Doubling position where XG Roller+ err

(B) The position is also a good example of the problematic use of truncation in Gnubg rollouts. In the table below, note how the Take or Pass decision swings back and forth as the truncation depth is incremented:

White	151

Blue	76
Position ID: `3psHACDYNpkEMA` Match ID: `AQHgAAAAAAAA`

Truncation Depth	No Double Equity	Double/Take Equity	Best Cube Decision
1	+0.848	+1.082	Double/Pass
2	+0.848	+0.947	Double/Take
3	+0.855	+1,018	Double/Pass
4	+0.818	+0.927	Double/Take
5	+0.855	+1.041	Double/Pass
6	+0.825	+0.961	Double/Take
7	+0.865	+1.072	Double/Pass
8	+0.825	+0.971	Double/Take
9	+0.870	+1.083	Double/Pass
10	+0.819	+0.964	Double/Take
11	+0.869	+1.082	Double/Pass
12	+0.816	+0.960	Double/Take
Full rollout	+0.840	+1.013	Double/Pass

(In the table, rollouts are 0-ply checker, 0-ply cube, 1296 trials for truncation depth 3 or more, 2592 trials for the full rollout. SDs range from 0.000 for depth 1 to 0.006/0.010 for both the depth 12 and the full rollout.)

(C) In that the rollouts using an odd-numbered depth agree with the full rollout on Double/Pass, it's also a counterexample to an observation that having ply plus truncation depth equal an even number generally gets the best out of Gnubg truncation.

(D) It's also -- since the full 0-ply rollout has it as a close Pass -- an example of why we'd often rather see a 2-ply (or better) rollout:

Cube decision

Rollout cubeless equity

+0.546

(Money: +0.523)

Cubeful equities:

Double, pass

+1.000

Double, take

+1.194

+0.194

No double

+0.914

-0.086

Proper cube action:

Redouble, pass

Rollout details

	Win	W g	W bg		Lose	L g	L bg	Cubeless	Cubeful
Player White owns 2-cube	0.775	0.098	0.004	-	0.225	0.106	0.022	+0.546	+0.914
Standard error	0.001	0.002	0.001	-	0.001	0.002	0.003	0.004	0.007
Player Blue owns 4-cube	0.795	0.114	0.010	-	0.205	0.100	0.041	+1.299	+1.194
Standard error	0.002	0.002	0.002	-	0.002	0.003	0.004	0.011	0.012

Full cubeful rollout with var.redn.

1148 games, Mersenne Twister dice gen. with seed 848991528 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]

Cube analysis
0-ply cubeless equity +0.532 (Money: +0.535)
0.783 0.077 0.000 - 0.217 0.103 0.005
Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.057 ( +0.057)
3. No double +0.852 ( -0.148)
Proper cube action: Redouble, pass

Cube analysis
1-ply cubeless equity +0.560 (Money: +0.560)
0.775 0.105 0.002 - 0.225 0.092 0.006
Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.073 ( +0.073)
3. No double +0.846 ( -0.154)
Proper cube action: Redouble, pass

Cube analysis
2-ply cubeless equity +0.484 (Money: +0.487)
0.760 0.085 0.001 - 0.240 0.112 0.006
Cubeful equities:
1. Double, take +0.948
2. Double, pass +1.000 ( +0.052)
3. No double +0.845 ( -0.103)
Proper cube action: Redouble, take
Cube analysis
3-ply cubeless equity +0.538 (Money: +0.537)
0.764 0.109 0.002 - 0.236 0.096 0.006
Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.022 ( +0.022)
3. No double +0.848 ( -0.152)
Proper cube action: Redouble, pass

Cube analysis
4-ply cubeless equity +0.479 (Money: +0.481)
0.755 0.091 0.001 - 0.245 0.114 0.007
Cubeful equities:
1. Double, take +0.935
2. Double, pass +1.000 ( +0.065)
3. No double +0.817 ( -0.118)
Proper cube action: Redouble, take

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