The 2-2 double is very good news. You can bring two builders down that can't be hit plus make your four point. You are 55.2% to win against an opening of 2-1.
There are several options including bringing up your back checkers. Full range of strong options explored in the video.
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The 3-3 double is a very attacking roll. You make both your 5 point AND your three point in one fell swoop.
You have jumped the gun a little bit. A few turns may have to be spend bringing up the reserves and reorganizing yourself.
Alternatively make your 5 point and bring up some back checkers. There are many alternatives and they are all strong.
The 4-4 double is pretty close to Backgammon heaven. The strongest move puts you at 59.4% against a 2-1 opening for example.
As soon as you are 60-40 in Backgammon you are getting close to thinking about using the cube. Equating Backgammon to poker you'd be happy to get your money in with a 70% chance of winning at Poker, but an expert I've followed says in Backgammon 60-40 is pretty good odds for a cube decision.
Of course in offering cube you have to weigh up a number of factors. Including (at lower levels) offering it a little bit late so that there is less chance of it backfiring (your opponent may be more liable to take the cube prematurity)
I'll talk about the actual choices in the video.
The 5-5 double is a bit awkward imho. The strongest move puts you at 52.1% against a 2-1 opening for example. Play a pair of checkers to both 8-3 and 6-1.
It's a horrible position because so many of your checkers can get taken out of the game. Other options also move checkers too far forward for comfort.
13-3 I think I like the most. Here you've taken a couple of checkers out of your builder section to a fairly decent point in your home board.
Other options are explored in the video.
Depending on what your opponent rolled the 6-6 double can be devastating. Against a 2-1 the strongest move will give you 63.6% chance of winning and you should start even thinking about immediately cubing if his next roll isn't sensational.
If you are willing to give up a lot of percentage (but still have a commanding position), then other options abound.
However if the bar points are covered then a 6-6 can become a little awkward.
All main options are explored in the video.
I hope you have enjoyed this series on backgammon, please do leave your comments. If I inspired you to take up the game - great! - let me know. That would be good to hear. :-)