3a 5a bearoff against 31 backgame

[Walt]

XGID=-bCbDB-------------acacab-:1:-1:1:22:2:0:0:5:10

X:You O:O
Score is X:2 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | X X O X O |
| | | X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 32 O: 130 X-O: 2-0/5
Cube: 2, O own cube
X to play 22

What's your play and why?

//Walt

[Bradley K. Sherman]

Walt <walt_...@yahoo.com> wrote:
>Score is X:2 O:0 5 pt.(s) match.
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | | | O O O O O O | +---+
> | | | O O O | | 2 |
> | | | O O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X |
> | | | X X |
> | | | X X O X O |
> | | | X X O X O |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+

>Pip count X: 32 O: 130 X-O: 2-0/5, X to play 22

I would play 4/off(2).

I believe that stacking checkers up on the 2pt is a good
thing in this position, and won't be surprised if XG says
that's the way to play it but it feels wrong to me, and
having 8 off rather than 6 off seems significant.

--bks

[badgolferman]

I play 4/off (2). On my next roll I want the 4-point available for the
inevitable die roll of 1.

[Tim Chow]

It looks like there might be a win/gammon tradeoff here, so let's
compute X's gammon value on a 2-cube. If X wins a single, he'll have
84% MWC. If he loses a single, he'll have 50% MWC. If he wins a
gammon, he wins the match. So his gammon value is 16/34, which is
basically normal. Of course X can't lose a gammon.

I can't believe that 4/off 2/off(2) is correct, so the real choice is
between 4/off(2) and 4/2(4). Let's count immediate blotting rolls
after each play. After 4/off(2), 64 62 54 52 43 41 32 21 blot; that's
16 blotting rolls. After 4/2(4), 64 62 61 54 52 51 43 41 32 31 21
blot; that's 22 blotting rolls. The only merit of 4/2(4) seems to be
that if X then clears the 5pt successfully, his future blotting danger
is diminished. But it looks to me that 4/off(2) wins more gammons
*and* games. 4/off(2) it is.

---
Tim Chow

[Walt]

I think everyone is surprised by this one. XG says stack 'em up on the 2
point, and it's not close. This appears to be a match score thing,
since the money play is to take two off (at 7a 7a, XG also says take two
off) . Stacking them up wins more games and gammons for both money and
AtS, but ripping two wins significantly more backgammons (which are
meaningless AtS) I'm also suspicious that there may be a "desparation
recube" when O realizes that almost all losses are gammons, but she
still has some wins.

I was thinking that perhaps O's abberant homeboard structure was a
factor, but smoothing it out doesn't change the play (although it makes
taking two off less of an error.)

Even giving O a great board and lots of timing doesn't change things
(variant 2)




1. Rolloutš 4/2(4) eq:+0.986
Player: 80.58% (G:60.37% B:29.53%)
Opponent: 19.42% (G:0.00% B:0.00%)
Confidence: ą0.009 (+0.977..+0.994) - [100.0%]
Duration: 7 minutes 17 seconds

2. Rolloutš 4/Off(2) eq:+0.897 (-0.088)
Player: 79.16% (G:55.51% B:37.37%)
Opponent: 20.84% (G:0.00% B:0.00%)
Confidence: ą0.011 (+0.887..+0.908) - [0.0%]
Duration: 5 minutes 09 seconds


š 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller


eXtreme Gammon Version: 2.03, MET: Kazaross XG2


//////////////Money play///////////////////////////////////

XGID=-bCbDB-------------acacab-:1:-1:1:22:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver

+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | X X O X O |
| | | X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 32 O: 130 X-O: 0-0

Cube: 2, O own cube
X to play 22

1. XG Roller++ 4/Off(2) eq:+1.301
Player: 80.79% (G:58.00% B:17.44%)
Opponent: 19.21% (G:0.00% B:0.00%)

2. XG Roller++ 4/2(4) eq:+1.268 (-0.033)
Player: 81.62% (G:61.14% B:8.94%)
Opponent: 18.38% (G:0.00% B:0.00%)



eXtreme Gammon Version: 2.03


//////////////variant//////////////////////


XGID=-bCbDB-------------abbbbb-:1:-1:1:22:2:0:0:5:10

X:Player 1 O:Player 2

Score is X:2 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O O | +---+

| | | O O O O O | | 2 |

| | | | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | X X O X O |
| | | X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 32 O: 128 X-O: 2-0/5

Cube: 2, O own cube
X to play 22

1. XG Roller++ 4/2(4) eq:+0.768
Player: 75.23% (G:53.89% B:21.66%)
Opponent: 24.77% (G:0.00% B:0.00%)

2. XG Roller++ 4/Off(2) eq:+0.735 (-0.033)
Player: 75.57% (G:49.51% B:29.26%)
Opponent: 24.43% (G:0.00% B:0.00%)

3. 2-ply 4/Off 2/Off(2) eq:+0.241 (-0.526)
Player: 62.50% (G:34.88% B:13.40%)
Opponent: 37.50% (G:0.00% B:0.00%)

4. 1-ply 4/2(2) 4/Off eq:+0.170 (-0.598)
Player: 60.13% (G:35.17% B:7.89%)
Opponent: 39.87% (G:0.00% B:0.00%)


eXtreme Gammon Version: 2.03, MET: Kazaross XG2

/////////////////////variant 2////////////////////////////


XGID=-bCbDBa------------bbbbb--:1:-1:1:22:2:0:0:5:10

X:Player 1 O:Player 2

Score is X:2 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+

| | | O O O O O | +---+
| | | O O O O O | | 2 |

| | | | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | X X O X O |
| | | O X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 32 O: 151 X-O: 2-0/5

Cube: 2, O own cube
X to play 22

1. XG Roller++ 4/2(4) eq:+0.446
Player: 67.30% (G:46.58% B:24.41%)
Opponent: 32.70% (G:0.00% B:0.00%)

2. XG Roller++ 4/Off(2) eq:+0.371 (-0.075)
Player: 65.77% (G:41.46% B:31.76%)
Opponent: 34.23% (G:0.00% B:0.00%)



eXtreme Gammon Version: 2.03, MET: Kazaross XG2


--
//Walt

[Tim Chow]

On Aug 3, 10:48 am, Walt <walt_ask...@yahoo.com> wrote:
> I think everyone is surprised by this one.

Well, I'm surprised, but Bradley said he wouldn't be surprised at this
result.

It must be that 4/2(4) results in X getting hit less often in the long
run, even though it creates more immediate blotting rolls. If I
counted correctly, it's 6 extra immediate blotters, which seems a lot
to me.

It does make sense that as far as gammons are concerned, the
overwhelming consideration is not getting hit, and taking 2 checkers
off now doesn't matter so much.

---
Tim Chow

[peps...@gmail.com]

On Saturday, August 4, 2012 12:54:12 AM UTC+1, Tim Chow wrote:
If I
>
> counted correctly, it's 6 extra immediate blotters, which seems a lot
>
> to me.

Tim,

That depends on what you mean by "correctly". You did a correct count of the wrong thing. The correct count needs to weight the blotting numbers according to the number of shots that the blotting numbers leave.
The correct counting would be much more favourable to the bot play because 54 and 64 are quadruple shots with the play everyone here (including me) would have done but they are double shots with the bot play.

This observation of mine, however, doesn't explain everything because the roll plays differently at match scores.

It's a great poser by Walt!

Paul Epstein

[peps...@gmail.com]

I think that, in retrospect, the main disadvantage of 4/Off(2) is that it gives X a 17% shot of leaving 2 blots on the next roll. The bot play gives a 0% chance of this happening. Since O's board is weak, hitting one blot might not be enough.

I would have played 4/Off (2) like everyone else, but I do think I understand the bot play.

Paul Epstein

[Walt]

On 8/5/2012 5:23 PM, peps...@gmail.com wrote:

>>
> I think that, in retrospect, the main disadvantage of 4/Off(2) is that it gives X a 17% shot of leaving 2 blots on the next roll. The bot play gives a 0% chance of this happening. Since O's board is weak, hitting one blot might not be enough.
>
> I would have played 4/Off (2) like everyone else, but I do think I understand the bot play.

The two-blot theory seems to have merit, but O's board strength doesn't
appear to be much of a factor, as the following variant shows:


XGID=-bCbDBa------------bbbbb--:1:-1:1:22:2:0:0:5:10

X:Player 1 O:Player 2

Score is X:2 O:0 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+

| | | O O O O O | +---+
| | | O O O O O | | 2 |

| | | | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X |
| | | X X O X O |
| | | O X X O X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 32 O: 151 X-O: 2-0/5

Cube: 2, O own cube
X to play 22