Paul wrote: One bad roll and one small error and the 1.121 theoretical equity of the start position has melted away very fast!
Paul, I sympathize with the point you made in your article, but I basically agree with Tim's (and Stick's, and higonfive's) criticisms.
Yes, an intermediate player will reach positions that he "knows" are objectively too good, and will be right to think they are only too good if he can extract all the equity due him with good play. I think I have made a similar point before along these lines: suppose you're given a cube in a difficult position (for you personally) that you "know" is a close take but you have absolutely no understanding of the ensuing strategy required. You might consider how you'd play your next roll and decide that you haven't a clue. In such positions, you might occasionally be right to pass (more often, though, you ought to suck it up, take, and see how it goes).
But if the intermediate player is good enough to accurately assess both the objective equity and the difficulty of playing out the position and his own personal equity, he is good enough, I'd argue, that (to paraphrase) "it's not very wrong to go ahead and collect a point in 'too good' positions because you don't play well enough to take full advantage of your obvious play-on" is the wrong lesson for that player.
A 0.120 EMG error (not "points," by the way) is a big one. A whopper with extra tomato, at least. A shock value illustration: A 0.120 EMG error is about what you earn at DMP by winning the opening roll 5-3 and playing 13/10 8/3. Who would do that?
I agree with Stick's guess (and what I think Nigel's statistics imply) that a decent intermediate player will not, on average, blunder away enough in misplays playing on to make up for the blunder of cashing in the problem position. It's true that if one plays out the position half-dozens of times one may find dozens of chances to make a mistake, but in any one play-out such chances will be few. Very often, everything goes well and the numbers play themselves.
I posted the position not in support of your article's main argument, but in support of its very good advice to set up the position, play it out, and analyze.
I played 13/10 8/7 (quickly, always a good excuse!) to diversify, since 6's play from the anchor. Analysis and review lets me see that I overlooked the other, safer, and better diversification play 13/12 8/5. 6's still play out, 1's and 3'a (which as you point out don't play out) cover the 2 point, and 52 from the bar doesn't hit. I can also work out that diversification and safety aren't the only issues, since 13/9 is also better than 13/10 8/7. Why? At least two reasons. (1) With builders on 9, 8 and 3, Blue has 28 numbers covering the 2 point. With builders on 10, 7 and 3, only 26. With builders on 12, 5 and 3, only 23 but with one extra point-making number and three in all, none of which play out. (2) 13/10 8/7 turns 52 from the bar into a hugely lucky roll, when Blue instead could be getting a single shot (after 13/12 8/5) or a double shot (after 13/9).
I'll repeat Paul's advice once again: set up the position, play it out, analyze and review. And think!
Might as well post a rollout of the cube decision:
The score (after 0 games) is: White 0, Blue 0 (match to 3 points)
Move number 7: Blue on roll, cube decision?
| White | 90 | ||
|---|---|---|---|
                        | |||
| Blue | 106 | ||
| Position ID: 1zFzgABz2wECQQ Match ID: cAlgAAAAAAAE | |||
• Blue cannot move
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.3087 | (Money: +0.2173) | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | No double | +0.1248 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.0000 | +0.8752 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | Double, take | +0.0594 | -0.0654 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | No double, take (7.0%) | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout with var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1296 games, Mersenne Twister dice gen. with seed 910285756 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] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
If Mr. Intermediate doubled here (I didn't, yay for me) that would have been a mistake. But notice that it's only a 0.065 EMG mistake, about half the cost of the blunder of cashing in the original position.