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You are guaranteed that if you hit, White will fan on her upcoming roll. In that case, how should you play double 1s (for money)? - Assuming the Jacoby rule is in effect then 22, 5*(2) should be a pass next turn so I don't need to look any farther.
Yes, Jacoby is assumed. However, without confirming or denying whether 22 5*(2) is the best move (given the conditions for question 5), after Blue plays 22 5*(2) and White fans, surely she has a take; indeed, Blue's cube seems questionable. (Perhaps you hallucinated that White has two checkers on the roof instead of one?)
If you (incorrectly) cube before the roll, what is your worst play with double 1s? - Seems like it would have to be 7, 5*, 3*, 1* though I'm sure I could be overlooking something.
That was my guess as well. However, XGR++ eval claims there is a worse play. (XGR++ could well be wrong -- I didn't do rollouts and even those may not produce the right answer.)
If you (for money) are permitted to turn the cube and then play as many aces as you like, how many should you play? - I made my play quickly and I counted 36 of them. I'll spend more time on this if others come up with a different answer (or you tell me it's wrong).
I also played 36 aces (presumably the same ones!), but just to give myself a little suspense I haven't yet checked that answer with the bot. [I mused that 25 or 26 might be a popular answer; we'll see.]
Nack