Stick Position No. 7/Answer

I'm rolling along here gammoning my opponent's face as I always plan to do.  I roll a great number but how to play it?  I looked at all three plays and the first I quickly dismissed, 17*, 1.  It makes the points out of order which isn't a huge deal but it also leaves only a 5 prime and both checkers on my bar point when bearing in always feels wrong unless the 6s have a good place to go.  (the ace point) 

One of the other plays has to be better.

The obvious play, making a closed board 7/2 7/1, and hoping to roll a five or a six before I crack.  I have six spare pips to play with my checker on the bar point and that translates into being able to play eleven of my non escaping numbers without cracking.  I have all 5s and 6s to escape so that yields twenty numbers or 31 numbers next turn where I don't crack.  My five bad rolls are [22 33 44 43].  There are of course variations where I crack in two turns since if I throw one of my 16 non escaping numbers now if they don't crack immediately then all 16 will crack the next turn if I repeat the blunder of rolling poorly. That's still pretty damn good, can I do better?

Let's look at 16, 2.  This is certainly the dmp play.  I can tell I win the most games as I keep the six prime and don't risk cracking nearly as much as closing the board immediately since I hop a checker.  I still reap the benefits of a large amount of gammons.  That is essentially the question, do I win enough extra gammons by closing the board now to make up for the games I lose when I crack?  I went on feel alone here and thought I didn't.  The rollout confirms my wild ass over the board guess.  I would be exchanging less than 7% extra gammon wins but losing ~4.5% more games.  The exchange rate these days is close enough to 2-to-1, like money.  (the actual gammon value is a bit higher on a 2 cube at -7 -7 but not enough to affect a decision like this.)

Rollout below:



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