So generally we want to avoid burying checkers deep on the ace point when higher points are not yet developed, but there seem to be some exceptions to this principle. In particular, the following circumstances seem to argue for doing so (at least some of the time):
-the only other reasonable plays strip points and/or stack checkers
-there is only one blot in the home board
-you have another blot to shoot at elsewhere

I'm still having trouble determining when I should hit loose when some or all of these conditions apply, vs when I should just bite the bullet and make the awkward stacking/stripping play.

Here are some situations where GNU says its right, and some where it says it's wrong. The roll to play is indicated in the picture.

What would you guys do in each situation, and why?

1.


2.


3.


4.

I think you left out one of the major reasons for hitting, which is to keep Villain from attacking and/or building his forward position. Sometimes you are are already split in the back, and sometimes you want to "hit and split".

In 1., after Villain has split to your 7-point, in addition to the issues above, now hitting turns his sixes from good numbers into bad. But all of that is still not enough for me in this spot. Villain isn't threatening much of anything on the offensive side, so I'd rather chill and play 13/8 24/20. But the "hit and split" may very well be right.

In 2., the issue is that I just can't find anything better than 13/9 5/1*. You have to leave a blot somewhere, so you might as well hit.

In 3., Villain has a threatening front position, but you can shut it down immediately with 21/20, so that's not an issue. Then I just bring down a builder/attacker with 13/8 and hope to contain his runner. It strips the midpoint, but such is life.

In 4., now you already have a builder on the 13-point, and 10 attackers poised for action, so go ahead and attack with 5/1*. If you get hit, you might enter deep in his board, giving you more defense, whereas in #3 you already have a runner back there so that's not going to help you.

OK, according to GNU, I only mangled 2 out of the 4 positions. Pretty good for me these days.

I agree with 1, 3 and 4. In 2, your suggested play might be right, but I might be tempted to escape one of the back men with 23/14.

Ok, here are the GNU rollouts for each position:

The rollouts are truncated after 10 moves, and assume a cash game with centred cube.

1.



2.



3.



4.


Interestingly, hitting loose turns out to be wrong in all 4 cases (though it is essentially tied in case 1). I'm actually quite surprised that it's worse in case 4 than in case 3-- it seems that already having a sapare on the 8pt would argue for not stripping the midpoint & stacking the 8 point... but it seems like the cost of either burying a checker out of play or losing 24pips in the race is just too high to be making this play.

Here's 2 more problems involving the same issue, both of which allow for a double hit:

5.


6.


Even the double hit in position 6 is not enough to warrant hitting loose on the 5 point! I imagine this is due to the fact that we're left with a much inferior point slotted compared to position 6 (9pt vs bar point).

I think position 5 may be unique-- can anyone provide another position where hitting loose on your ace point without any inner-board points is the right play?

If you don't hit on the ace point, in position 5 opponent has many more return hits than in 6. This must be more important than which point is slotted.

There are some responses to an opening roll where a loose hit on the ace point is right : 6-X played 24/18 13-X then 5-2 or 5-4. In some of these, the best 5 is 6/1*.

This is the same idea as in your position 5 : after 6/1*, anchoring on the bar point is much less likely.

So i'm trying to get a better of understanding of what principles govern when the best five is 6/1* and when it's not. Any suggestions?

That's what I would have thought too... and yet the GNU rollout favours the double hit in 5 but not in 6, despite the fact that it leaves significantly fewer shots!

I think you misunderstood him. In pos. 5 if you play 13/7* 13/8 you give returnshots on 65,64,63,62,61,52,43,33 (15 shots). If you doublehit you only leave 11 shots (all aces). In position 6 if you play 13/8 13/9* you only leave returnshots on 63, 54 and 44, so doublehitting here doesn't cut down on the returnshots as in pos. 5 (in fact it leaves more).

Usually that sort of play early in a game is a committal one. You're going to want to follow it up with a cover, and once you have the ace point made you're usually looking for an attacking game. Because it pushes you towards one particular game, it's usually done only when you can't really find anything else to do with the 5.

Am I missing something obvious?

In #5, 13/8 13/7* leaves 15 shots (any 6 that's not 66, plus 52, 43, 22), but 13/7*, 6/1* leaves only 11 shots. Shot-counting suggests hitting twice.

In #6, 13/9* 13/8 leaves only 4 shots (63/54), but 13/9* 6/1* leaves 11 shots. Shot-counting suggests only hitting once.

Edit: I missed a couple, but it doesn't change the balance of shots

5 definitely leaves more shots than 6--- that's why I'm asking why it is that GNU agrees with 6/1* in 5 but not in 6.

Oh I get it now... nevermind

Comparing the number of shots left between #5 and #6 is not really helpful for understanding why hitting loose may or may not be good. You're essentially comparing two completely different situations.

You listed a few principles in your OP but you didn't even mention the most important one, which is how your opponent's rolls play.

Usually the loose hit on the ace point is a tempo hit designed to keep your opponent off balance. In positions 1 and 2 your opponent isn't threatening to do very much since all his checkers are stacked. It would be clearly right to hit on the ace point if he had a builder on his 9 point or 11 point.

In positions 3 & 4, he's already made all the points he's going to make. So hitting loose just gives your opponent the opportunity to gain 24 pips in the race for no gain. Hitting loose in 4 is atrocious since the race is close.

In 5 & 6 the issue is again how your opponent's rolls play...after just hitting one you give him good 6s with the blot on the 7 but very bad 6s if you hit two. With the blot on the 9 it's different. And you also have more covers if you hit two with 13/7* 13/8 (not going to count how many but it is a lot more...say 31 vs. 21, and all the misses will make the 5 point).

Wonderful explanation, thanks!

For position 1 at least you get a different result with a full rollout, favoring the ace point hit:

1. Rollout 24/20 6/1* Eq.: -0.222
0.438 0.110 0.003 - 0.562 0.138 0.006 CL -0.155 CF -0.222
[0.003 0.002 0.000 - 0.003 0.002 0.001 CL 0.007 CF 0.020]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 864555810 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 0-ply cubeful [expert]
2. Rollout 24/20 13/8 Eq.: -0.245 ( -0.023)
0.439 0.096 0.003 - 0.561 0.136 0.005 CL -0.163 CF -0.245
[0.002 0.002 0.000 - 0.002 0.002 0.001 CL 0.006 CF 0.017]
Full cubeful rollout with var.redn.
648 games, Mersenne Twister dice gen. with seed 864555810 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 0-ply cubeful [expert]

On review, a even longer rollout goes back to favoring the safe play:

1. Rollout 24/20 13/8 Eq.: -0.245
0.440 0.094 0.003 - 0.560 0.132 0.006 CL -0.160 CF -0.245
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.008]
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 864555810 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 2-ply cubeful prune [world class]
2. Rollout 24/20 6/1* Eq.: -0.250 ( -0.005)
0.438 0.107 0.003 - 0.562 0.139 0.006 CL -0.159 CF -0.250
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.009]
Full cubeful rollout with var.redn.
2592 games, Mersenne Twister dice gen. with seed 864555810 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 2-ply cubeful prune [world class]