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Highest possible gammon rate

Are there any (money game) positions in bg where all of one player's wins
are gammons, but his/her winning percentage is less than* (i.e. not) 100%?
I'm thinking about cubeless play (or cubeful with a completely dead cube;
no Jacoby).
Maybe it's relevant to assume "perfect" theoretical play.
* and more than 0% of course!


RobertJan Veldhuizen writes:
What is the highest gammon rate (relative: Wg/Ws) possible, in a game that
is not yet decided on who wins?


Tom Keith writes:
Here's my try.
1 2 3 4 5 6 7 8 9 10 11 12
++++++++++++++
 O   
 O   
 O   
 O   
 O   
  O  
XXX O   
XXX OO   
XXX OO   
XXX OO   
XXX OO   
++++++++++++++
24 23 22 21 20 19 18 17 16 15 14 13
It's O's turn with a checker on the bar.
The only way X can't win a gammon here is if O keeps rolling double 1's
from the bar until X is down to one checker on his ace point. The chance
of that happening is about 0.0000000120346, if I calculated right.
At that point, X still wins a gammon about 95.6% of the time according to
a GNUBG rollout. This gives a gammon rate of .999999999470478.
Tom




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