Answer:

No, they cannot. Plainly a Builder cannot both attack a Home Stone and cut off every flight square that the Home Stone has. For instance, a Red Home Stone in the corner of the board - say, Ubar's Initiate One - can move to any of three squares - Initiate Two, Builder One and Builder Two. A Yellow Builder at its own Ubar's Builder Nine would cut off all three of these squares (as the Home Stone cannot capture it) but it does not also attack the Home Stone; and on any other square, it would leave at least one of these three squares free.

The defending Home Stone's weakness is that it cannot capture, but this is shared by the attacking Home Stone. It can cut off one of the defender's flight squares by occupying it, since the defender cannot take it, but this is not enough to force the win.

An interesting situation, and the closest approach to a forced win, arises where the Red Home Stone is on Ubar's Initiate One and the Yellow Home Stone is on Ubar's Builder Ten, and the Yellow Builder at Ubar's Initiate Nine. Here the Builder does attack the Home Stone, and covers the flight square at (Red's) Builder Two, so this looks like the win we were looking for. But what was Yellow's last move? Not to move the Home Stone to Builder Ten, for if so, Red must have illegally left his Home Stone exposed to capture (as it and the Builder would have already been on the squares they now occupy). Nor to move the Builder down the Initiate's file to Initiate Nine, for the same reason. Therefore Yellow must have just played his Builder along his ninth rank. Then what was Red's previous move? He must have moved his Home Stone from his Initiate Two (or Builder Two) to Initiate One, in response to a move by Yellow that attacked the Red Home Stone. But Red had no need to move the Home Stone to Initiate One - not when he had the whole board open to him. Hence the win is possible only with the weaker side's cooperation, and cannot be forced against correct and obvious defence.

Looked at another way, it is easy for the Builder to drive the weaker Home Stone towards the corner of the board, and it can easily restrict it to the two squares Initiate One and Builder One, and hold it there while its own Home Stone approaches. This can force the position: Red Home Stone at Ubar's Builder One, Yellow Home Stone at Ubar's Scribe Ten and Builder at Ubar's Scribe Nine. Red now has no move but Home Stone to Initiate One. But to effect capture of Home Stone, Yellow must move Home Stone to Builder Ten - to make this square unavailable to the Red Home Stone - and Builder to Ubar's Initiate Nine - to attack the Home Stone. Since Yellow cannot do both of these in one move, he can only draw by making either of these moves singly (or Builder to Ubar's Builder Nine.)

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