Well you could change the rule in chess to allow a 3-1 knight move only being allowed if you are in check if you want it to apply to fewer situations but that I feel still misses the point. What I am trying to explain is not the number of moves it actually applies to but how you think about the game. If a 3-1 knight move was allowed then clearly every move you make you would have to take into account that your opponent had that option as indeed you would too. It is the same with backgammon, you must think about what your opponents rolls can be and how they can move them and also what your next roll could be and how you can move that given any possible move your opponent makes. Knowing that your opponent or you could make a move that allows only one die to be used, whereas the rules state both must be used if possible, will then come into many more moves you make than appear likely at first sight, and therein lies the problem. I do like Big Bad Wolf's analogy of the en-passant move at chess but would also say I feel that this backgammon rule affects many more moves than that would at chess.
As I said before though, without a cube, even if the rule is fixed we still won't have true backgammon, it will just be nearer is all. Anyone here could beat the current world champion in a 1 point match, I doubt anyone would if it was 21 points!!
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