This is a continuation of a discussion raised in the current thread on Phil's podcast with Matt. I'm wondering again about the way that equities 'add up' in various ways, and whether it makes sense sometimes to "give up equity" at times when there is a prospect of "getting even more back" by giving your opponent enhanced 'opportunities for error.'
Let's say you have an opponent whom you know will always take a straight 3-roll position in a bear-off race. Would you still want to double the usual 4-roll position? I'd think you'd want to go ahead and wait an extra roll to capitalize on this reliable error, wouldn't you? If you instead doubled the 4-away position, wouldn't you in effect be giving him an equity gift by saving him from himself? . . . or maybe is it the case that the only time you can really gain equity from his flaw is in the 5-roll sequences where somebody rolls doubles and get down to a 3-roll positions 'naturally?'
My inclination is to think I should cleverly hold off cubing in the 4-roll position . . . but I'd be sacrificing .172 (with cube centered) . . .
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| XGID=-DD--------------------dd-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 75.27% (G:0.00% B:0.00%) | 75.27% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 24.73% (G:0.00% B:0.00%) | 24.73% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.505 | +1.011 |
| Cubeful Equities | ||
| No double: | +0.773 (-0.172) | |
| Double/Take: | +0.945 | |
| Double/Pass: | +1.000 (+0.055) | |
| Best Cube action: Double / Take | ||
eXtreme Gammon Version: 2.10
. . . while my opponent would 'only' be giving uo .160 via his improper Take:
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| XGID=-DB--------------------bd-:0:0:1:00:0:0:3:0:10 | |||||
| Blue on roll, cube action? | |||||
| Analyzed in XG Roller++ | No double | Double/Take |
| Player Winning Chances: | 79.40% (G:0.00% B:0.00%) | 79.40% (G:0.00% B:0.00%) |
| Opponent Winning Chances: | 20.60% (G:0.00% B:0.00%) | 20.60% (G:0.00% B:0.00%) |
| Cubeless Equities | +0.588 | +1.176 |
| Cubeful Equities | ||
| No double: | +0.768 (-0.232) | |
| Double/Take: | +1.160 (+0.160) | |
| Double/Pass: | +1.000 | |
| Best Cube action: Double / Pass | ||
eXtreme Gammon Version: 2.10
. . . so does this mean I lose out on a net .011 in equity every time I try to exploit his weakness, over-matching it by a bigger blunder of my own?
This is very counter-intuitive to me (do others not find it so?) -- so it will be very helpful if I can be shown/persuaded that it would indeed be equity-positive to double 4-roll positions where it is known your opponent is committed to taking 3-roll positions!
The thing I would assume is going on is that the initial Equity evaluation on my 43-roll position (-.171 not cubing) is predicated on the ideal, robot-like behavior of your opponent.
. . . with the result that it simply isn't appropriate to compare these equity, subtracting them to see who is "giving up more equity." Rather, if your imperfect opponent could be characterized as a "dumb-bot" the equity evaluations would simply reflect that and a 4-roll position would come out as "No Double".
If I'm thinking right, then my suggestion in the other thread that it can be good practical strategy to hold off cubing positions that are "technically" doubles by small margins but are manifestly easy takes would seem to hold water?
Albert