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Something I learned about backgames at 3-away/3-away

Posted By: Timothy Chow
Date: Saturday, 3 April 2010, at 10:37 p.m.

I spent some time trying to understand the comments by neilkaz and Neil Robins about backgames at 3-away/3-away, made in response to a position posted by Paul Weaver (MCG vs Falafel). I thought other readers might be interested in what I learned.

A rule of thumb about the 3-away/3-away score is that the checker play is similar to that of money play, and that initial doubles and passes come slightly quicker than for money. An important caveat, however, is that this rule of thumb applies only if the initial doubler's equity in a money game is not very sensitive to 8-point wins (i.e., re-recubes or gammon wins on a 4-cube). When one considers doubling against a backgame, this subtlety is important. It's true that a significant proportion of the backgamer's recubes come rather late in the day, after a hit or (if the hit comes very late) after a closeout, when an 8-pointer is not likely. But there are also cases when the backgamer recubes relatively early, when the game is still double-edged and the backgamer could still get gammoned or face an 8-cube (for money). In these situations, the backgamer will typically recube much more aggressively at 3-away/3-away than for money since 8-pointers are not in the picture. This recube vig means that one should be more cautious about early initial doubles against backgames at 3-away/3-away than for money.

To illustrate these points I have rolled out three different positions below. The first is a position posted by neilkaz a couple of weeks ago where the backgamer is contemplating doubling after getting a shot but before hitting. For money it's far from a redouble, but at 3-away/3-away it's a borderline redouble according to the rollout. The second position is a reference position: three points left to clear in front of the more advanced anchor in a well-timed 1-3 backgame. This is a borderline initial double for money but far from an initial double at 3-away/3-away. Finally comes the original MCG/Falafel position. The rollout says that it's not an initial double even for money, perhaps because of MCG's somewhat awkward distribution. And, in accordance with everything that has been said so far, it's an even bigger ND at 3-away/3-away, with Falafel's pass being (in neilkaz's words) a "SuperDeluxeWhopper combo."

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Unlimited game: Blue on roll, cube decision?

White	72
Blue	140
Position ID: H7k7AADabgEAGw Match ID: UQkAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.334
Cubeful equities:
1.	No double	+0.563
2.	Double, pass	+1.000	+0.437
3.	Double, take	+0.447	-0.116
Proper cube action:		No redouble, take (21.0%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.627 0.175 0.006 - 0.373 0.099 0.002 +0.334 +0.563 Standard error 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.005 Player White owns 4-cube 0.638 0.170 0.006 - 0.362 0.089 0.002 +0.725 +0.447 Standard error 0.001 0.002 0.000 - 0.001 0.001 0.000 0.008 0.010
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 847335075 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

The score (after 0 games) is: White 0, Blue 0 (match to 3 points)

Blue on roll, cube decision?

White	72
Blue	140
Position ID: H7k7AADabgEAGw Match ID: UQlgAAAAAAAA

Cube decision
Rollout cubeless equity		+0.298	(Money: +0.339)
Cubeful equities:
1.	Double, take	+0.574
2.	Double, pass	+1.000	+0.426
3.	No double	+0.572	-0.001
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.631 0.191 0.010 - 0.369 0.122 0.004 +0.298 +0.572 Standard error 0.001 0.003 0.001 - 0.001 0.002 0.000 0.003 0.004 Player White owns 4-cube 0.644 0.216 0.011 - 0.356 0.178 0.004 +0.574 +0.574 Standard error 0.001 0.005 0.001 - 0.001 0.004 0.000 0.005 0.005
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 847691268 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

Unlimited game: Blue on roll, cube decision?

White	158
Blue	68
Position ID: 2G4DADPmew8AAA Match ID: cAkAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.585
Cubeful equities:
1.	No double	+0.746
2.	Double, pass	+1.000	+0.254
3.	Double, take	+0.734	-0.013
Proper cube action:		No double, take (4.7%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.587 0.347 0.064 - 0.413 0.000 0.000 +0.585 +0.746 Standard error 0.001 0.001 0.001 - 0.001 0.000 0.000 0.003 0.010 Player White owns 2-cube 0.585 0.348 0.067 - 0.415 0.000 0.000 +1.168 +0.734 Standard error 0.001 0.001 0.001 - 0.001 0.000 0.000 0.007 0.012
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 847567540 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

The score (after 0 games) is: White 0, Blue 0 (match to 3 points)

Blue on roll, cube decision?

White	158
Blue	68
Position ID: 2G4DADPmew8AAA Match ID: cAlgAAAAAAAA

Cube decision
Rollout cubeless equity		+0.658	(Money: +0.643)
Cubeful equities:
1.	No double	+0.645
2.	Double, pass	+1.000	+0.355
3.	Double, take	+0.500	-0.145
Proper cube action:		No double, take (29.0%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.584 0.352 0.123 - 0.416 0.000 0.000 +0.658 +0.645 Standard error 0.002 0.002 0.004 - 0.002 0.001 0.000 0.008 0.014 Player White owns 2-cube 0.577 0.346 0.195 - 0.423 0.000 0.000 +1.093 +0.500 Standard error 0.002 0.003 0.005 - 0.002 0.001 0.000 0.015 0.020
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 847753922 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

(Hypothetical) unlimited game: MCG on roll, cube decision?

Falafel	160
MCG	69
Position ID: bJtIADPmuw8AAA Match ID: cAkAACAAEAAA

Cube decision
Rollout cubeless equity		+0.423
Cubeful equities:
1.	No double	+0.464
2.	Double, pass	+1.000	+0.536
3.	Double, take	+0.360	-0.103
Proper cube action:		No double, take (16.1%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.530 0.307 0.056 - 0.470 0.000 0.000 +0.423 +0.464 Standard error 0.001 0.001 0.001 - 0.001 0.000 0.000 0.004 0.010 Player Falafel owns 2-cube 0.530 0.307 0.057 - 0.470 0.000 0.000 +0.848 +0.360 Standard error 0.001 0.001 0.001 - 0.001 0.000 0.000 0.008 0.012
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 847868634 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

The score (after 0 games) is: Falafel 0, MCG 0 (match to 3 points)

MCG on roll, cube decision?

Falafel	160
MCG	69
Position ID: bJtIADPmuw8AAA Match ID: cAmgACAAEAAA

Cube decision
Rollout cubeless equity		+0.530	(Money: +0.465)
Cubeful equities:
1.	No double	+0.401
2.	Double, pass	+1.000	+0.599
3.	Double, take	+0.010	-0.391
Proper cube action:		No double, take (39.5%)
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.530 0.314 0.091 - 0.470 0.000 0.000 +0.530 +0.401 Standard error 0.001 0.002 0.003 - 0.001 0.000 0.000 0.006 0.010 Player Falafel owns 2-cube 0.521 0.316 0.171 - 0.479 0.000 0.000 +0.676 +0.010 Standard error 0.002 0.002 0.004 - 0.002 0.000 0.000 0.012 0.016
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 847618316 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Messages In This Thread

• Something I learned about backgames at 3-away/3-away
  Timothy Chow -- Saturday, 3 April 2010, at 10:37 p.m.
  • Something I learned about backgames at 3-away/3-away
    Neil Robins -- Sunday, 4 April 2010, at 6:17 a.m.