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Rollout...more or less

Posted By: Daniel Murphy
Date: Monday, 5 December 2011, at 12:29 a.m.

In Response To: Rollout...more or less (Klaus Evers)

The score (after 0 games) is: White 9, Blue 0 (match to 13 points)

White80

1X3X4X2O '3X2X ' ' '1X2O

1O1O2O2O '3O1X2O ' ' ' '
Blue119
Position ID: 3eOGgAC1OYMBBg Match ID: QQm3AZAAAAAE

The appeal of 13/7* 6/1 is that if White fans Blue has 21/36 ways to make the deuce point next turn instead of only 15/36 ways after 13/7*/2. 13/7* 6/1 also gives White only 5/36 ways to enter and cover his home board blot instead of 7/36.

However, in favor of 13/7*/2:

(1) Blue gets 4/36 ways (33 31 11) instead of 3/36 (33 32) ways to make the 5 point, and the 4/36 ways all give Blue a 5-prime in front of the slotted ace point (after 13/7* 6/1 ... fan, 32 only makes a 4-prime).

(2) White's 52 does not hit 2 checkers -- after 13/7* 6/1 White will play bar/23*/18*.

(3) White's 22 does not hit, cover the ace point and make the 5 point -- after 13/7* 6/1 White will play bar/23* 8/6(2) 3/1.

(4) In any sequence that leads to White anchoring on a low point(White enters, Blue hits on White's acepoint or in the outfield, White anchors), the anchor is on the inferior ace point.

Entering hit and cover numbers
After 13/7* 6/1After 13/7*/2
62 22 21 61 51 21 11

If White fans
Play After 13/7* 6/1 ... fan After 13/7*/2 ... fan
Make 2 point 66 65 64 63 62 55 54 53 51 42 41 22
Make 1 point 66 65 55 54 53 51 44 41 32
Make 5 point 33 32 33 31 11
Hit outfield blot61 52 43 61 52 43
None of the above44 31 21 11 64 63 62 42 22 21

In the altered position below, doublet 2 isn't quite the joker, and the two plays are about even.

The score (after 0 games) is: White 9, Blue 0 (match to 13 points)

White82

1X3X4X2O '3X '2X ' '1X2O

1O1O2O2O '3O1X2O ' ' ' '
Blue119
Position ID: 3eOMgAC1OYMBBg Match ID: QQm3AZAAAAAE

# Ply Move Equity
1 R 13/7* 6/1 +0.4379
0.62270.24190.0087-0.37730.14610.0184 +0.4563 +0.4379
0.00090.00150.0003-0.00090.00160.0019 0.0028 0.0037
Full cubeful rollout with var.redn.
2593 games, Mersenne Twister dice gen. with seed 938622850 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 13/7*/2 +0.4364 ( -0.0015)
0.62610.22170.0068-0.37390.11470.0117 +0.4574 +0.4364
0.00090.00140.0003-0.00090.00180.0016 0.0027 0.0033
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 938622850 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]

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