I originally posed the question here.
From the starting position of backgammon, one move (i.e., two rolls) are played. What is the maximum racing lead that one player can attain over the other?
Miran and Casper presumably found my intended solution, which is
21: 8/7 6/4... 33: 24/21* 24/18* plus any other 3
That gives the second player a lead of 48 pips.
The runner-up solution is 41$-44 (double hit and any other two 4s), which is a difference of 47. (You can think of it this way: Opp lost a spare from her midpoint instead of her 8pt, saving 5 pips, and you only gain 4 pips back by rolling double 4s instead of double 3s.)
Havard suggested a variant where doublets are allowed on the first roll (i.e., different from the standard rules of backgammon). In that case, as Ray and I found the biggest attainable lead is 57 pips: First player rolls 33, playing 8/5 8/2 6/3; replier rolls 11, playing 24/23*/22*/21/20*. (Runner up is 56 pips: First player rolls 33, playing 13/7 8/5 6/3; replier rolls 22, playing 24/22*/20*/18* and another 2.)
Okay, back to standard backgammon rules. In my other thread, I posed:
From the starting position of backgammon, TWO moves (i.e., four rolls) are played. What is the maximum racing lead that one player can attain over the other?
Stein found my intended solution of 115 pips. It goes like this:
1) 51: 8/3 6/5... 66: 24/18 13/7(3)
2) 22: Bar/23 6/4 6/2... 11: 24/23*/22*/21* 18/17*
Nothing can be altered; no subpart of any move. The solution is unique in every detail.
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Nack