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To move your checkers you throw two dice, and can use either number on any checker (or both to one.) A lone checker on the board is named a blot, and if an opponent lands a checker on it (lands directly, not jumping) makes it go back to the bar. Then you need to re-enter the playing field, from the bar to the inner board of your opponent. If a position has more than one checker, it is known as a point (short of made point) and your opponent can’t land on it, needing to jump over it. So, the main strategy involves making points strategically, so you reduce your opponent mobility, and knowing when it is worth leaving a blot somewhere. A row of 2 or more points in succession are known as primes, and prime-making is a fundamental strategy. The best of course is to make all points in your home board and then hitting your opponent: since all points are closed there is no way to re-enter from the bar. But strategies are varying depending on how the rolls go, and as such several kind of “games” (in chess lingo they have open and closed games, in go we have moyo games and territory games… backgammon has also different kinds depending on strategy picked.)
Rules are simple (verbalising them is the hardest part, I have just found :D) but make up for a very interesting and fast-paced game. Oh, before I forget there are two more things. Backgammon is played in matches for points, because a backgammon game can end with 3 different results: A normal win is scored when you just get all your checkers to home and your opponent also got some to hers. A gammon (which scores twice) happens when you get all and your opponent got none to home, and a backgammon (scores thrice) when there are still enemy checkers in your home board when you finish. In addition to the different game results, a game changer (and something I really like about backgammon) is the doubling cube. The game starts with a dube numbered in powers of 2 from 2 to 64 between the players. When a player feels ahead, he can pick it up and offer a double. Then, the opponent can accept (hence, they play the game for 2–4–6 points instead of 1–2–3 points) or reject it (resigning for just 1 point.) The player who accepts now owns the cube and can double at her own discretion. The process could go up indefinitely, but of course it doesn’t. The doubling cube just works perfectly to shorten matches and games, greatly speeding play.
Back to reading suggestions, Bill Robertie’s Backgammon for Winners (Amazon | Book Depository) has enough strategy to get you covered, but eventually you’ll find yourself needing something more, and I can heartily recommend Magriel’s Backgammon (Amazon). Huge book, very interesting and well-written. I have read it 1.5 times already, and there’s still lots of things I get wrong in my games.
If you have never played backgammon I recommend you pick some free app and start playing in your computer, tablet or smartphone. I personally can recommend Backgammon NJ which is available for Android and iOS and GNU Backgammon for Mac (or Windows, or Linux.) I actually don’t recommend playing on a real board. You’ll get slogged by counting where 6 goes from here to there, computers make it easier by showing all valid moves. It took me 4 months and several hundred quick games against computers until I got good at “moving” so I know by sight where moves go.
If you are looking to play with real people, once you have picked up rules and have some knowledge, head over to Dailygammon. It is 100% free, turn-based play, and has an awesome feature that lets you play much faster than usual. You roll and move, and then the computer assumes your opponent did the best move for their roll, gives it to you and lets you enter more moves. If your opponent is good (so, he actually picks the best move when offered) games are really fast, since you are effectively playing in parallel. And if he does not, the game is “as slow” as any turn-based. Neat, isn’t it?