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3a/2a Are you doubling? Part 1 *XG++
Posted By: Daniel Murphy In Response To: 3a/2a Are you doubling? Part 1 *XG++ (Prince Barlow)
Date: Saturday, 30 June 2012, at 6:36 a.m.
i couldn't decide if my opponent would actually take even if it was a take. ... If i was strongly convinced from his previous cube decisions that he would drop (i was on the fence and doubled anyway ) i would have played on to try to get to Crawford with g or win the match with a unlikely bg. If that's right or wrong I'm not sure.
It's wrong. Stop doing that ;-
If you have a double, and he has a take, double. If you think there's a good chance he'll drop, double just the same. You gain equity when he drops. You're better off winning a point than playing on hoping for a gammon. If you have a opponent that drops takes, double your doubles and be happy with your point, and think about doubling your no doubles, if he might drop those too. That point is more than you expect to win with a proper double/take or by playing on.
If, for example -- more or less your position -- you can expect about 45% MWC from not doubling now, and 47% MWC from a double and a proper take, all the better if you double and he passes, which gets you an immediate 50%. You can't do better not doubling. If you could, you wouldn't have a double.
To want to win 2 points isn't enough reason not to double a timid passer:
(1) If you don't double now, you're not going to play to the end and win an undoubled gammon all the time. Your XG analysis gives you only a 30% gammon chance.
(2) You won't even win that many gammons playing on, because sometimes you'll have to double him out in games where you might have won a gammon but aren't good enough to play on.
(3) It's likely, I think, that by wrongly playing on now you will cost yourself equity on many subsequent turns, too, by continuing to play on when your gammon chances have increased but you haven't become too good to double.
(4) Since you have a proper double/take now, by definition your MWC doubling is better than your MWC not doubling. Subsequent doubles and takes and passes (by both players) and wins and losses of 1, 2 and 3 points are all represented in your -- lower -- no double MWC -- here, 45%, less than 47%, and a lot less than 50%.
(5) You might think: He's passing now, I'll put off deciding on the cube for a roll and maybe double next roll. But how is that better? If next roll you double and he takes a take, you've lost equity, since you could have had 50% by doubling him out now and, by definition, his proper take next roll can't give you more than 50% MWC -- if it did, he'd have a drop, not a take. If next roll he passes, you win the same point you could have won now, so you haven't gained anything. If next roll you play on and eventually win the undoubled gammon you were hoping for, sure, now you get 68% MWC. But you can't justify your no double by comparing 68% to 50%. You weren't favored to have a sequence that would win you an undoubled gammon. Instead of comparing 68% to 50%, suppose you compare 50% to 30% (at best, as noted above) of 68% -- and that's only 20%? Having won your undoubled gammon, did not doubling gain 18% MWC or cost you you 30%? Well, neither. You could have had 50% with a double/pass. Instead you played on with an expectation of the combined sum of something less than 20% MWC from winning a gammon, something more than 12.5% from eventually winning a single game, and something more than 12.5% from eventually losing a single game -- adding up to 45%. Which is less than 50%.
(6) Look at it from your opponent's point of view. He can't wait to pass your takable double. What better gift could you give him than to give him one more try at jokering himself back into a take?
(7) If you were wrong about him dropping if you had doubled, you lose big time even when you win your undoubled gammon. That got you 68%. It should have got you 100%.
It's possible that your knowledge of what your opponent would do on subsequent turns after no double now could justify not doubling. In the extreme, for instance, if he's passing now and you knew that no matter what happened you could always double him out later, then you'd have a free play-on now. But in less extreme scenarios, you'd need to figure out what exactly you knew about what he would do in whatever sequences might follow, and then make a case for not doubling what appears to be a clear double absent any knowledge of your opponent (or of yourself). Possibly, that case could be truly made. But more likely not.
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