You can also adjust the classes for what GNU Backgammon considers lucky and unlucky rolls. The luck of a roll is defined as the differnce of equity after the best move after rolled dice and the equity after best move avergaged over all possible rolls.
Not hitting is, as Gnu told you, a big blunder. You are correct to say that generally speaking in this type of situation you want to avoid sending a fourth checker back, because it gives your opponent the chance to make a second anchor. Here though you pay a big price if you eschew the hit, because it leaves one of your men still on the ace point and it gives your opponent the opportunity to make a five prime with his next six or make his bar with an ace. It also allows him to play all of his next roll, notably 6-6, 3-3 and 6-3 his disaster rolls if he is on the bar, are now very bad for you. The swing on these four numbers alone is enormous. Even if he does make a 1-2 back game next turn, well that isn't very bad and certainly not as bad as the alternative.
GNU Backgammon Position ID: 2NbgADSMt4MBJA Match ID : cAk3AAAAAAAE
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg | X O O | | O O O X X | 0 points | X O | | O O O | | | | | | | | | | | | | v| |BAR| | 1 point match (Cube: 1) | | | | | | | X | | O X | | X | | O X X | | X X O | Rolled 65 | O X X | | X X O O | 0 points +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: pilzgift Pip counts : O 163, X 140
The best play according to gnubg is to hit 24/18*/13. If he will re-enter from the bar, this will give him the opportunity to build a prime on the 2 and 1 point and the situation will possibly lead for him to play a back-game. I played against the advice of gnubg not hitting his 18 point and eventually won the game. Is it a good tactical decision to prevent the opponent to play back-games or prevent him to have a even number of checkers in my home (which can lead to a dangerous prime) as in this situation?
The luck adjusted result is calculated as the actual result plus the total unnormalised luck rate. This is also called variance reduction of skill as described in Douglas Zare’s excellent article Hedging Toward Skill. This should give an unbiased measure of the strengths of the players. Whether it does or not is of course another matter! http://www.bkgm.com/articles/Zare/HedgingTowardSkill.html