The first three rolls were:

2-1 White: split, 24/23, 13/11
5-2 Black: split, 24/22, 13/8
4-4 White: make 5 point, 13/5(2)

Now Black has rolled 2-1. What is his best play and why?

24/22 6/5
You have to make an active play. If you play something that doesn't make the anchor white's checkers are so diversified you simply risk being attacked against a stronger board.
Once you have the safety of the anchor you slot the better point.


IB

I don't want to leave the double shot in my homeboard so that means I have to play 13/11 leaving me with a 1 to play. I figure the best 1 is 22/21 because my opponent has the same amount of direct shots on it whether it is on 22 or 21. If his builder where on 13 instead of 14 then I would have played 24/23 instead. I also didn't play 24/21 because that would give him too many shots at my guys in his homeboard.

With that said, Insidebackgammon makes a pretty good argument. Any rollouts on this?

13/11 22/21 is a serious blunder.
The best way to see this is to note that all white's rolls now either hit 1 or 2 checkers (he also has the stronger board) or play very constructively.

Getting hit after sloting isn't great but the anchor gives you long term equity.
If missed, the chances to cover are good and puts you right back in the game.

When to slot in the openings is crucial to becoming a better player.
I highly recommend to start with learning which second move replies should be slotted and then moving on to some third move examples.
After a while you will begin to notice and hopefully remember patterns of when slotting is correct which can then be applied throughout the whole game.

IB

The crucial part of the problem is seeing that 24/22 is vital once White has made his 5-point and has plenty of attackers ready to unload on you. After that, 6/5 is clearly a little better than 8/7.

If you can't bring yourself to play 24/22 for some reason, then 6/3* would be the play. At least it stops White from using his whole roll to attack.

6/3*? Probably an oversight, Bill, because there's no White checker on the 3-pt.

I didn't do a rollout, but I did put this position into GnuBG and examined the move with a 2-ply examination. Of course Mr. Robertie and Insidebackgammon are correct. It is a huge blunder (-0.142 equity difference) to play 22/21 13/11.

BTW, I agree with IB's recommendation of learning openings and replies thoroughly.

I have a javascript program with which I'm almost done programming that will drill me on the Openings (at Cubeless, DMP, GG, and GS) and the proper Opening Replies. Once I have these positions drilled into my head I think my understanding of the proper move in positions like the one above will come more naturally.

Once I have all the bugs worked out of the program I'll make it available to others who think it might improve their game.

Initially just memorising the correct replies will improve your game but it's more important to understand WHY they are correct and look at the features of the position that make it so.

IB

24/22 6/5 seems clear to me.

Let me give a hearty thanks to the posters who have explained this problem.

I encountered this position a game against GNUBG, and was shocked that the slot against a double shot was GNUBG's recommened play. I was so suprised, in fact, that I rolled it out. Even with the numbers before me, I could not fathom why GNUBG prefered slotting. The thing I couldn't see was that the anchor is the critical issue here. The slot occurs only because there is no better one after making the anchor.

1. Rollout 24/22 6/5 Eq.: -0.446
0.395 0.087 0.003 - 0.605 0.170 0.007 CL -0.297 CF -0.446
[0.003 0.002 0.000 - 0.003 0.003 0.001 CL 0.007 CF 0.018]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883063438 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

2. Rollout 24/22 8/7 Eq.: -0.536 ( -0.090)
0.380 0.080 0.004 - 0.620 0.185 0.007 CL -0.349 CF -0.536
[0.003 0.002 0.001 - 0.003 0.004 0.001 CL 0.008 CF 0.025]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883063438 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

3. Rollout 22/21 8/6 Eq.: -0.592 ( -0.146)
0.374 0.092 0.004 - 0.626 0.242 0.009 CL -0.409 CF -0.592
[0.002 0.002 0.001 - 0.002 0.003 0.001 CL 0.007 CF 0.017]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883063438 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

4. Rollout 22/21 13/11 Eq.: -0.604 ( -0.158)
0.366 0.093 0.006 - 0.634 0.265 0.016 CL -0.451 CF -0.604
[0.003 0.002 0.001 - 0.003 0.004 0.002 CL 0.008 CF 0.025]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 883063438 and quasi-random dice
Play: 1-ply cubeful prune
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Cube: 2-ply cubeful prune [world class]

I understand the reasoning behind the different plays that are considered. The concepts of slotting, making anchors, risking getting closed out, exposing men to double direct shots, having men hit in my homeboard vs. my opponent's homeboard is all fairly straight forward. It is knowing how to weight these criteria against each other that is difficult. This comes by lots of playing and examining positions that we judge incorrectly. Learning how to weight the criteria upon which we make decisions is an ever evolving process. I happen to respect Taper_Mike's analysis of various positions and he too judged this position incorrectly, so I don't feel too bad. As for your criticism, I'm doing just fine thank you.

I am very, very interested. Can it be the structure for a "Backgammon Informator"?
By the way, Walter Trice stopped playing chess and went to Backgammon, because he no longer wanted to loose against young nerds, who had read variants out of this http://www.chessinformant.rs/

I, too, am interested in this. Please keep us apprised of your progress.

And thanks for the kind words.

+1 on the javascript program, that sounds like a great idea.

This!