Matt: On the other hand, if you make a mistake and double when it's really ND/T, and your opponent takes, you've likely given up a lot more equity than he would have if he passed.
I'm not sure that is possible together with the other information Matt provided. I think 2-away 4-away should double. He's not entirely clueless. He knows something about the position.
He knows that "it doesn't figure to be a gross blunder one way or the other" if opponent takes or passes. What's a gross blunder -- an error larger than 0.100 or so? That sets a range for his D/T equity. It can't be higher than about 1.100, else taking would be blunder. It can't be lower than about 0.900, else passing would be a blunder.
He also knows that opponent's GWC is about 18%, his match equity at 4-away 1-away. If it weren't about 18%, he'd have no clue that passing "doesn't figure to be a gross blunder."
Can a position be constructed where 2-away 4-away has GWC of about 82%, wins lots of gammons, double/take equity is between 0.900 and 1.100, ND equity is over 1.000, and doubling is a blunder?
Or is the position below typical of the position Matt described?
The score (after 0 games) is: White 1, Blue 3 (match to 5 points)
Move number 21: Blue on roll, cube decision?
| White | 113 |
|---|---|
| |
| Blue | 55 |
Position ID: 7O4GADDuuw0AAA Match ID: cAmgABAAGAAA | |
• Blue doubles
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.930 | (Money: +0.857) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | Double, pass | +1.000 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, take | +1.098 | +0.098 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | No double | +0.923 | -0.077 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | Double, pass | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 391 games, Mersenne Twister dice gen. with seed 1056812348 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: 0-ply cubeful prune [expert] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Blue wins about 83%, wins lots of gammons, double/pass is correct, take is a blunder, but not doubling is a pretty big error too. (There's goes my monthly quota of 0-ply checker rollouts.) One more position:
The score (after 0 games) is: White 1, Blue 3 (match to 5 points)
Move number 22: Blue on roll, cube decision?
| White | 113 |
|---|---|
| |
| Blue | 53 |
Position ID: 7O4GADDetw0AAA Match ID: cAmgABAAGAAA | |
• Blue doubles
Alert: wrong double ( -0.056)! [doubtful]
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.842 | (Money: +0.805) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.888 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.000 | +0.112 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.832 | -0.056 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No double, take (33.4%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 495 games, Mersenne Twister dice gen. with seed 1056812348 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: 0-ply cubeful prune [expert] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Blue wins about 80%, wins lots of gammons, passing is a blunder, doubling is an error too but as big an error as passing. Correct action is no double, but Blue should double. That's an error, but Blue doesn't know that. What he knows is that he doesn't know whether it's a take or a pass. For all Blue knows, his equity could be much better. It could hardly be much worse, for then passing would be an even larger blunder.
One more position, last one:
The score (after 0 games) is: White 1, Blue 3 (match to 5 points)
Move number 23: Blue on roll, cube decision?
| White | 113 |
|---|---|
| |
| Blue | 51 |
Position ID: 7O4GADB+tw0AAA Match ID: cAmgABAAGAAA | |
• Blue doubles
Alert: wrong double ( -0.310)! [very bad]
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.771 | (Money: +0.756) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.820 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.000 | +0.180 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.510 | -0.310 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No double, take (63.3%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 818 games, Mersenne Twister dice gen. with seed 1056812348 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: 0-ply cubeful prune [expert] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Aha! Doubling is a triple blunder. This looks the kind of error that 2-away 4-away was hoping to avoid by not doubling.
But this position doesn't meet the requirements. Passing is a double whopper. Blue doesn't win close to 82%.
But ... suppose Blue's judgment was simply off. He thought he won about 82%, and thought White's decision was close. Does the Woolsey Rule still apply?
I'd say: yes. If that's what Blue thought, then he should have doubled. He could not have simultaneously thought that White's decision was close, and Blue won about 82%, and Blue won about 75%. The Woolsey rule does not guarantee that Blue makes the right decision. In this case, White had an easy take. Blue needs to go home and study. The more he studies, the better his decisions will be. In the meantime, he will win more often if he doubles whenever he thinks the take is in doubt, than if he never doubles because he might be wrong.
"Luck determines if you win or lose. Skill determines how much luck is needed." -- Tak Morioka, Chicago Point, February 1989
http://www.chicagopoint.com/tak10.html