I happen to believe that backgammon is a great game, just the way it is. From time to time, however, it is fun to change the game up a bit. Here are some alternative ways to play that you not only will enjoy, but you will find them to be interesting learning exercises as well.
Nackgammon: This is the most popular backgammon variation amongst highly skilled players. When Nack Ballard found that other players were approaching his skill level, he invented an even harder game to prove his superiority over us mere mortals. You start the game with 4 checkers back instead of two. (See Position 1 below.) Nackgammon is generally much more complicated and leads to more back games and double-back games and is very challenging.
The Simborg rule: Named after one of my favorite people, this rule is often used in side events at major tournaments. The Simborg Rule states that on the very first roll of the game, the player cannot make a point. Also, if the roll is 6-5, he must not run one checker from his 24 point to the 13 point. The affect of this rule is elimination of the huge advantage that is gained from an excellent first roll. Also, since you now must play rolls such as 3-1, 2-4, 6-1, 6-4, and 5-3 creatively, more blots are left around the board on the opening roll, and that leads to more back games and more complex games.
Backgammon-to-lose: This is a really fun variation that has been played as a side event at many major tournaments. For the first three rolls of the game, each player makes the worst moves he can possibly make. Then, the players switch sides and try to win from there. You will find yourself in positions that you would never see in a normal game of backgammon, and you will truly have to be creative and insightful to play well. (It is no surprise that at major tournaments the winner of this event is usually one of the best players in the room ... the game takes real skill to play well.)
The roll-over option: Each player has the option of canceling out one of his rolls and rolling over, one time each game. However, the option must be exercised before the doubling cube is activated. Another variation is to force your opponent to roll over one time. This option eliminates a major joker early in the game that could completely turn the game in one player's favor.
The non-doubles rule: Once there is no contact (both players' checkers are clear of each other), doubles no longer count double. With this rule, where there is a pure race, the luck factor is reduced and the odds of a player who is far behind catching up is greatly reduced.
Set position play (props): Once in a while, during a game, we come across positions that are particularly challenging. It may be that one player has a very strong back game with many points in his opponent's inner board, or it could be a prime vs. prime position. Once we find a position that we believe is very interesting and challenging to play, we agree to play the game out, starting from that position, a number of times ... usually 10 times. What is really fun is that we take turns playing each side and see who wins the most points. This is a terrific way to learn how to play complicated and complex positions. (I recently posted my favorite prop which is now being played out by players all over the world. See Position 2 below. If you take turns playing Black and White you will learn a lot about how to play complicated games like this.)
My favorite prop
Advance rolling: The game is played normally, except you get to see what your opponent's next roll is before you play. It's a dream come true ... except that your opponent has the same dream!
Call your roll: One time, every game, you get to call your roll. So that the call is not a complete disaster, this option must be invoked before the doubling cube is turned.
Multiple doubling cubes: We do this in head's up money games. We might have one doubling cube that is worth $1 per point; another that is worth $5 per point; and another that is worth $10 per point. All three cubes work independently. This makes for a most interesting and exciting gambling game. This is one of the most fun and exciting gambling games I have ever played. It often turns out that the big cube gets dropped, but you get to play out the game anyway because the smaller cubes are still in play. It's fun to see how games that are usually dropped turn out. You'd be surprised how often they turn around!
Three dice: Roll three dice, but pick your best 2. There are many variations on this. You might only do this once before the cube is turned, or you might only get to do this twice a game. In pure race situations, you could use all three dice, but not have doubles count. And of course, there's the nasty way to play, where you roll 3 dice and your opponent gets to pick which two you have to use.
The Snowie challenge: This is another variation I invented and I believe it is one of the best ways to sharpen your backgammon skills. If you have two players of relatively equal skill, you actually play the match on Snowie (or Jellyfish or GnuBG), and either player has the option of challenging the other players move or cube decision. If you think your opponent made the wrong decision, you challenge him, state what you think the right play or decision is, and then you let the computer settle the bet. Sometimes we even play that if you are challenged and you think you are right, you can beaver the bet and double it. (There must be at least a .020 difference or it is a draw.)
Non-consulting challenge doubles: Bob Zavoral and I used to play this for hours against David and Sakura Wells, and it was not only fun, but a great learning experience. Each player on a team takes turns moving, and there is no consulting, except on the cube. If I play first, and the next player to play on the opposing team is David, he is allowed to challenge my play if he thinks it is wrong. Then David plays, and Bob is allowed to challenge his play, and so on. It's a great way to play doubles even if you don't play challenges, but the challenge adds a lot of pressure, and gambling, to the game. (We had to stop playing this after a while, simply because David Wells was just too good for the rest of us. I consider every dollar I lost a great investment because I learned so much playing this way.)