:8IloACAACAAA  score -1c, -2
        23YHAEC/AQAAAA:cIloABAACAAA  score -2, -2  
I could not see any difference in Win, gW in the Hint window at the two 
different scores simply because the recommend move (highest
equity) is the same for both scores ***on my machine***, contrary to what you 
said (play safe at -2,-2; gammon go at -1c,-2).
I find this a little bit annoying. How comes?
Nevertheless, as I said, I think your reasoning is correct (and thank you again 
for the explanation). 

So I took another position from W. Trice's, Backgammon Boot camp, where the 
right play is clearly dependent on the score:


The score is: GnuBG 1, Alain 4 (match to 5 points), Crawford game
Alain to play 61

    GNU Backgammon  Position ID: BgAA2LYbEAABAA
                    Match ID   : 8AmnABAAIAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: GnuBG
OOO | X  O             |   |                X |  1 point
OOO |    O             |   |                  |  
OOO |                  |   |                  |  
 OO |                  |   |                  |  
 OO |                  |   |                  |  
    |                  |BAR|                  |v 5 point match (Cube: 1)
    |                  |   |                  |  
    |                  |   |                  |  
    |             X    |   |                  |  
    | X  X  X  X  X  X |   |                  |  Rolled 61
    | X  X  X  X  X  X |   |                  |  4 points
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Alain
Pip counts: O 4, X 84


The best move at this score is 13/6. If loosing a backgammon, the match will be 
decided at the next game at -1,-1. If loosing a
gammon, the match will also be decided at the next (post Crawford) game at 
score -1, -2, may be after a free drop. So there is no
penalty for risking a backgammon in order to try to save the gammon (about a 9% 
chance) and play the next game at -1,-3 with a 70%
MWC.
Of course at -1c,-2, X should play safe, 24/18, 13/12 to avoid loosing the 
match by losing a backgammon, and retaining a slight
chance of saving the gammon if rolling 66.

Then I followed your idea of building a position leading to this one. I get 
this one:

The score is: GnuBG 4, Alain 1 (match to 5 points), Crawford game
Match Information:

Move number 5:  Alain to play 36

    GNU Backgammon  Position ID: 23YDAiA2AAAAAA
                    Match ID   : 8Im5AEAACAAA
    +24-23-22-21-20-19------18-17-16-15-14-13-+  O: GnuBG
    | O  O  O  O  O  O |   |                  |  4 points
    | O  O  O  O  O  O |   |                  |  
    |             O    |   |                  |  
    |                  |   |                  |  
    |                  |   |                  |  
    |                  |BAR|                  |v 5 point match (Cube: 1)
 XX |                  |   |                  |  
 XX |                  |   |                  |  
 XX |                  |   |                  |  
 XX |    X  X          |   |                  |  Rolled 36
XXX | O  X  X          |   |                O |  1 point
    +-1--2--3--4--5--6-------7--8--9-10-11-12-+  X: Alain
Pip counts: O 84, X 10

At this score, the only possible move has the following W/L chances 

   1. Cubeful 2-ply    3/off(2)                     Eq.:  +2,021
       0,987 0,928 0,682 - 0,013 0,000 0,000
        2-ply cubeful prune [world class]



But if in the same position I change the score to -1c, -3, the W, Wg etc. 
change to:

   1. Cubeful 2-ply    3/off(2)                     Eq.:  +1,420
       1,000 0,986 0,182 - 0,000 0,000 0,000
        2-ply cubeful prune [world class]

And I can get these figures without rollouts.
Thanks for your help.
Alain 


-----Message d'origine-----
De : Misja Alma [mailto:address@hidden 
Envoyé : dimanche 28 juin 2009 10:39
À : Alain Redlinger
Cc : address@hidden
Objet : Re: [Bug-gnubg] Bearoff dB position, few questions

Hi Alain,

The position was an example of how the matchscore could influence
checkerplays and therefore also GWC; it is true that the same move
will give the same Win, gW etc for every score, but the point was that
at different scores a different move was correct.
So if you would go back in time to one roll before the position was
reached, you would find that the position itself would have different
Win, gW etc for different scores too.
So in the example, place two extra checkers on the 2 point and ask gnu
how to play 3-2 (not really a difficult problem ;)
You'll see that the only possible move gives different Win and gW
depending on the score.

Cheers,
Misja

On Sun, Jun 28, 2009 at 1:03 AM, Alain
Redlinger<address@hidden> wrote:
> 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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>>
>>
>
>
>