Concession stand, part 3

Tim Chow

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Jun 28, 2012, 5:24:58 PM6/28/12

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The last in this series. I've changed this from DMP to a money game.
After people have had a chance to try this, I'll go back and post
rollouts of all three positions.

XGID=-BBBBBB-----bB-----dAcabc-:0:0:1:65:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Money session, Jacoby
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O O |
| X | | O O O O |
| | | O O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| O | | X X X X X X |
| O | | X X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 88 O: 72 X-O: 0-0
Cube : 1
X to play 65

---
Tim Chow

Bradley K. Sherman

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Jun 28, 2012, 5:38:12 PM6/28/12

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Tim Chow <tchow...@yahoo.com> wrote:
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X | | O X O O O O |
> | X | | O O O O |
> | | | O O O |
> | | | O |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | |
> | O | | X X X X X X |
> | O | | X X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+

>Pipcount X: 88 O: 72, Cube:1, X to play 65

Hmmm, my hands say 13/7,13/8, but my previous
analysis says:

20/9

On the basis that my smooth board is better for
the bearoff, negating O's slight lead in the race.

--bks

badgolferman

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Jun 28, 2012, 7:02:22 PM6/28/12

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13/8, 13,7. If O rolls a six I have a chance. And if he doesn't then
he'll be crunching and I may run next opportunity.

Walt

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Jun 28, 2012, 7:44:10 PM6/28/12

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After this play X will be down by only 5 pips. That might make it worth
running. But why run from the 20 when we can run from the 13? We'll
still be the same in the race either way, but staying on the 20 gives us
a chance to possibly hit something, or if O rolls small and we roll big
run like hell.

13/7 13/8

//Walt

S

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Jun 30, 2012, 9:33:25 AM6/30/12

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While the wastage here does favor the on roll player it certainly
isn't enough to compensate for being down not only 5 pips but also not
being on roll. Being on roll is generally accepted to be equal to 4
pips. Every pip in a medium length race is said to be worth between
two to two and a half percent. I don't even consider 20/9 for more
than a nanosecond here being so far down in the race and our opponent
being unable to attack of for the most part.

Once that play is out the window can we blindly and mindlessly rip two
checkers down 13/8 13/7?

Stick

Bradley K. Sherman

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Jun 30, 2012, 10:03:13 AM6/30/12

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S <jacob...@gmail.com> wrote:
>
>..... Every pip in a medium length race is said to be worth between
>two to two and a half percent. ...
>

Wow! Is it just said, or is it correct?

--bks

Tim Chow

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Jun 30, 2012, 7:28:06 PM6/30/12

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On Jun 28, 5:24 pm, I wrote:
> XGID=-BBBBBB-----bB-----dAcabc-:0:0:1:65:0:0:3:0:10
>
> X:Player 1 O:Player 2
> Score is X:0 O:0. Money session, Jacoby
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X | | O X O O O O |
> | X | | O O O O |
> | | | O O O |
> | | | O |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | |
> | O | | X X X X X X |
> | O | | X X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pipcount X: 88 O: 72 X-O: 0-0
> Cube : 1
> X to play 65

In my discussion of the previous position in the series, I mentioned
the possibility of running a single checker from the midpoint, leaving
blots on the 20pt and 13pt as sentinels. Here is a position and a
roll that illustrates that possibility. X can boldly play 13/2 here,
counting on his closed board and O's inflexible position with a blot
in her board to protect him from being attacked. Alternatively, X can
play safely with 13/8 13/7. Finally, X can more-or-less break contact
and transition to a straight race with 20/9.

We can eliminate 20/9 fairly quickly here. X is behind in the race.
13/8 13/7 maintains contact with little risk and doesn't waste pips.
It must be considerably better than 20/9.

The choice between 13/8 13/7 and 13/2 is more delicate. The important
thing to note here is that O's 1's are duplicated everywhere. In the
variant below, O's 1's are not duplicated, and the choice is very
close. In the given position, however, X can afford to play 13/2 and
play for the extra contact. O must break the midpoint with a 6 and X
will then often have a direct shot at O's blot.

After I rolled this out, I realized that the Jacoby rule may have a
slight effect here, because it means that O can't play on for the
gammon if she rolls her best joker (snake eyes) after 13/2. However,
this effect seems to be mostly negligible since it's only 1 roll in
36.

=======
Rollout
=======

1. Rollout: 13/2 eq:-0.276
Player : 41.15% (G:4.38% B:0.17%)
Opponent: 58.85% (G:2.89% B:0.04%)
Confidence: ±0.007 (-0.283<E<-0.269)

2. Rollout: 13/8 13/7 eq:-0.327 (-0.051)
Player : 40.05% (G:2.19% B:0.04%)
Opponent: 59.95% (G:0.35% B:0.00%)
Confidence: ±0.007 (-0.334<E<-0.320)

3. Rollout: 20/9 eq:-0.475 (-0.199)
Player : 34.69% (G:0.08% B:0.00%)
Opponent: 65.31% (G:0.00% B:0.00%)
Confidence: ±0.008 (-0.483<E<-0.467)

1296 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply

=======
Variant
=======

XGID=-BBBBBB-----bB-----dAcbac-:0:0:1:65:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Money session, Jacoby
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O O |
| X | | O O O O |
| | | O O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| O | | X X X X X X |
| O | | X X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pipcount X: 88 O: 73 X-O: 0-0

Cube : 1
X to play 65

1. Rollout: 13/8 13/7 eq:-0.334
Player : 39.46% (G:2.42% B:0.04%)
Opponent: 60.54% (G:0.47% B:0.00%)
Confidence: ±0.004 (-0.338<E<-0.330)

2. Rollout: 13/2 eq:-0.335
Player : 38.39% (G:4.64% B:0.23%)
Opponent: 61.61% (G:3.03% B:0.04%)
Confidence: ±0.003 (-0.338<E<-0.332)

5184 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply

eXtreme Gammon Version: 1.21

---
Tim Chow