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I like 15/9 2/1 best because if we are hit, we have two possible shots coming back.  ;)))

15/8
two less shots

There are only two real choices here 15/8 and 15/9 15/14.  

Simple math says that you minimize direct shots by being as close as possible and indirect shots by being as far as possible.  So, 3-away and 10-away leaves fewer shots than 4-away and 9-away.  If I counted correctly, 16 shots vs 18 shots.  44% vs 50% chance of being hit.

But the shot count isn't everything.  Moving both checkers leaves them in "communication" at 5 points apart instead of 7 points apart.  So which is more important?  Less chance of being hit, or being able to make a landing spot?  My take is that we don't really want to make an outfield point, we want to bring our checkers home without being hit; the positional advantage with 15/9 15/14 doesn't make up for the 6% difference in being hit.

Minimize shots with 15/8.

Not getting hit is by far the most important consideration here. 15/8 immediately looks best for that, but let's do a shot count:

After 15/8: 3,10 away: 11 3's plus 2-1 and 6-4,5-5 (1-1 is blocked): 16 shots
After 15/9 2/1: 4,10 away: 11 4's plus 3-1, 2-2 and 5-5 (6-4 was already counted and 1-1 is blocked): 15 shots(!)
After 15/9 15/14: 4,9 away: 11 4's plus 3-1, 2-2 and 3-3, 6-3, 5-4 (1-1 is blocked edit: 5-4 was already counted): 19 17 shots.

(I hoped I counted correctly!)

The third option leaves  one or two extra shots. But there's more. We don't want communication here. As Kit might say, communication is a two-way street. It's rkb's roll after this. We don't want him to double hit, or to hit us now and then hit the other checker right away next turn. So having our outfield checkers more than 6 apart here looks like an advantage. Of course, one can also look at our return-hits, but we have only very few of them. Sixes will often be needed to enter from the bar, so they won't hit in the outfield. So return-hits are just not a very important scenario here. Not getting hit is most important; not getting both checkers hit is second most important.

Based on that, I think 15/8 is the best move, despite the one extra shot it leaves: it leaves no double hit and gives us better chances of survival after a single hit. Also, the checker on the 8 point is a bit easier to bring tosafety next turn than a checker on the 9 point.

Still, it's interesting that 15/9 2/1 actually leaves one fewer shot.

15/9 15/14 even leaves a double hit with 4-5 while 15/8 doesnt leave any double hit!!!!!!!!

I also counted 16 hits for 15/8 and 18 17 for 15/14  15/9.

The hit and cover numbers are:

3-2,3-1 for 15/8 4 numbers
4-1,4-2,2-2 for 15/9 15/14 5 numbers

2 out of 3 arguments point to 15/8.

@socksey: the number of return hits depends pretty much on rkb's roll.Your move leaves 17 15 hitting numbers, where 4-6 is again a double hit, and 4-2, 4-1 and 2-2 as hit and cover.

So the principle of moving as far forward as possible to leave as few shots as possible again applies  does not apply here.Sometimes this is not true due to leaving more indirect shots or duplicating some hitting numbers.  ;)

Now that I've read the other responses* and thought about it a bit more I have this to add:  

Socksey's choice (15/9 2/1) is worth looking at. If the goal of the move is to keep the back checkers in communication, 6 points away is better than 5, so this might be as good or better than 15/9 15/14.  But this communication is a double-edged sword - on one hand, it allows us to make a point with much higher probability next turn (assuming we don't get hit) but it also allows a devastating double hit and a consequent increase in the gammon rate.   Keeping our backmen 7 points apart prevents the double hit.

That convinces me - there are fewer shots and no chance of a double hit with 15/8.  

*this was written before Zorba's and Viking Blood's 2nd posts;  it repeats what they said more or less...

No real surprises here.  Note how the moves that allow a double shot lose significantly more gammons.




    1. Cubeful 2-ply    15/8                         Eq.:  +0.337
       0.616 0.076 0.002 - 0.384 0.055 0.001
    2. Cubeful 2-ply    15/14 15/9                   Eq.:  +0.246 ( -0.091)
       0.584 0.079 0.002 - 0.416 0.078 0.001
    3. Cubeful 2-ply    15/9 2/1                     Eq.:  +0.241 ( -0.096)
       0.592 0.055 0.001 - 0.408 0.075 0.001
     4. Cubeful 2-ply    15/9 4/3                     Eq.:  +0.065 ( -0.272)
       0.543 0.037 0.000 - 0.457 0.100 0.001
    5. Cubeful 2-ply    15/9 3/2                     Eq.:  +0.005 ( -0.332)
       0.527 0.040 0.000 - 0.473 0.107 0.001
        2-ply cubeful prune [world class]

    1. Rollout          15/8                         Eq.:  +0.326
       0.617 0.078 0.003 - 0.383 0.057 0.002 CL  +0.246 CF  +0.326
      [0.001 0.001 0.001 - 0.001 0.001 0.001 CL   0.003 CF   0.009]

    2. Rollout          15/9 2/1                     Eq.:  +0.248 ( -0.078)
       0.591 0.058 0.002 - 0.409 0.072 0.001 CL  +0.156 CF  +0.248
      [0.001 0.001 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.007]

    3. Rollout          15/14 15/9                   Eq.:  +0.234 ( -0.092)
       0.585 0.079 0.003 - 0.415 0.075 0.002 CL  +0.160 CF  +0.234
      [0.001 0.001 0.000 - 0.001 0.001 0.000 CL   0.003 CF   0.007]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 868041210 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]