In each of these problems, red has an awkward 56 roll that forces him to either a) sacrifice defense by breaking an anchor, 2) sacrifice connectivity by breaking the midpoint, or 3) sacrificing flexibility by burying checkers from the 8pt.

I'm having trouble understanding how circumstances should dictate which "sacrifice" is best. (match score , white 10 away/ red 11 away, centred cube)

1.


2.


3.




*Spoilers*

I'll post rollouts now so I don't need to post them later:

1.


2.


3.


Best moves:
1. 22/11
2. 22/11
3. 13/7 13/8

Obvioulsy the risk of being attacked is a key factor here, but can anyone explain why 2 builders for white's home board is still safe enough to break anchor, but 3 builders is not?

Look at the race. It usually will give you a lot of good information to help you make your decision.

In the first case, you've got a racing lead and 65 is a racing roll. The back checker is not going to be under any real threat (55 is the only pointing roll). If red misses, you're in great shape. If white hits, it's a disappointment, but you're still in decent shape.

In the second case, your lead is smaller, but it's still there. You are coming to the end of your running window. You want to run BEFORE red's position becomes too threatening. Otherwise, you'll have to sit tight (and crunch or be squeezed off the anchor, depending how the dice fall).

In the third case, you're losing the race, so you don't want to run. You need to hold the midpoint, so there are no other options.

Two factors, race and builders.

#1: You are up a mile in the race, 22 pips after the roll. You already have the stronger board and your position is deteriorating at this point. White only has 8 men in the zone and won't do any damage to you unless he rolls a miracle 55. If you can convert to a race you will probably win, otherwise you will probably lose. So run and hope you get missed.

#2: OK, you're up 15 pips after the roll, but White will be shooting at a 2-shot and can attack inside. But you still have the stronger board and just not that many good moves so 22/11 it is and hope for the best. Running is more dangerous because 1) when it works, it doesn't win as often and 2) it doesn't work as often.

#3: Three builders and 10 men in the zone spells danger. Additionally you are only up 7 pips after the roll so you are basically entering a 50-50 prop when this works and losing badly when it doesn't (and it usually doesn't). White should cube if you break anchor.

Somewhat of an anomaly in that you are supposed to play 8/3 8/2. The reason for this is the 4-shot. Move that checker to the mid and 13/7 13/8 is better even though it sacrifices some connectivity. Of course in that case 22/11 goes back to being better since now you are playing a one-blot game.

Basically, the three point anchor is not a bad point to have, but camping and dying there is also a bad idea. When you have the necessary prerequisites to break anchor you should do so. Those are usually a racing lead and safety. Your 4 point board gives you safety here.

Could you explain the 4-shot? Not sure I'm following here...

Basically White needs to move the checker on the 16-point before he does anything else, unless it's hitting. And it opens up tactical counterplay where White hits loose and gets hit back.

Thanks all for the insights; very helpful!