If your online opponent makes the top play, he's cheating unless he is Nack

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If your online opponent makes the top play, he's cheating unless he is Nack

Posted By: Chris Yep
Date: Saturday, 28 February 2015, at 3:33 a.m.

In Response To: If your online opponent makes the top play, he's cheating unless he is Nack (David Rockwell)

White is Player 2

score: 4
pip: 8

11 point match

pip: 20
score: 3

Blue is Player 1

XGID=-----A---------A-------bd-:2:1:1:43:3:4:0:11:10
Blue to play 43

eXtreme Gammon Version: 2.19.208.pre-release

Eventually, Nack made the obvious move in the outfield, then rolled a 63 instantaneously making the error of moving both checkers to the deuce, recubed receiving the reward of an incorrect take and then won the match...
Actually, if the above position was the correct position, Nack didn't make any technical errors. Assuming he played 15/8 ("the obvious move in the outfield"), his 63 (played 8/2 5/2) wasn't a technical error at all. In other words, 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; see below).
For example:

White is Player 2

score: 4
pip: 4

11 point match

pip: 13
score: 3

Blue is Player 1

XGID=-----A--A---------------d-:2:1:1:63:3:4:0:11:10
Blue to play 63

1. 3-ply 8/Off eq: +0.667
Player:
Opponent: 71.76% (G:0.00% B:0.00%)
28.24% (G:0.00% B:0.00%)
2. 3-ply 8/2 5/2 eq: +0.667
Player:
Opponent: 60.19% (G:0.00% B:0.00%)
39.81% (G:0.00% B:0.00%)

eXtreme Gammon Version: 2.19.208.pre-release, MET: Kazaross XG2

Both moves have the exact same equity, though 8/2 5/2 wins a lot less cubeless, which is maybe what you meant.
On the other hand, if Nack's opponent was more than about 30 elo worse than him, Nack chose the wrong move.
Consider the following position:

White is Player 2

score: 4
pip: 2

11 point match

pip: 4
score: 3

Blue is Player 1

XGID=--B---------------------b-:2:1:1:00:3:4:0:11:10
Blue on roll, cube action?

eXtreme Gammon Version: 2.19.208.pre-release

If white has a take in the above position, that means that Nack would have been better off with 8/off on the previous roll.
Using the Jacobs/Trice "Fish" METs we get the following:
0 elo difference: D/T = 1.070
50 elo difference: D/T = 0.955
100 elo difference: D/T = 0.848

Interpolating between the 0 elo and 50 elo lines, Nack's opponent has a correct take if he's more than about 30 elo worse than Nack. So, if Nack's opponent is more than 30 elo worse than Nack, Nack would have been better off playing 8/off with the 63 roll.
Using the Kazaross XG2 MET, the base case (0 elo difference) is D/T = 1.091 instead of D/T = 1.070, so there's slightly more cushion (it probably takes an elo difference of close to 40 before it turns into a take), but the bottom line is that it doesn't take much of a skill difference for Nack's 8/2 5/2 move to be wrong in practice.
So, if the first position (above) is correct, I wonder whether Nack additionally considered the skill difference between the two players. It would be amazing if he did, though of course he could have also worked some of this out at an earlier time away from the board.