The slotting option

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The slotting option

Posted By: Chuck Bower
Date: Wednesday, 30 December 2009, at 2:30 a.m.

In Response To: Containment checker play, take 2 (Chuck Bower)

All at DMP.
Case 1: keep Blue's position the same; bear off White checkers (and simultaneously deteriorate White's board strength) until slotting is equally as good as not slotting.
The score (after 0 games) is: JellyFish 0, Player2 0 (match to 1 point, post-Crawford play)
Move number 9: Player2 to play 45

Pip counts: JellyFish 52, Player2 101
Position ID: 2x0AALRtg0QJAA Match ID: cAk2AAAAAAAA

• Player2 moves 16/11 10/6

# Ply Move Equity

• 1 R 16/11 10/6 +0.2380

0.6190 0.0000 0.0000 - 0.3810 0.2480 0.0307 +0.2380 +0.2380

0.0005 0.0000 0.0000 - 0.0005 0.0011 0.0010 0.0010 0.0010

Full cubeful rollout with var.redn.

12969 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

2 R 16/11 15/11 +0.2373 ( -0.0008)

0.6186 0.0000 0.0000 - 0.3814 0.2218 0.0183 +0.2373 +0.2373

0.0005 0.0000 0.0000 - 0.0005 0.0015 0.0008 0.0009 0.0009

Full cubeful rollout with var.redn.

12969 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

3 4 16/12 15/10 +0.1919 ( -0.0461)

0.5959 0.0000 0.0000 - 0.4041 0.1197 0.0042

4 2 15/6 +0.2334 ( -0.0046)

0.6167 0.0000 0.0000 - 0.3833 0.2325 0.0161

5 2 18/13 10/6 +0.2053 ( -0.0327)

0.6026 0.0000 0.0000 - 0.3974 0.2206 0.0109

6 2 12/7 10/6 +0.1348 ( -0.1032)

0.5674 0.0000 0.0000 - 0.4326 0.2528 0.0127

7 2 18/13 16/12 +0.1275 ( -0.1105)

0.5638 0.0000 0.0000 - 0.4362 0.1007 0.0025

8 2 18/14 16/11 +0.1244 ( -0.1136)

0.5622 0.0000 0.0000 - 0.4378 0.1322 0.0049

9 2 18/14 15/10 +0.1109 ( -0.1271)

0.5554 0.0000 0.0000 - 0.4446 0.1007 0.0018

10 2 18/13 15/11 +0.1084 ( -0.1296)

0.5542 0.0000 0.0000 - 0.4458 0.1323 0.0051

Slotting improves in value for two reasons: 1) If hit Blue has chances of entering and catching White on his way around; 2) White's improved racing chances mean Blue has more incentive to make the 6-point and prevent White from entering until Blue has checkers borne off (i.e. after catching up in the race.)
Case 2: Put Blue's rearmost checker in his homeboard, reducing the number of outfield builders/shooters to four from the original five. Now deteriorate White's position until slotting is roughly equal in equity to not slotting.
The score (after 0 games) is: JellyFish 0, Player2 0 (match to 1 point, post-Crawford play)
Move number 11: Player2 to play 45

Pip counts: JellyFish 64, Player2 88
Position ID: 2+4AANC2HSQKAA Match ID: cAk2AAAAAAAA

• Player2 moves 16/11 10/6

# Ply Move Equity

• 1 R 16/11 10/6 +0.2748

0.6374 0.0000 0.0000 - 0.3626 0.2354 0.0158 +0.2748 +0.2748

0.0006 0.0000 0.0000 - 0.0006 0.0037 0.0015 0.0013 0.0013

Full cubeful rollout with var.redn.

3564 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

2 R 15/6 +0.2732 ( -0.0016)

0.6366 0.0000 0.0000 - 0.3634 0.2348 0.0151 +0.2732 +0.2732

0.0007 0.0000 0.0000 - 0.0007 0.0036 0.0015 0.0013 0.0013

Full cubeful rollout with var.redn.

3564 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

3 R 16/11 15/11 +0.2609 ( -0.0139)

0.6305 0.0000 0.0000 - 0.3695 0.1522 0.0073 +0.2609 +0.2609

0.0007 0.0000 0.0000 - 0.0007 0.0035 0.0011 0.0014 0.0014

Full cubeful rollout with var.redn.

3563 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

4 R 16/12 15/10 +0.2492 ( -0.0256)

0.6246 0.0000 0.0000 - 0.3754 0.0995 0.0039 +0.2492 +0.2492

0.0006 0.0000 0.0000 - 0.0006 0.0031 0.0007 0.0013 0.0013

Full cubeful rollout with var.redn.

3564 games, Mersenne Twister dice gen. with seed 868869504 and quasi-random dice

Play: world class 2-ply cubeful prune [world class]

keep the first 0 0-ply moves and up to 8 more moves within equity 0.16

Skip pruning for 1-ply moves.

Cube: 2-ply cubeful prune [world class]

5 2 15/10 5/1 +0.1964 ( -0.0783)

0.5982 0.0000 0.0000 - 0.4018 0.0420 0.0009

6 2 16/11 5/1 +0.1647 ( -0.1100)

0.5824 0.0000 0.0000 - 0.4176 0.0987 0.0044

7 2 16/7 +0.1386 ( -0.1362)

0.5693 0.0000 0.0000 - 0.4307 0.0929 0.0043

8 2 16/12 10/5 +0.1365 ( -0.1383)

0.5682 0.0000 0.0000 - 0.4318 0.0248 0.0004

9 2 12/7 10/6 +0.1350 ( -0.1398)

0.5675 0.0000 0.0000 - 0.4325 0.2272 0.0112

10 2 15/10 12/8 +0.1327 ( -0.1421)

0.5663 0.0000 0.0000 - 0.4337 0.0411 0.0007

With just one less outfield checker to work with, Blue must slot earlier (i.e. only 2 White checkers borne off instead of 4 and only one open point in White's board compared to the previous position).
My recollection of these class of positions is that you usually have only a few checkers in the outfield (two or three) to work with. As follows from above, slotting the open homeboard point is then more of a realistic option.
Similar tweaking can be done for the more common situation of gammons counting to find the tipping points for those.

Messages In This Thread

Containment checker play, take 2
Timothy Chow -- Tuesday, 29 December 2009, at 2:40 a.m.
- Containment checker play, take 2
  Stick -- Tuesday, 29 December 2009, at 2:48 a.m.
  - Containment checker play, take 2
    Nack Ballard -- Wednesday, 30 December 2009, at 4:27 a.m.
- Addendum
  Timothy Chow -- Tuesday, 29 December 2009, at 2:50 a.m.
  - Addendum
    Daniel Murphy -- Tuesday, 29 December 2009, at 3:41 a.m.
    - Addendum
      Timothy Chow -- Tuesday, 29 December 2009, at 3:40 p.m.
- Containment checker play, take 2
  Chuck Bower -- Tuesday, 29 December 2009, at 2:12 p.m.
  - Containment checker play, take 2
    Timothy Chow -- Tuesday, 29 December 2009, at 3:51 p.m.
    - Containment checker play, take 2
      Chuck Bower -- Tuesday, 29 December 2009, at 4:30 p.m.
      - The slotting option
        Chuck Bower -- Wednesday, 30 December 2009, at 2:30 a.m.
        
        The slotting option
        Timothy Chow -- Wednesday, 30 December 2009, at 5:16 p.m.
        
        The slotting option
        Chuck Bower -- Wednesday, 30 December 2009, at 6:15 p.m.
    - Containment checker play, take 2
      Rich Munitz -- Wednesday, 30 December 2009, at 6:33 p.m.
- Rollout
  Timothy Chow -- Saturday, 2 January 2010, at 9:05 p.m.

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