Thanks, David, for posting an interesting position. I got this one way far wrong. I figured I could learn something by finding the break-even position, in which White's equity is the same whether he plays 7/6 7/4 or 4/1 3/2. With a difference of 20 or more pips, 4/1 3/2 is better. With a difference of 19 or fewer pips, 7/6 7/4 is better.
If you care about whether it is better to say "fewer than 20" or "less than 20," you can read what I have to say below the third diagram.
I am posting three positions and rollout results below.
         
 
        
 | | White is Player 2
score: 0
pip: 101 | Unlimited Game
Jacoby Beaver | pip: 81
score: 0
Blue is Player 1 |
|
| XGID=-C-BBbBBB--B-----aacbbbb--:1:-1:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 4/1 3/2 | eq: +0.286 |
| Player:
Opponent: | 68.38% (G:0.76% B:0.01%)
31.62% (G:2.09% B:0.06%) | Conf.: ± 0.005 (+0.281...+0.291) - [98.0%]
Duration: 1 minute 27 seconds |
|
| 2. | Rollout1 | 7/6 7/4 | eq: +0.279 (-0.007) |
| Player:
Opponent: | 67.65% (G:1.04% B:0.02%)
32.35% (G:1.83% B:0.04%) | Conf.: ± 0.005 (+0.275...+0.284) - [2.0%]
Duration: 1 minute 16 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.03
| | White is Player 2
score: 0
pip: 101 | Unlimited Game
Jacoby Beaver | pip: 81
score: 0
Blue is Player 1 |
|
| XGID=-C-BBbBBB--B------cbbbbb--:1:-1:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 4/1 3/2 | eq: +0.279 |
| Player:
Opponent: | 68.22% (G:0.76% B:0.01%)
31.78% (G:2.03% B:0.06%) | Conf.: ± 0.005 (+0.274...+0.284) - [69.3%]
Duration: 1 minute 33 seconds |
|
| 2. | Rollout1 | 7/6 7/4 | eq: +0.277 (-0.002) |
| Player:
Opponent: | 67.93% (G:1.02% B:0.01%)
32.07% (G:1.71% B:0.03%) | Conf.: ± 0.005 (+0.273...+0.282) - [30.7%]
Duration: 1 minute 23 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.03
| | White is Player 2
score: 0
pip: 100 | Unlimited Game
Jacoby Beaver | pip: 81
score: 0
Blue is Player 1 |
|
| XGID=-C-BBbBBB--B------bcbbbb--:1:-1:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 7/6 7/4 | eq: +0.274 |
| Player:
Opponent: | 67.58% (G:1.06% B:0.02%)
32.42% (G:1.75% B:0.04%) | Conf.: ± 0.004 (+0.270...+0.278) - [99.2%]
Duration: 1 minute 19 seconds |
|
| 2. | Rollout1 | 4/1 3/2 | eq: +0.266 (-0.008) |
| Player:
Opponent: | 67.66% (G:0.79% B:0.01%)
32.34% (G:2.22% B:0.06%) | Conf.: ± 0.005 (+0.261...+0.271) - [0.8%]
Duration: 1 minute 32 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.03
This is not a big deal, and nobody cares if your grammar is not perfect, especially if English is not your native language. (My grammar is certainly not perfect.) But just in case you care:
I believe it is wrong to say, "Less than 20 pips." I believe it is better to say, "Fewer than 20 pips." I believe the signs you see in the grocery store that say, "Less than 20 items" are grammatically incorrect. If you are referring to an integer, than it is better to say "fewer" than "less." If you are referring to an amount that is not an integer, then use "less." For example, "He has less water than I have," but "He has fewer jugs of water than I have." Better to say, "Fewer checkers in the zone" than to say, "Less checkers in the zone."