The Best Opening Moves:
Two basic things you need to know about backgammon opening moves: Having studied opening moves for many years, having had the benefit of experience, the use of computer softwares, and tremendous personal skill and intuition, the experts have virtually all agreed on the best backgammon opening moves for every possible dice combination can be.
If you don't want to reduce your odds of winning don't make any move other than what the experts recommend.
It's very easy. You must memorize the best backgammon opening moves, and do it. Also understanding the reasoning for each move will help you greatly and it will also help you to go to the next step and know and understand the experts' recommendation on what you do on the next? roll in response to opening moves if your opponent gets the opening. Of course, none of that will be really helpful unless you understand how to play the rest of the game... But since I cannot possibly explain the entire theory of how to become an expert of backgammon with a single article, let me offer some tips for the opening moves.
All the players know, there is no question what to do with 3-1, 6-1, 4-2 and 6-5. How to play these opening moves has been agreed to and proven to be correct for many playing years, and the correct plays are correct for any match, whether you are winning or losing by a little or a lot. There is some debate for all other moves, there are some different plays depending on the score; and the decision is not so obvious.
First you should take care of the sure ones. With 3-1 you make your 5 point. Not only do most experts agree that the 5 point is the most important point to make, but any other 3-1 move will put you at an unnecessary risk of getting hit by your opponent. Why is getting hit so bad, especially so early in the game?- Because one of the principles of backgammon is that every game, no matter how complex it is, ends up as a race to see who can get his checkers around and off the board first. Between the first roll and the removal of the last checker, everything else that happens is just preparation for who the one is that gets to remove the last checker. Even games that end as a result of a double/drop are because the dropper is sure that he is less likely to be the first one removing that last checker.
With 6 -1 you make your 7 point (bar point) as that is the second most important point on the board, and any other move leaves exposed to hit blots. The same thing goes for 4 -2 -you make your 4 point - that is also an important point, and again, you don't want to leave exposed blots. With 6-5 you simply run a back checker all the way because it is the best thing to do and again, you won't leave exposed blots.
An opening of 5-3; There used to be much debate about how to play. Some experts in the 70's and 80's believed that making the 3 point was'nt right. That they were better off making several other moves that provided them with more flexibility? on the next move and put there checkers in better strategic places for it. The problem with the others moves is twofold: it leaves exposed to hit blots, and if hit, gives the opponent an immediate advantage, second, an opportunity to take the 3-point has been passed up, and the 3-point, maybe not as critical as the bar, 5, and 4 points, but is still a good position to have. It is agreed by the experts of the new millennium virtually that it is right to make the 3 point with your 5-3.
Let's simply go now through the list of what is the best backgammon opening moves, and reasonable variations for it;
2 - 1 Split your back checkers (24-23) and bring one checker down (13-11). If you wish to gamble, slotting your 5 point and bringing one down is not a bad play.
3 - 1 You make your 5 point
3 - 2 there are many variations for this play, but generally the experts think that the best play is bringing you back checker up 3 (24-21) and bringing a 2 from the midpoint (13-11) down.
4 - 1 usually, it's right to split the back checker and bring one checker down (24-23, 13-9), but it's not a bad gambling play, to bring one down and slot your 5 point
4 - 2 The best is to make your 4 point.
4 - 3 The most possible variation are in This move, depending on score, but generally, the it is agreed that the best is to move up 3 off your back point (24-21) and bring down the 4 (13-9).
5 - 1 Generally, the right move is to split the back checker and bring one checker down (24-23, 13-8). When behind in the match and a gammon win is a major plus, you might bring one down and slot your 5-point on the next move (13-8, 6-5).
5 - 2 Two plays: take a back checker 2 (24-22) ,and bring one down (13-8), or bring two checkers down (13-8, 13-11)
5 - 3 Obviously, make your 3 point
5 - 4 Two options: you can move a back checker up (24-20) and bring one down (13-8), or two down from the midpoint (13-8, 13-9)
6 - 1 Make your bar.
6 - 2 Two plays: you can run all the way, or you can run to the bar and bring one checker down
6 - 3 Two plays: either run a checker all the way off your 24 point, or run to your opponent's bar and take one down from your midpoint.
6 - 4 There are 3 plays: you can run a back checker all the way out to your 14 point ; You can make your two point; you can run a back checker to your opponent's bar (24-18), and bring down one checker off your midpoint (13-9).
6 - 5 one option; run a back checker.

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