Quite a gap since my last post, as my ancient computer took a week off and went on holiday. It's back now, looking relaxed and tanned, but on its return I took the opportunity to give my own game a much needed overhaul. Like the great majority of players, I miss a lot of doubling opportunities. I would go as far as to say that it is the worst single mistake that humans make. I have been concentrating on getting that cube over earlier, even if it means sometimes doubling too early. Better that than missing a double.
So here are a few interesting positions from a recent match against a world class opponent.
White is leading 2-0 to 5 here and I am on roll. This looks like a good number, what would you do with it?
The first thing to note here is that this a correct double (and take) before I rolled the 6-1!
So what did you want to do with it? I went for 8/2*/1, a blunder. 18/17*, 11/5 is better but best of all is 18/17*/11.
Is this obvious? Now I know the right answer I understand what's going on! Two points; firstly 18/17* costs White 17 pips, compared to 2 after 8/2*/1, secondly leaving the blot on the ace point is actually safer than covering it. Count those shots. Even without these two obvious signposts to the correct way forward, a comparison of the two sides shows quite clearly that Black has a strong positional advantage. He has the deadly 6-5-4pts block and he still has the midpoint and all his checkers are in play. White has the less than deadly 3-2-1pts block which equates to 7 checkers out of play and her midpoint is long gone. What all this means in practice is that Black needs to be playing strategically, rather than going for the tactical option of making the 1pt. (In backgammon, tactical means hitting).
Later on in the same game, after some fairly lively exchanges, we got down to this next position, with me on roll and the cube of course still in the middle. Cube action?
The point I need to make here, is that if I had doubled the first position, I wouldn't have a cube decision to make now, even if, as I thought at the time, it was too early! Doubling means that you can only make one doubling error in the game. Leaving the cube in the middle means that you can make a mistake later and sometimes a whole string of them.
Pretty clearly if Black doubles here he will cash. Nobody takes this. A very useful rule is that if you are in the air against a four point board and your opponent is shooting at a second blot, give it up. It's almost always a pass and usually a correct double. Here though Black has a chance to pick up two blots and that's enough to push this position into the "too good to double" bracket.
I'm sorry to say that I cashed this, a blunder, but note that it is a blunder I couldn't have made if I had correctly doubled position 1. This is the hidden benefit to early cubing. It keeps doubling errors down to a maximum of one per game.
In the next game, with White leading 2-1 to 5, she came on roll in this position and made an excellent double.
If you can't see this as a double, particularly when leading, it is the two Black checkers out of play on the ace that are my weakness. You really do need 15 checkers to play with, as White has. It's a fairly comfortable take though, as White's gammons only win three points and the cube is very useful for Black, as if it is turned to 4, he can use all the points. However the key feature is this. A lot of Black's equity lies in his cube ownership and if he isn't going to make good use of it, he should probably pass.
At this score (White 3-away, Black 4-away) White can pass a 4 cube and still retain 40% of the Match Equity at 3-away, 2-away. It follows that Black should be pretty aggressive with the recube and his doubling window actually opens at around 30%! White failed to jump my prime and bust her own with a 5-5, so we came down to this.
It's not often that you get the chance to recube with two men still on the roof, but I reasoned, "I have to throw two sixes and so does she, but I get first go". I recubed. It's a small error. I can lose my market here by throwing a 6 when she doesn't, but it's just as likely that I don't and she does or that we both do, in which case I will be very sad. Better to wait one turn even though I am in the window. Then if neither of us rolls a 6, she has to play and burn one or both of those useful outfield checkers. Then I'll have a correct cube and of course she should take. Note this feature where Black keeps his prime when he dances, but White has to keep playing and busts her board when she can't roll a six.
I learned a lot from looking closely at these decisions and I hope that you did too. With any luck, I'll have something else for you tomorrow, so until, enjoy the game!
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Great problems! I think I personally lose more equity from incorrect take/pass decisions than from missed doubles, but I certainly mishandle my share of doubling decisions.
In the first position, is your analysis of the checker play with the cube centered or with the cube turned? I find that in many cases, the bot rollout of the checker play can be rather strange if you've just missed a double. With the cube turned, I would have played 18/17* 11/5 here. I don't quite understand why 17/11 is better than 11/5 (if it is). It seems natural to me to bring forward more ammunition for the blitz.
One of the many ways that XG is superior to earlier bots is its comprehensive player profile, that displays information about your play in many different ways. One of these is a pie chart that shows you where you lose equity. Mine shows that about 20% is lost with cube decisions, of which about 9% comes from missed doubles. Wrong takes and passes combined account for about 6.5% and I would expect this to be a typical proportion, as you can miss several doubles in a game, but usually only make one wrong take/pass decision.
If I had doubled before the roll, 11/5 is much closer to being correct, but still an error. The reason why you don't play 11/5 to provide more ammo for a blitz is that a blitz is not the best game plan. If it was, then 8/2*/1 would have been best.
If White hits on the ace point, Black will be very happy to have the 11pt. In the other variations, White is probably passing after either play, so the 11pt is a form of insurance if you like.
Thanks for pointing out that feature of XG, Paul! I hadn't paid any attention to it before. In my case, 23% of my equity loss comes from cube decisions, 7% from missed doubles, and 7.5% from wrong takes and passes combined. So while about 45% of your equity loss from cube decisions comes from missed doubles, only about 30% of mine does.
Still, you make a good point that I had overlooked, that typically, more equity loss comes from doubling errors than from take/pass errors, simply because one is faced with more doubling decisions than take/pass decisions (just as more equity loss comes from checker-play errors than from cube errors because one has to face so many checker-play decisions). Even by XG's somewhat narrow definition of what constitutes a "doubling decision," I face roughly four times as many doubling decisions as take/pass decisions. So even though my doubling "error rate" is about half of my take/pass "error rate," I throw away about twice as much total equity via doubling errors.
There's one caveat in all of this, which is that I believe that XG's statistics here are all EMG based rather than MWC based. I wonder if the picture looks different from an MWC point of view.
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