Save the gammon or stay back for a shot?
paulde...@att.net
Match ID : UQkOAIAAAAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| | | O O X O | OO 8 points
| | | O O O | OO
| | | O O | O
| | | | O
| | | | O
v| |BAR| |
| | | X |
| | | X |
| | | X X |
| | | X X X X X | Rolled 43
| | | X X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: user (Cube: 2)
Money play: checker play problem.
Thanks in advance for your suggestions and analysis.
Paul Epstein
David C. Ullrich
Seems clear that there's no win even if you do get
a shot, since you'll have a four-point board, O already
has seven men off and there's no way O can be forced
to leave a second blot. So the question is just
whether running or staying back maximizes the
chance of a gammon.
And it seems like your chance of saving the gammon
is _very_ good if you run, so I think it's clear you
should just run.
(Note I'm not saying I'm certain that running is
the best play. But I'm pretty confident that if
it's not the best play it's still clearly close enough
that you may as well just run and save your brain cells
for positions where the choice of play makes more difference:
Winning after staying back is not impossible, but it seems
so unlikely that it can't matter much. Similarly, even if
staying back increases your chance of saving the gammon(?)
it still seems clear that your gammon-saving chances are
high enough if you run that it can't matter much -
for example, decreasing your gammon chances from .02 to
.01 isn't really a big difference even though it looks
like a factor of 2, because .99 is so close to .98.)
Oops. Checking with gnu I see there's a third play
that I totally overlooked...
>Paul Epstein
************************
David C. Ullrich
paulde...@att.net
"There's no win". Perhaps my guess for X's winning chances would be
greater than yours.
Suppose it's DMP, what do you think X's winning chances are? [Even if
these chances happen to be much higher than you think, it doesn't
contradict your there's-no-win reaction because it may be the case that
the only way X can play for a win is by taking very high gammon risks.]
Anyway, I think the above is an interesting supplementary question.
I estimate X's winning chances at DMP to be around 5% (with no real
basis -- just a wild guess.)
Paul Epstein
Stick
One thing I believe most are overlooking here is that if you do break
the board and stay back with either play (5/1 5/2 or 5/1 4/1) you are
still a huge favorite to save the gammon even if you don't get a shot.
I'll stay back and try to get my shot, if no shot I run next turn.
Stick
paulde...@att.net
Stick, I would agree.
I hope I'm not gnuing this too early but gnu's play (eval, not rollout)
is to break contact and run. This really surprises me, as I don't
think X is ready to give up the game. Although X only has a 4 point
board immediately available, X can create a 5 point board at a later
stage, and O seems very likely to leave a shot.
Paul Epstein
David C. Ullrich
If you're ever in Stillwater let me know...
>and O seems very likely to leave a shot.
>
>Paul Epstein
************************
David C. Ullrich
David C. Ullrich
That's true.
>Anyway, I think the above is an interesting supplementary question.
>
>I estimate X's winning chances at DMP to be around 5% (with no real
>basis -- just a wild guess.)
Your estimate of X's winning chances is also greater than gnubg's.
I did a very fast low-setting rollout, having more important things
to do than wait for a more accurate one. Note that I overlooked
the play 23/20 5/1; from your comments to Stick it seems you did
too. Let's ignore that play, seems intermmediate between 23/16
and 5/2 51.
Summary:
23/165: P(X Win) = 0, P(X Lose Gammon) = .015
5/2 5/1: P(X Win) = .03, P(X Lose Gammon) = .119.
Staying all the way back increases winning chances by .03,
but it increases gammon chances by .104. The difference
in the gammon chance is _much_ greater than the difference
in the winning chance.
I don't see why a more accurate rollout would change the
chance of a gammon much; doesn't seem like there are going
to be many tricky decisions there. I suppose that it _could_
have a larger effect on the winning chances, maybe 2-ply
will change whether or not we slot a point or something.
But if a more accurate rollout changes the winning chances
so much that staying all the way back is better I'll be
amazed.
Looks to me like I was right that it's correct to abandon
the win, and also that it really doesn't make _much_
difference; an equity swing of -.035 counts as fairly
small by my modest standards - I'd rather worry first
about avoiding the -.1 errors...
1. Rollout 23/16 Eq.: -1.015
0.000 0.000 0.000 - 1.000 0.015 0.000 CL -1.015 CF -1.015
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.000]
Truncated cubeful rollout (depth 11) with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1037627207
and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
2. Rollout 23/20 5/1 Eq.: -1.049 (
-0.034)
0.008 0.000 0.000 - 0.992 0.068 0.000 CL -1.052 CF -1.049
[0.000 0.000 0.000 - 0.000 0.001 0.000 CL 0.001 CF 0.001]
Truncated cubeful rollout (depth 11) with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1037627207
and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
3. Rollout 5/2 5/1 Eq.: -1.050 (
-0.035)
0.030 0.000 0.000 - 0.970 0.119 0.001 CL -1.061 CF -1.050
[0.000 0.000 0.000 - 0.000 0.001 0.000 CL 0.001 CF 0.002]
Truncated cubeful rollout (depth 11) with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1037627207
and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
4. Rollout 5/1 4/1 Eq.: -1.070 (
-0.054)
0.024 0.000 0.000 - 0.976 0.126 0.001 CL -1.078 CF -1.070
[0.001 0.000 0.000 - 0.001 0.001 0.000 CL 0.001 CF 0.002]
Truncated cubeful rollout (depth 11) with var.redn.
1296 games, Mersenne Twister dice gen. with seed 1037627207
and quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
David C. Ullrich
>
>One thing I believe most are overlooking here is that if you do break
>the board and stay back with either play (5/1 5/2 or 5/1 4/1) you are
>still a huge favorite to save the gammon even if you don't get a shot.
True. But in deciding which play is better the _difference_ between
the gammon chances with the two plays is what matters. What do you
estimate the difference to be?
>I'll stay back and try to get my shot, if no shot I run next turn.
>
>Stick
************************
David C. Ullrich