A common bearoff dilemma 2

[Timothy Chow]

XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X |
| | | X X X X |
| | | O X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 21 O: 82 X-O: 0-0
Cube: 2, O own cube
X to play 21

---
Tim Chow

[badgolferman]

I would probably play 2/off, 2/1. There is a chance to gammon so
getting another checker off will help. Also if I unstack the 4-point
then I will have three on the last point and that could become awkward.

[Timothy Chow]

Compared to the previous bearoff problem, X has three more checkers
off, so his gammon chances are better, as are his winning chances if
he gets hit, especially since O's board is crunched, with an open 6pt.
XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
worth the risk. On the other hand, with an extra checker on the 1pt,
XG prefers the safe play.

1. Rollout¹ 2/1 2/Off eq:+1.554
Player: 98.81% (G:57.22% B:1.01%)
Opponent: 1.19% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.553..+1.555) - [100.0%]

2. Rollout¹ 4/3 4/2 eq:+1.492 (-0.062)
Player: 99.57% (G:49.91% B:0.29%)
Opponent: 0.43% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.492..+1.493) - [0.0%]

3. Rollout¹ 3/2 3/1 eq:+1.461 (-0.093)
Player: 98.94% (G:48.48% B:0.19%)
Opponent: 1.06% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.460..+1.462) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release

-------
Variant
-------

XGID=aDBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

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

Pip count X: 22 O: 82 X-O: 0-0

Cube: 2, O own cube
X to play 21

1. Rollout¹ 4/3 4/2 eq:+1.462
Player: 99.42% (G:47.32% B:0.24%)
Opponent: 0.58% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.461..+1.463) - [100.0%]

2. Rollout¹ 2/1 2/Off eq:+1.415 (-0.047)
Player: 98.40% (G:45.04% B:0.21%)
Opponent: 1.60% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.414..+1.416) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

[Timothy Chow]

On 9/5/2021 8:22 AM, Timothy Chow wrote:
> XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

> Compared to the previous bearoff problem, X has three more checkers
> off, so his gammon chances are better, as are his winning chances if
> he gets hit, especially since O's board is crunched, with an open 6pt.
> XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
> worth the risk.  On the other hand, with an extra checker on the 1pt,
> XG prefers the safe play.

I should have said that it's not just that with an extra checker, X's
gammon chances go down. XG also prefers clearing the 4pt with one fewer
checker on the 1pt (see below). There is an odd/even effect at play,
meaning that X's chances of saving a roll by bearing off a checker now
are low. And X still doesn't want to get hit, not because he's afraid
of losing the game, but because it will greatly reduce his chances of
winning a gammon.

XGID=aBBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | |
| | | X X X X |

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

Pip count X: 20 O: 82 X-O: 0-0

Cube: 2, O own cube
X to play 21

1. Rollout¹ 4/3 4/2 eq:+1.714
Player: 99.66% (G:71.09% B:1.10%)

Opponent: 0.34% (G:0.00% B:0.00%)

Confidence: ±0.001 (+1.713..+1.715) - [100.0%]

2. Rollout¹ 2/1 2/Off eq:+1.685 (-0.029)
Player: 99.07% (G:69.23% B:1.49%)
Opponent: 0.93% (G:0.00% B:0.00%)
Confidence: ±0.001 (+1.683..+1.686) - [0.0%]

[peps...@gmail.com]

On Sunday, September 5, 2021 at 1:35:37 PM UTC+1, Tim Chow wrote:
> On 9/5/2021 8:22 AM, Timothy Chow wrote:
> > XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10
> > Compared to the previous bearoff problem, X has three more checkers
> > off, so his gammon chances are better, as are his winning chances if
> > he gets hit, especially since O's board is crunched, with an open 6pt.
> > XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
> > worth the risk. On the other hand, with an extra checker on the 1pt,
> > XG prefers the safe play.
> I should have said that it's not just that with an extra checker, X's
> gammon chances go down. XG also prefers clearing the 4pt with one fewer
> checker on the 1pt (see below). There is an odd/even effect at play,
> meaning that X's chances of saving a roll by bearing off a checker now
> are low. And X still doesn't want to get hit, not because he's afraid
> of losing the game, but because it will greatly reduce his chances of
> winning a gammon.

...
Experienced players are very used to losing overwhelming positions from 1% parlays
so players will actually be "afraid" of being hit and losing.

Paul