BTW, XG's estimate that we lose with the safe play
0.02% seems like a massive overestimate to me.
There is zero chance of the opponent losing a backgammon after we make the safe play in the original position. Even after an immediate roll of [21] and we play both to the six point the opponent is on roll with a 3 roll position. No matter what weroll over the course of two rolls [21 followed by 21 for eg] we get off the backgammon. Even 3 ply knows this.
Now suppose X rolls something like 65, taking two checkers off, and
then O rolls 21 again. Evidently, 21/20 and 8/6 and 21/18 have exactly
the same equity
Besides making an error in your previous post, your logic (as well as Stick's) is hard to follow.
You say that "evidently ... and ... have exactly the same equity." However, such an assertion can't
possibly be "evident" unless we can show that all future sequences (of any possible ply) lead to
the same outcome. It's not like you attempted to show this and made an error in your demonstration:
you didn't attempt to show it.
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