Nack writes: Errors at DMP mean more than they do for Money. I'm not referring to MWC; I'm going purely by an empirical testing of EMG error sizes / margins of the closest few plays (as reported by rollouts) for DMP, GS and GG and Money. The ratio is roughly 9:14:14:20
Nick, two questions:
(1) I'm probably missing a point, but I'm reading "mean more" to mean "cost more." But if the same error costs 2.2 times as much equity in money play as at DMP, then don't errors mean less, not more, at DMP than for money?
(2) And then in your next paragraph, first, for whatever difference it makes, 0.063 x 20/9 = 0.14, not 0.014. But why not just use actual rollout data for that play? Stick's DMP rollout for 32 has the reverse split as only a 0.006 error, not much of a handicap to be made up for by opponents' potential 2nd-move misplays.
Random notes on equity loss caused by errors at $game and DMP:
(1) Comparing Stick's rollouts of opening plays for $ and at DMP, we find that for the second best play the reported error for money is usually larger than the reported EMG error at DMP, but not in one of the ten comparable cases.
| Roll | 2nd best play | $game error | DMP error | DMP is larger, by | $game error is larger, by |
| 21 | 24/23 13/11 | 0.0156 | 0.0130 | 0.0026 | |
| 41 | 13/9 6/5 | 0.0087 | 0.0072 | 0.0015 | |
| 51 | 13/8 6/5 | 0.0099 | 0.0001 | 0.0098 | |
| 32 | 13/10 13/11 | 0.0058 | 0.0044 | 0.0014 | |
| 52 | 13/8 13/11 | 0.0131 | 0.0048 | 0.0084 | |
| 62 | 24/16 | 0.0253 | 0.0075 | 0.0178 | |
| 53 | 24/21 13/8 | 0.0570 | 0.0229 | 0.0341 | |
| 63 | 24/15 | 0.0126 | 0.0062 | 0.0064 | |
| 64 | 24/18 13/9 | 0.0037 | 0.0018 | 0.0019 | |
| 54 | 13/8 13/9 | 0.0141 | 0.0228 | 0.0087 |
(2) Cube location affects the reported cost of an error (if future action is possible). For example, how bad is playing an opening 3-1 24/23 13/10? The Gnubg 2-ply evaluation:
| Game parameters | Error |
| Money, centered cube | -0.2347 |
| Money, opponent holds 2-cube | -0.1898 |
| Money, holding 2-cube | -0.1896 |
| DMP | -0.1187 |
(3) But it's also trivial to create positions in which the reported equity lost by the wrong play is exactly the same at DMP and for money ...
Move number 3: Blue to play 52
| White | 4 |
|---|---|
| |
| Blue | 10 |
Position ID: DwAAAAkAAAAAAA Match ID: cIkqAAAAAAAA | |
• Blue moves 6/off
6/off is a 0.0926 error at DMP and in money play with White holding the cube (if Blue has the cube, the two plays are equal).
(4) ... or where the reported error is only slightly larger for money play than at DMP:
Move number 3: Blue to play 61
| White | 24 |
|---|---|
| |
| Blue | 58 |
Position ID: 7z0AAGDb7QEAAA Match ID: cAknAAAAAAAA | |
• Blue moves 6/5 6/off
Gnubg reports 6/5 6/off as a 0.0108 error at DMP and a 0.0124 error in money play if Blue has the cube (other cube positions being irrelevant).