Playing Doublets Part II

Hello again, Doublet-Master here

Last time we'd elaborated on the method to deal with these tricky bugs.

Then, for the sake of simplicity we'd left out of our analysis factors like match score, cube position, gammons. Now we're going to see an example where these factors do weigh in the situation so that it turns advisable tailoring your play accordingly.

 

The following position was brought to us in rec.games.backgammon, the backgammon newsgroup, by a controversial character from there, our fellow Monty.

Black (you) is on the bar and has to play 11, he moves counter-clockwise (from 24 to 1). After the obvious: bar/24, the analysis goes on to the remaining three moves.

On a first attempt, we'll use the method explained last time in a general way, assuming the simplest game condition -- a 1-point game. On a second attempt, we'll compare the main alternative plays available, over different game conditions and see whether their relative merits change.

So you ask yourself the three questions:

A: What's your top priority goal in the current situation?
To decide what kind of game you'd strive for, you have to assess how you're standing in the race:
Black: 99 - 4 = 95, White: 125; big racing lead for Black, therefore you should try running.

B: Which is the first one(s) out of the three aces to move, that best fit your top goal?
Clearly, 24/23 23/22, anticipating the prime. But this leaves us with an ugly last ace to move. Okay, let's stop at 24/23 so we can play the last two aces without creating any outer or inner blots: 13/12(2) or 6/5(2). But this leaves us with a menacing 5-point prime coming up. Which way would you feel the worse? Stuck, not even at the edge of a 5-prime. Then you stoically come up to the 22-point, take a deep breath and see which inner point to sacrifice.

C: What's the most efficient use of the remaining moves?
Just one remaining ace to move. This is an instructive play, kind of bonus beyond the article's subject.

Since you're under the gun and will likely be attacked back there, you should move the last ace so that you could retain as strong a board as possible on the next turn.

Many of you will be surprised to know that the move that best accomplishes this goal is: 6/5!

Excuse me...?! As strong a board?! Yes -- had you played 4/3 or 3/2 or 2/1 and get attacked, you'll use one die to enter and the second die to jump out if you got lucky ...or else have to give up a second inner point!

The other way, 6/5, you'll safety one of your inner blots, leaving only one exposed and retaining a 4-point board. Paradoxical isn't it?

Conclusion: in a general way, best play is: bar/22 6/5.

Now let's see how diverse game conditions may effect the relative value of the various plays available. For these evaluations, I've used a Snowie 3-ply evaluation (no rollout), so please excuse any inaccuracy you could eventually find by doing a rollout yourself. What matters is understanding how the reasoning goes.

Scenario # 1: Moneygame, Score: irrelevant, Cube: any value and side, Jacoby rule in effect.
Now gammons do count. Despite losing quite a few more gammons than the conservative play, the bold play: bar/22 6/5 is still more profitable -- it wins both more gammons itself and more single games.

Scenario # 2: 3-point match, Score: 0-0, Cube: 1
Gammons do count; and, given the very short match length, you do fear them! Here the prudent play's recommended: bar/23 and 13/12(2) or 6/5(2).

Scenario # 3: 5-point match, Score: 0-0, Cube: 1
Gammons do count. Note that the longer the match, the more you can afford losing a gammon, trading for more gammons and single wins for yourself.

Scenario # 4: 5-point match, Score: 0-0, Cube: 2 (either side)
Gammons do count (almost the whole match!). This is a transition scenario -- both bold and conservative plays are roughly equivalent. You should assess some outside factor, such as your personal preference, or your opponent's style or strength. Always keep in mind that 6/5 leads to more gammons for both sides.

Scenario # 5: 3-point match, Score: you lead 2-0 Crawford, Cube: 1
Gammons don't count -- your opponent would double next game anyway. The preference is for 6/5 just as we saw in Scenario # 0.

Scenario # 6: 3-point match, Score: you lead 2-1 Crawford, Cube: 1
Gammons count for your opponent! A gammon wins the match for him, and is likely enough to much prefer the conservative play.

Scenario # 7: 3-point match, Score: you trail 0-2 Crawford, Cube: 1
Gammons are useless to your opponent, so you go for the plain best play: 6/5.

Scenario # 8: 3-point match, Score: you trail 1-2 Crawford, Cube: 1
Gammons win the match for you, so you go for the most gammonish play: 6/5.

Well, enough for today. You're left the homework of rolling out some of these scenarios and seeing for yourself how the key plays get ranked up and down over the changing conditions.

Good games

Grunty

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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