Yes i haven't seen this Domino variant i was refering from the other known Domino Backgammon, but from somewhere else....I don't like the Domino as described at bkgm.com as it has some rules of "not move your back men until move 4, etc".
There can be of course many different variations and the proposed by me variant is just one that i remembered. I haven't really played this variant for the last 5-6 years so i don't remember if there was a better one Domino-variant....

As for the computer programs part, i see that many of you don't have a real idea of what computers can do and highly overestimate the abilities of them....

In the Chess game, human programmers needed around 70 years from the time they started their real and serious occupation with computer Chess, after Adriaan de Groot's and Claude Shannon's publications on computer Chess algorithms. Only recently (probably the win of Deeper Blue against Kasparov is the most known) computers started to show signs of equality or even superiority over humans at Chess. Before 3-4 years i could beat occasionaly and very seldom of course a top Chess program with some anti-comp play. Now i can't!
All this knowledge of course all this years, that came from Chess programming is used to produce for example Gothic Chess programs or Atni-Chess programs or Reversi, Checkers programs etc. Today no one can beat a Reversi 8x8 program indeed. They are invincible! They might solve the game in the next 7-8 years or sooner.

Checker programs have for a long time prevailed over humans in the game. After Marion Tinsleys' death computers have completely dominated at Checkers. The freeware and top Cake Manchester for example if inserted in a tournament with humans will dominate easily!

Gothic Chess type programs or to say CRC type programs, have yet a long way to travel before they can be like their Chess relatives....In this site i have beaten such a program at Embassy Chess with a humiliating way. I gave my Bishop and while the program thought it will clearly win i knew that its loss was obvious! That shows that at CRC type games humans can still beat computers. I have yet to lose from November from a computer at CRC type games. ChessV, Smirf, Vortex, Zillions are all losing. So CRC is still at humans hands!

Anti-Chess: Here computers again prevail but this is logical since this game has some long forced variations that computers with proof-number-search can find in a second while us have to be tortured to find....

Three Checks Chess, Atomic Chess, etc: I don't know another computer player for this game except Zillions and ChessV and are both very weak at it, so human is still above them....

Backgammon: Probably one of the first tries for a Backgammon program was made by Hans Berliner at 1979 with a program called BKG(and a version number i don't remember). Due to the brilliant mind of Berliner one would not expect anything else except BKG to be a good program even in 1979. And BKG in an exhibition match against the world champion of that time L.Villa, won the human with a 7-1 and a won a symbolic 4000$ prize.....Although BKG played well the mistakes that made were more than the mistake of Villa and it was obvious that it was far away from an expert level. It was until G.Tesauro created a neural net Backgammon program. A method that all todays top Backgammon programs (GNUBG,Jellyfish,Snowie,BGBlitz) use.... He first tried an approach in which the net used some Backgammon knowledge and the program was trained on games of expert players and with this way the program derived its weights....That was called NeuroGammon and was good eanough to win the computer Olympiad, but not good enough to become an expert. It was G.Tesauro's TD-Gammon that changed all. TD-Gammon used a neural network that was trained using temporal-difference learning. That means the program (networks) without having almost any knowledge at all played against itself some thousands of games became very strong. The networks using as starting weights the Neurogammon's and playing again thousants of games became the most strong bot ever at Backgammon until that time. Final TD-Gammon 2.0(or 2.1 i don't remember) used 1500000 games of training against itself and reached level of expert!
Todays programs are on the strength of top human players or even stronger....

Domino Backgammon. As Playbunny has said the branching factor is very big and the number of 36 dominoes or even 21 is big enough that no program could play it perfectly for the next AT LEAST 18-19 years! Consider this: 21 dominoes with for each domino to have around 3-5 possible plays. That means a branching factor of around 84 for the first move! Second move would have ~20·4=80 That means to be able a program to solve it should calculate (84·80·....·4)^2 which is a very big number.....!
Not even dedicated neural net with super computers could do it in less than 15 years and that may even be a huge underestimation.....