2-1 Answer

Red to play 2-1

The "obvious" play is 13/10--just make your 10 point.  If this position occurred "over the board" that is what most people would do, almost without giving it a lot of thought.  When presented in this fashion, as a question, there is a "quiz factor" which probably would cause people to look around the board and wonder why not make the obvious play.  If you did that, congratulations, because 13/10 is wrong.  

When you are considering alternative plays, you must consider what your position is likely to be like after you finish your play and after your opponent's next play, and here, clearly, Red is in big trouble if Blue makes his 5 point or even just the 3 point.  Red's back checkers simply have to get moving, even at the cost of leaving an extra blot in the outfield.  Red is greatly stuck in the race anyway, so getting hit isn't as big a penalty as it seems. 

Now that we've established its better to move the back checkers, it's interesting that 24/22 is better than 24/23, simply because that checker can now escape with a 6, or, if it doesn't escape, Red is better off making Blue's 3 point on the next roll.