Curling. Yeah, Steely Dan used this here: http://www.lyricsdepot.com/steely-da...-the-most.html

On bgonline this theme is called a "Anchor and Guard position". It is like putting a wide reciever in the backfield of a prevent defense.
As far as i see, the black position is a little bit frontloaded with holes on five and seven. Moving on 15 the black blot has to declare, and if white is hit, the holes persist. If the blot stays on 7, black can close it a tempo. Moving forward, making the bar, will make the work for white, because the two holes suddenly disappear. And slotting the 5 is than easy, once we have found this terrific 3.

This turned out to be a more interesting problem than I originally thought.

First, let’s look at some rollout results. I did a 2-ply rollout on Snowie with a live cube, with results that looked like this:


Live cube Cubeless

21/18 8/3 -0.688 10/5 8/5 -0.649
21/18 10/5 -0.707 18/15 10/5 -0.654
18/15 10/5 -0.721 21/18 8/3 -0.658
10/5 8/5 -0.723 18/13 8/5 -0.660
18/13 8/5 -0.725 21/18 10/5 -0.671
13/5 -0.740 13/5 -0.674
8/3 6/3 -0.746 8/3 6/3 -0.675


Here are the XG results, as reported by InsideBackgammon:

18/15 10/5 -0.739
10/5 8/5 -0.757
21/18 10/5 -0.760


I didn’t do enough trials on the Snowie results to have confidence in the answers, especially the live cube results, which don’t employ any variance reduction. However, 18/15 10/5 finishes near the top in both cases, so it’s certainly a strong contender for best play. I’ll set up one of my machines for a longer 3-ply rollout over the weekend and see what happens.

If 18/15 10/5 is the best play, why would it be right and how could you reason it out?

There is a class of positions (fairly large, actually) where the bots will like some play which at first glance seems odd and pointless. Rollouts back up the bots. Almost always in these cases the play hinges on one or two rolls where the bot’s move swings a big chunk of equity your way, while all the other rolls balance out.

The most obvious example of these positions is where you have a 5-point board, your opponent has two men on the bar, and you’re moving home. Every turn, you try to avoid getting hit by double-whatever from the bar. It’s only a 1 in 36 shot, but it’s the only roll that matters, and all plays are pretty much equivalent if your opponent throws anything but double-whatever.

That situation is easy to see, but if the same kind of thing arises in the middle game, it’s much harder to spot because you can’t convince yourself that all the other rolls wash out. Here, instance, leaving the blot on the 15-point is much better if White’s next roll is 2-2 or 2-1, and if all the other rolls are equivalent, that could be all you care about.

The way you convince yourself of this is to create a table listing each possible play, then list all the possible replies and the equity associated with each one, then scan the table and see if any individual roll jumps out. If it does, then you have your answer. I call this method ‘panning for gold’ and if you’re willing to spend the time, it’s a way of getting the answer when you just don’t see what’s going on.

I actually rolled out 12 candidates first with XG 3-ply and the top 3 plays
all included 18/15. I narrowed it down to the 3 different themed plays for the 4-ply rollout.

IB

If white rolls 2-1 black plays 14/13 8/6 in all of the top 3 XG 4-ply rollout plays?

It is funny. If you check this position with XGRoller+, XG doesn't even take 18/15 10/5 into account for evaluation. If you mark simply all, it turns out first in a XGRoller+ evaluation.
That leads me to the question, do you really check every time every candidate? And how useful than is the PR of a match?
Will you post this also at bgonline? Could be interesting.

Well as my error rates becomes lower I have changed my training style. Instead of playing lots of matches and running an analysis to check my errors I now play 1 long match and do a very thorough analysis of ALL the interesting plays not just my errors. I even roll out some plays where I agree with XGR+ but some different themed top plays are close in equity to check etc.
The beauty of XG is that it runs so fast (if you are fortunate enough to have a fast PC and about 20 times faster then Snowie) you can perform strong rollouts in very little time.
Unfortunately Xavier prefers not to have user defined search intervals so yes occasionally as XGR+ is limited to 8 moves even on huge search interval it sometimes misses the best play but without thorough user intervention they are hard to spot. Maybe if enough users requested it, he might change his mind.
You can post this position on BGO if you like but will the giants be brave enough to chose their play without checking with their favorite bot first?
I think this play is very hard to spot for nearly all humans over the board.

IB

It will be funny, because there were some very interesting positions, which involved big themes like splitting and slotting both 5 points or slotting both edges of a prime. This is funny because it is so "hole-in-the-wall" and doesn't pop out at the drop of a hat.

It's not terribly unusual in backgames that the play that eventually shows up best in the rollouts doesn't make it to the bots' top level of evaluation. It can also happen in endgames like containment positions and others.

What makes this position so unusual is that it occurs early in the game in a fairly standard sort of position, where the bots are usually producing highly optimal results. For 18/15 10/5 not to make it into either XG's or Snowie's top 8 choices is remarkable.

This entire problem/rollout/solution is facinating. Thx a lot for posting it IB.

I can take some small solace in the fact that my play to take the 5 point comes in second on XG but would never have guessed 18/15 10/5 was the solution here in a million years.

Stick was not amused. And making the 5 point isn't so bad at all, it is the "right" play. Summing up the tenor (Stick Rice/Neil Kazaross) of the posts for this position on bgonline: The margin you can win with the "best" play is a pyrrhus win. This is probably a "cute" position, but for practical purposes way off aside. If you make in similiar positions the 5 point, your net equity win will be higher, because you can blunder more often, if you will not make the 5. For match analysis set XG Options/settings/analysis/SI to huge.

Very interesting. Stick has posted an even longer XG rollout showing the same result as the foregoing ones.

http://www.bgonline.org/forums/webbb...mes;read=90841

Yeah I said before in this thread I'm struggling to see how you could incoporate this into your game without opening up massive leaks. It's a great little problem but I'm not sure anyone but a total genius could gain much from it.

The backgammon universe is full of problems which I call 'freaks' -- positions where there is a very unusual and clearly correct played according to rollouts, but which depend on the exact arrangement of the checkers and the way in which some future upcoming rolls will play -- like 2-2 for White in this example. If you alter the position even a little bit, the solution vanishes and the play reverts to something more normal.

That's why it's good practice, when you get a rollout with a weird and non-intuitive answer, to try moving the checkers around a little bit and see if the solution still applies. Freaks are very seductive because it looks like you've discovered something remarkable, but you may have just stepped in a pothole.

Without using the word, that is basically what Stick is calling this position in the bgonline thread sited above.

http://www.bgonline.org/forums/webbb....pl?read=91182