I was playing XG in an unlimited session. I was black in this position. XG doubled here and it was an easy take. But I disagreed with XG's decision to double here.
Even after the session, I rolled this out to confirm the D/T according to XG.

Now I know XG uses a "math" analysis for it's decisions. But as a human I use the following thought process:

1) Woolsey's rule - The pertinent parts are if I know my opponent has a take, it is a double when there are enough market losers.

2) O'Hagan's rule - give an initial double when there are 9 net market losers.

#2 makes sense, If you are likely to get a take next turn, don't double yet in case the worst happens in the next 2 ply.

Anyway, when I count the market losers here, I come up with 7 - 66/55/44/33/22/62. These are the rolls that either build a 5 prime in front of me or rolls so many pips I don't have the race equity to take. And not all of those are market losers against all of my rolls in reply. So using the guidelines above, I do not think this is a double yet.

Is there something wrong with my logic of this decision?

I suspect that you're not taking into account that white is up 16 pips in the race.

I am. That is why the high doubles are counted as market losers as they would clear the mid-point and crush any race equity I would have. But even if he rolls the highest non-double 65 and I would have to respond with 21 and now trail by 25 pips for a borderline pass. If I respond with an average roll say 43, it is still a pretty trivial take.

The point is that traditional thought is that you should double one roll before the doubling window will close. That is why in low volatility positions where the take is trivial it is usually not a double. Because you can always double next roll without concern of losing your market.

But imagine you roll in that position instead of doubling then a negative parlay happens against you, say you roll 21 and I respond with 66. Wouldn't you be happy you did not ship the cube? By holding the cube when you will not lose your market, it gives you the opportunity to change your mind on the double when the next 2 ply reduces your equity.

I'm not sure that's true. Before the roll, white is ahead by 16/112 = 14%. That's a big deficit as far as the race goes. Without contact, it would be a pass according to the 8-9-12 rule.

If white rolls 65 and you roll 43, white would have 101 pips to go and you would be behind 20 pips, putting the lead at 20%. I don't think that's a trivial take.

I think your doubling window is closer to closed than you are giving it credit for.

That's like saying "Aren't you glad you called even though you didn't have odds to draw?"

The bolded is the point of disagreement. I think you're much further behind than you think, which makes white's double much better than you think.

If this was a pure race, you are correct, I am down in the race and I am past the point of last take if this was a purely racing cube. But you have to remember in high anchor games which this is, you have 2 way equity, shot equity and race equity. If your shot equity is about 10%, you can take way beyond the traditional 25% equity racing cube, because now you only have to be able to win about 15% of the races, so the 8/10/12 rule does not apply here.

That only applies to a pure race with no contact. If you use the Trice racing formula n + 10% + 1 as the point of last take, here that would be 123 pips for the trailer, you can usually double the difference in a high anchor game for the respective pip count for borderline take/pass points when your opponent still has checkers on the mid-point.

So here, with the player on roll white can consider taking with pip counts up to @ 136.


I adjusted the original position to the above position where I would be down 24 pips, and this position is a borderline take/pass with XG++ giving a take as a 0.003 error.

And if I move one checker from the 11 to 10 and run that XG++ gives this position as D/T.

In general, whenever you have a high anchor and your opponent still has the mid-point it is almost always still a take if you have decent structure on your side of the board.

Edit: Question - How do I copy XG analysis to post on the forum?

The 9. 8, 6, 5 vs the 4 point in a holding game like this is very race-dependent. If white rolls big and black small it can definitely become a pass. Also the double is close to a freeroll - there are not a lot of times where you lose your double on the next sequence and you're DEFINITELY going to want to double when you have 2 on the midpoint.

Sure. Contact prevents that pure race number from being a pass. I think I acknowledged that. But that's still not changing anything about the observation that I made.

The point is that you're very far ahead in this race, and that's a meaningful observation that was not a part of the analysis that you gave. And that is the error that led you to the wrong conclusion about the position.

66/55/44 are market losers even if the race is a whole lot closer. These are absolute market crushers. So that has little to do with the size of your racing lead.

33/22/62 are market losers because you make the 5 prime.

I would have counted 65/64 as probable market losers as well. Once you run the spare on the midpoint with either one, you're going to ship the cube and black may not be in position to take. And one of the reasons black may not be able to take is because he's just too far behind in the race.

If white rolls 65, then white has 101 pips to go. n + 10% + 1 = 112 pips.

If black rolls 43 in reply, then black has 121 pips to go, and that's beyond the point of last take. In fact, black needs 16 pips for it to be a take, which only happens on 44/55/66. The market window is just about to be slammed shut by 65 according to that formula.

Re-read my comment regarding Trice's point of last take. The borderline is usually somewhere around double the difference of the point of last take. Here at 101 the racing point of last take would be 112 a difference of 11. Double that difference and it gives a rough estimate of the edge of the pass decision in a high anchor game. So at 123 and -22 pips it is near the borderline of a pass. Once you get this far back that is when you should consider a drop. But the take comes shortly after that point, usually within 1 pip. Sometimes a little more.

So 65/64 are not market losers. There is potential, 65 with a reply of 4 pips or less. 64 with a reply of 3 pips or less. So 8/1296 with these 2 numbers are a net market loser. Not nearly enough to count them as a full market loser. You have to count the net market losers, that is after his roll/my roll.

And rounding it to 7 is pretty safe here, since in most of those I have a response that would keep me in the game. 66 after any of the rolls but 66/55 will keep me in the game. 6/3 is additional after 33.

Aaron, if you have XG or GNU, put in a high anchor position and move some checkers around to see how far back you can go and still have a take. Then go the other way and see how much of a lead the player on roll needs for an initial double. The doubling window usually does not open in a high anchor game until you have a pip lead greater the point of last take in a pure race.

Edit: I just checked on XG and after 65 followed by 21 I still have a take being -24 pips at 101 - 125. I had to tweak the position and move it back another 3 pips to -27 before I had a pass.

Thanks. I did misread that.

I downloaded XG just to check. (I used to have XG a computer or two ago, but haven't done much with backgammon in a while.)

White 65 - 13/8 9/3
Black 21 - 11/9 8/7

This evaluates to a drop on XG++. Using XG+ it's a double/take by 0.005. Even if it's not technically a market loser, it's super-super close.

Ultimately, I look at this position, and my "human" analysis is that we're right up on the edge of market window, which inclines me to double. From a practical point of view, I'm not confident after the next exchange that my opponent will take if I can clear the spare from the midpoint, and a lot of rolls do that for me.

It's true you [White] only have a few large market losing sequences, but you don't have many sequences where you regret doubling by a large amount either. Say you have 7 good rolls, but if you don't roll one of them, you shuffle checkers around and then you have 7 or more good rolls the next time, and that can happen for a few rolls. Eventually you'll probably roll one of them and lose your market, and so you want to double before it does.

Here's a more extreme example of the same concept. Only 4 market losers and a huge take, and yet it's still a pretty big double.