                         |
| ||||
| XGID=aB-Aa-E-B---dCa--c-e----B-:0:0:1:00:0:0:0:7:10 | |||||
| Blue on roll, cube action? | |||||
eXtreme Gammon Version: 2.10
I believe that the weaker the opponent offering you this blitz cube, the bigger an error it is to drop it. More generally, when the character of a position is such that one side (such as Blue above) is likely to face considerably more checker-play complexity than the other side (such as White above), then bot-vs.bot-generated cube analysis becomes wildly inaccurate as a tool to guide humans to the best cube action. This is true regardless of the relative strength of the human opponents, but the greater the absolute skill deficiency of the attacker in an asymmetrically complex position, the deeper the defender should be taking his cube.
It follows that the cube above is a huge take for White ATS in any match between just about any two human opponents, regardless of their relative skill. But change the position a little, and then you will indeed present a meaningful dilemma for White. For example, move Blue’s 5th checker from his 6 point out to the 9 point, and split the two back checkers as shown below, and then you will have an interesting problem:
  |
| ||||
| XGID=aB-Aa-D-BA--dCa--c-e--A-A-:0:0:1:00:0:0:0:7:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 67.01% (G:39.55% B:1.26%) | 66.92% (G:39.99% B:1.29%) |
| Opponent Winning Chances: | 32.99% (G:7.24% B:0.35%) | 33.08% (G:7.39% B:0.38%) |
| Cubeless Equities | +0.680 | +1.411 |
| Cubeful Equities | ||
| No double: | +0.822 (-0.178) | |
| Double/Take: | +1.143 (+0.143) | |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
XG++ tells us that it is a ~.150 blunder for Blue to take this cube. I believe that it is not only correct for White to take this cube against a substantially weaker opponent, but that it is also correct for ANY human player to take this cube against ANY human opponent, regardless of playing strength. (To put it another way, I believe that even the best human players will win, on average, one or two fewer gammons than XG as Blue playing from here in a 100-game trial against a human opponent, and will lose ~1+ more games while trying, which is enough to turn this big pass into a take for White.)
The reasons human players should not rely on bot results for guidance in this position are closely related to the reasons why many the values in the Rockwell/Kazaross MET are likewise not applicable to human players:
1) XG will win significantly more gammons as Blue from this position, and from the vast majority of positions in general, than ANY similarly situated human player (including top experts) will win against any reasonably competent opponent. The bot’s gammoning superiority over similarly situated humans holds true even though its opponent on defense is an equally strong bot, because, in general, it takes far more skill to accurately prosecute a gammon attack than it does to defend against it. White, the defender, when she is not rolling from the bar with all or half of her move forced, may still have some tough decisions in certain iterations, but not nearly as many on average as Blue, the attacker, who has (or is more likely to have) most of his checkers in play on the board each time he rolls the dice. Even when the defender gets lucky and anchors, she often ends up just methodically building a prime on her side of the board, unpressured by difficult big-PR-swing choices, biding her time while waiting for a shot, while her opponent deals with tricky, high-stakes checker-play decisions with multiple candidate choices, and more opportunities to make PR errors.
2) XG will lose fewer games as Blue from this position if the attack fails, and will lose less often from busted-attack positions in general, than its human counterpart will lose from the same position. Again, this holds true despite XG’s world class bot opponent, because, in general, busted gammon attacks are more likely to result in awkward, over-extended, over-committed, or otherwise difficult-to-play positions for the failed attacker than for his reprieved opponent. Admittedly, such busted-attack positions can end up complicated for both sides, but on average they are more challenging, and more mistake-prone, for the failed attacker.
Perhaps 80-90% of checker plays in a typical match are “nexts” that don’t require expert skill. It is the other 10-20% – the hard plays that tend to regularly present themselves to the attacker in complex, early-game blitz positions, for example – that cost human players most of their checker-play equity in the long run. Even the top experts are PR donkeys compared to XG when playing the attacking side of complex positions. Yes, PR giants may play their checkers to something like a PR 2.5 when averaging in the 80% “easy” checker plays from all kinds of routine positions. But these experts are not playing PR 2.5 as attackers in complex types of games, such as the one from which the position above is taken. Try playing from this position (or, even better, from a similar but even more complex early-game blitz position) 20 or 30 times against yourself. You will quickly see that your PR will be much higher, on average, playing the attacking side than the defending side. I estimate (with no supporting data, admittedly) that a top expert who normally plays checkers to an overall 2.5 PR will, in 100 trials as the attacker in the position above (or something similar), play over 5, while the same expert’s PR playing defense as White will end up close to his 2.5 standard. Typical open players, intermediates and beginners will fair even worse as attackers when compared to their usual PR standard. Meanwhile, the bot’s analysis is based on a PR of ~0.00 on both sides.
Likewise, the values in the Rockwell/Kazaross MET are based on ~0.00 PR, bot-vs.bot gammon and win rates that are beyond the abilities of even the very best human players, and far beyond the abilities of average open players, to say nothing of intermediates and beginners. It’s true that today’s experts have learned from the bots, and that they are better checker players than the experts of 25 years ago, but they still can’t bring home gammons as well as XG can, and they still lose more games when trying. For example, at 4-away/2-away I believe even the best players should taking and auto-recubing as the trailer with about ~17% win chances, not the ~19% or so that the R/K MET suggests and XG recommends. Why? Because if human players drop a cube as the trailer at 4-away/2-away and play on at 4-away/1-away Crawford, they will not win as many gammons in the next two games as XG, and they will lose more games while trying. Indeed, I believe that all human players, experts included, would be better off if they scrapped the bot-vs.-bot R/K MET and relied, instead, on something like the pre-bot Woolsey MET, which incorporated a much more realistic assessment the abilities, and limitations, of human backgammon players.