Containment 1

[Tim Chow]

Enough blitzing problems for now. Let me turn to containment, which is an area of the game where I still routinely whopper.

XGID=-AACaBC---B--C-a--abcabbb-:1:-1:1:41:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O O O O O | +---+
| X | | O O O O O | | 2 |
| X | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X X |
| X | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 99 O: 81 X-O: 0-0
Cube: 2, O own cube
X to play 41

---
Tim Chow

[Bradley K. Sherman]

Tim Chow <tchow...@yahoo.com> wrote:
>Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O O O O O | +---+
> | X | | O O O O O | | 2 |
> | X | | O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X |
> | X | | X X X |
> | X | | X X O X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+

> X:99 O:81, X to play 41

6/1

--bks

[badgolferman]

I'd play 6/2, 13/12.

[smcrtorchs]

This is not what I call typical exciting containment, though I still do not know what to do.

I will try 13/9 2/1.

2/1 seems auto. 13/9 can certainly backfire and will lose more gammons. But, it is not like that if X plays 6/2 he will win many more games without builders pointing on the 4 point, with 2 open points and with a blot in his board. This way, X has no blots and 3 builders that point directly on X, who might stay there or roll a number like 63, 31 33 and just hop to the 18 point. If X had better chances containing that checker, then I would look at a safer option.

[Walt]

On 2/3/2014 9:23 PM, Tim Chow wrote:

> XGID=-AACaBC---B--C-a--abcabbb-:1:-1:1:41:0:0:0:0:10
>
> X:Player 1 O:Player 2
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O O O O O | +---+
> | X | | O O O O O | | 2 |
> | X | | O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X |
> | X | | X X X |
> | X | | X X O X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 99 O: 81 X-O: 0-0
> Cube: 2, O own cube
> X to play 41

X is down by 20 pips or so and if O can escape she'll have the game in
the bag. But her board is very strong, and a hit can easily turn into a
gammon. I wouldn't leave a direct shot here (does O have a cash after
13/8? or is she too good?), but the passive 6/1 or 6/2 3/2 seem like the
wrong idea.

I'll go for 13/12 6/2 - cover a homeboard blot, only leave 6 shots ( all
of which will leave O's homeboard blot uncovered), and aim another
builder at the runner.


--
//Walt

[Tim Chow]

On Tuesday, February 4, 2014 11:50:06 AM UTC-5, Walt wrote:
> I'll go for 13/12 6/2 - cover a homeboard blot, only leave 6 shots ( all
> of which will leave O's homeboard blot uncovered), and aim another
> builder at the runner.

If you look carefully, you'll see that it's only 3 shots. 22 and 62 don't hit.

---
Tim Chow

[check...@yahoo.com]

And 44 was so good anyway that's hardly worth counting as a *shot. It gets you a shot this way.

Stick

[Tim Chow]

XGID=-AACaBC---B--C-a--abcabbb-:1:-1:1:41:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O O O O O | +---+
| X | | O O O O O | | 2 |
| X | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X X |
| X | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 99 O: 81 X-O: 0-0
Cube: 2, O own cube
X to play 41

There are many types of containment decisions. Sometimes you have to decide whether to attack or prime. Sometimes your opponent is on the bar and you have to decide whether to leave a home-board point slotted. Sometimes, as in this position, you just have to decide how best to control the outfield. In outfield-control problems, I think there are usually three main goals for the container, which can compete with each other:

1. Flood the outfield for maximum coverage.

2. If getting hit is bad, then avoid leaving shots.

3. Block specific numbers, usually large doublets.

In the current position, blocking doublets doesn't come into it, and it's just a matter of weighing shots against coverage.

How bad is it to get hit? Very bad, since O has a five-point board, but not as bad as it would be if O had a closed board, or a five-point board with no blot. So 13/12 must be better than 13/9, since it's not clear that 13/9 gives any better coverage, whereas it certainly gives O lots of extra shots. As already noted in my other post, 13/12 leaves only 3 shots, or 2 if you follow Stick's suggestion not to count 44.

How much value is there in playing 13/12? Quite a bit. If O tries to hop into our outfield with a small roll, then it gives us a triple shot rather than a double shot, and in any case, 13/12 gives us a builder to make another blocking point in our outfield. Since we're behind in the race, an extra blocker definitely helps.

I played safe here but the computer calls it a whopper. To give you a better sense of the tradeoff between coverage and safety, I've included two variants. In Variant 1, I've moved X's checkers back from the 10pt to the 11pt. Now 13/12 gives O 5 hitting rolls instead of 3. 13/12 still comes out ahead but by a much smaller margin. In Variant 2, I've also closed O's board. This is enough to induce the computer to play safe.

1. Rollout¹ 13/12 6/2 eq:-0.403
Player: 40.36% (G:1.87% B:0.11%)
Opponent: 59.64% (G:10.16% B:0.12%)
Confidence: ±0.004 (-0.407..-0.398) - [100.0%]

2. Rollout¹ 6/2 3/2 eq:-0.512 (-0.109)
Player: 35.87% (G:0.92% B:0.02%)
Opponent: 64.13% (G:6.48% B:0.08%)
Confidence: ±0.005 (-0.518..-0.507) - [0.0%]

3. Rollout¹ 6/1 eq:-0.545 (-0.142)
Player: 34.95% (G:0.91% B:0.03%)
Opponent: 65.05% (G:7.86% B:0.12%)
Confidence: ±0.006 (-0.551..-0.539) - [0.0%]

=========
Variant 1
=========

XGID=-AACaBC----B-C-a--abcabbb-:1:-1:1:41:0:0:0:0:10

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

Pip count X: 101 O: 81 X-O: 0-0

Cube: 2, O own cube
X to play 41

1. Rollout¹ 13/12 6/2 eq:-0.727
Player: 30.76% (G:2.05% B:0.15%)
Opponent: 69.24% (G:11.82% B:0.08%)
Confidence: ±0.010 (-0.736..-0.717)

2. Rollout¹ 6/2 3/2 eq:-0.755 (-0.029)
Player: 28.22% (G:0.53% B:0.01%)
Opponent: 71.78% (G:6.29% B:0.05%)
Confidence: ±0.008 (-0.764..-0.747)

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

=========
Variant 2
=========

XGID=-AACaBC----B-C-a--abbbbbb-:1:1:1:41:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O O O O O |
| X | | O O O O O O |

| X | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X | +---+
| X | | X X X | | 2 |
| X | | X X O X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 80 X-O: 0-0
Cube: 2, X own cube
X to play 41

1. XG Roller++ 6/2 3/2 eq:-0.418
Player: 27.02% (G:0.47% B:0.01%)
Opponent: 72.98% (G:6.78% B:0.06%)

2. XG Roller++ 6/1 eq:-0.435 (-0.017)
Player: 26.41% (G:0.46% B:0.01%)
Opponent: 73.59% (G:6.91% B:0.09%)

3. XG Roller++ 13/12 6/2 eq:-0.483 (-0.065)
Player: 27.15% (G:0.45% B:0.01%)
Opponent: 72.85% (G:13.38% B:0.07%)

eXtreme Gammon Version: 2.10

---
Tim Chow

[smcrtorchs]

Still it is hard for me to understand why 6/2 3/2 wins 35%.

[Tim Chow]

On Wednesday, February 5, 2014 9:33:54 PM UTC-5, smcrtorchs wrote:
> Still it is hard for me to understand why 6/2 3/2 wins 35%.

Although X is behind in the race, he's not that far behind, so he doesn't need to close his board to win. A hit and a dance will often be enough for X to pull ahead.

---
Tim Chow