Switching points 2

[Tim Chow]

XGID=-a-B-aE-B---aD---cbeBb----:1:1:1:22:0:0:0:0:10

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 X O |
| X O O | | O X O |
| X O | | O |
| X | | O |
| | | O |
| |BAR| |
| | | X |
| | | X |
| | | X | +---+
| X | | X X | | 2 |
| O X | | X O X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 144 O: 133 X-O: 0-0
Cube: 2, X own cube
X to play 22

---
Tim Chow

[Bradley K. Sherman]

Tim Chow <tc...@mit.edu> 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 X O |
> | X O O | | O X O |
> | X O | | O |
> | X | | O |
> | | | O |
> | |BAR| |
> | | | X |
> | | | X |
> | | | X | +---+
> | X | | X X | | 2 |
> | O X | | X O X O | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+

> X:144 O:133, X to play 22

13/11(2),6/4(2)

--bks

[badgolferman]

The obvious play is 6/4(2), 13/11(2). But you would not be posting
this problem if it was obvious so I must try something different.
6/4(2), 3/1(2)*

[Tim Chow]

This decision was apparently so obvious to badgolferman that he was tricked into voting for switching points, but it wasn't obvious to me. Not only did I switch points here, I switched points in a similar position a few months later because I hadn't learned my lesson the first time (see Bonus 1 below).

Why is this different from "Switching points 1" where the computer favored switching points? An important factor is that "downgrading" from the 3pt to the 1pt is a much more significant sacrifice than downgrading from the 2pt to the 1pt. A second important factor is that 13/11(2) makes a point six-away from a gap in X's prime, creating a strong blockade. Finally, since O has the 5pt slotted, she has good chances of bringing X's attack to an abrupt halt by anchoring.

In "Bonus 2" we see a similar decision. Switching points downgrades from the 3pt to the 2pt, and initiates an attacking attempt that could be stymied if O anchors, while the priming play produces a strong blockade, with again the gap in the prime being guarded by a point six pips away.

1. Rollout¹ 13/11(2) 6/4(2) eq:+0.604
Player: 61.44% (G:15.49% B:0.48%)
Opponent: 38.56% (G:6.04% B:0.25%)
Confidence: ±0.010 (+0.594..+0.614) - [100.0%]

2. Rollout¹ 6/4(2) 3/1*(2) eq:+0.514 (-0.090)
Player: 57.72% (G:17.14% B:0.63%)
Opponent: 42.28% (G:6.60% B:0.23%)
Confidence: ±0.007 (+0.507..+0.522) - [0.0%]

-------
Bonus 1
-------

XGID=-a-B-aD-B---dE---c-d--b-B-:0:0:1:22:0:0:0:0:10

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 X |
| X O | | O O X |

| X O | | O |
| X | | O |

| X | | |
| |BAR| |
| | | |
| O | | X |
| O | | X |
| O X | | X X |

| O X | | X O X O |

+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 159 O: 150 X-O: 0-0
Cube: 1
X to play 22

1. Rollout¹ 13/11(2) 6/4(2) eq:+0.118
Player: 53.09% (G:16.66% B:0.76%)
Opponent: 46.91% (G:14.39% B:0.76%)
Confidence: ±0.013 (+0.105..+0.131) - [100.0%]

2. Rollout¹ 13/9 6/4(2) eq:-0.064 (-0.182)
Player: 48.71% (G:14.38% B:0.59%)
Opponent: 51.29% (G:15.18% B:0.90%)
Confidence: ±0.014 (-0.078..-0.050) - [0.0%]

3. Rollout¹ 6/4(2) 3/1*(2) eq:-0.076 (-0.194)
Player: 47.52% (G:16.63% B:0.38%)
Opponent: 52.48% (G:15.72% B:0.72%)
Confidence: ±0.012 (-0.088..-0.063) - [0.0%]

4. Rollout¹ 13/5* eq:-0.103 (-0.221)
Player: 47.60% (G:15.27% B:0.61%)
Opponent: 52.40% (G:16.82% B:1.13%)
Confidence: ±0.016 (-0.119..-0.087) - [0.0%]

-------
Bonus 2
-------

XGID=-aaB--D-B-B-dC---c-d-B-b--:0:0:1:11:0:0:0:0:10

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 X O |

| X O | | O X O |

| X O | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| O | | X |
| O | | X |
| O X X | | X X |
| O X X | | X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 147 O: 151 X-O: 0-0
Cube: 1
X to play 11

1. Rollout¹ 8/7(2) 6/5(2) eq:+0.859
Player: 68.75% (G:23.25% B:0.85%)
Opponent: 31.25% (G:6.07% B:0.22%)
Confidence: ±0.011 (+0.848..+0.871) - [100.0%]

2. Rollout¹ 21/20(2) 6/5(2) eq:+0.817 (-0.042)
Player: 68.35% (G:19.62% B:0.73%)
Opponent: 31.65% (G:5.69% B:0.17%)
Confidence: ±0.014 (+0.804..+0.831) - [0.0%]

3. Rollout¹ 6/5(2) 3/2*(2) eq:+0.761 (-0.099)
Player: 66.01% (G:24.74% B:1.02%)
Opponent: 33.99% (G:7.28% B:0.29%)
Confidence: ±0.015 (+0.746..+0.775) - [0.0%]

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

eXtreme Gammon Version: 2.10

---
Tim Chow

[Walt]

6/4(2) makes a homeboard point and unstacks the six. This has to be the
right start. What next? I see two options:

13/11(2) blocks sixes from the five point and brings two more checkers
into the zone for a total of 11, which is worth something.

3/1*(2) sends a checker back and takes away half of O's roll making it
more likely that X can follow through with the blitz while O is off balance.

I think the key here is that if O doesn't anchor the 11 checkers in the
zone after making the eleven make for a strong recube. OTHO, if O
dances after switching, it's probably a strong recube also.

Any 4 or 31 makes the anchor after we make the 11, that's 13 shakes. If
we hit, there are nine dancing numbers, or 27 that enter.

I'll go for making the eleven and push the cube if she fails to anchor.
Maybe nine checkers in the zone is enough if she enters without
anchoring, in which case switching would seem to be correct. but I'll
bring two down.

13/11(2) 6/4(2)

--
//Walt