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BGonline.org Forums
If your online opponent makes the top play, he's cheating unless he is Nack
Posted By: Chris Yep In Response To: If your online opponent makes the top play, he's cheating unless he is Nack (Bob Koca)
Date: Monday, 2 March 2015, at 8:24 a.m.
Is it conceivable that opponent would have taken after 8/off? That would mean there is indeed some risk to the play.
I guess that depends on what assumptions we're assuming for players no more than 30 elo worse than Nack. I originally noted that "8/2 5/2 was a risk-free try at inducing an error (unless Nack's opponent was more than about 30 elo worse than Nack)." Technically you're right. There's a very tiny chance that such a player would have taken after 8/off. But under reasonable assumptions Nack was better off playing 8/2 5/2 if his opponent was no more than 30 elo worse.
For example, if Nack's opponent was actually equal to Nack in strength, had a 0.001% chance of taking after 8/off (followed by a non-doublet), and had a 0.1% chance of taking after 8/2 5/2 (followed by a non-doublet), Nack would have been better off playing 8/2 5/2 (assuming 7-away/4-away = 30%).
How many opponents were that close to Nack then?
From what I've read, very few (close to zero) players were within 30 (or 40) elo of Nack in the 1990s.
And if the opponent is weak enough to think it is a technical take does that mean it is a practical take?
Probably. The most popular MET in the 1990s was the Woolsey-Heinrich MET (7-away/4-away = 30%). Jacobs-Trice (1996) uses 29.6% for 7-away/4-away. Other common METs in use in the 1990s also have similar values for 7-away/4-away (close to 30%). So, if an opponent didn't know that the position was a technical pass, then he almost surely would have been more than 40 elo worse than Nack.
For this analysis I think it makes the most sense to assume a MET that's in line with the playing styles of the leading players at the time. That means that we should probably use a MET close to the Woolsey-Heinrich MET (which indicates that Nack's opponent had a practical take if he was more than about 40 elo worse than Nack).
In general, if Nack's opponent was no more than 40 elo worse than Nack he almost surely would have thought the position was a technical pass. He also almost always would have passed. Also note that most backgammon players overestimate their skill; if he was actually 40 elo worse than Nack, he usually (but not always) would have thought he was equal to or even better than Nack.
There are still at least two other possibilities:
1. He thought it was a technical pass, but took based on an incorrect estimate of skill difference. For example, he might "nominally" have been equal to Nack in strength, but he thought that he was significantly worse than Nack (by, say, 50 elo). Note that because he had an incorrect estimate of skill difference, in general he would have made some checker/cube plays that were errors when playing against Nack. However, perhaps this incorrect estimate of skill difference only cost him an average of 10 elo every time he played Nack.
2. He knew the equity of 7-away/4-away (about 30%), but made a very rare calculation error (i.e. he thought he had more than 30% wins in the bearoff position).
In both of the above cases Nack's opponent could have been within 40 elo of Nack.
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