-2:-1 post-crawford doubling strategy

[Igor Sheyn]

I was playing a match yesturday and encountered following
situation. It was, as subject indicates, -2:-1 post-crawford. I opened
with 3-1, my opponent rolled 6-4 and misplayed it 24/14. After a short
thinking process I decided not to double. I figured he has an easy
drop. I have a number of huge rolls after which I am stuck to play for
gammon, using Walter's terminology. He's unlikely to become a favorite
after upcoming roll exchange, which would make me wish I had cashed. I
figured if there exists a situation where it's better hold the cube
trailing in -1:-2 post-crawford, then it must be the case here. Of
course after correct play 24/18, 13/9, or EVEN 8/2, 6/2, I must
double. THe basic reasoning is that by cashing I stand at 50% for
match, while playing on at least for 1 roll I am a game, hence a
match, favorite.
Any valuable insights on this situations out there?
Igor

[Kit Woolsey]

Igor Sheyn (sh...@cs.bu.edu) wrote:
: I was playing a match yesturday and encountered following

I have wondered about this for some time. The general concept is that if
you are very unlikely to "gain your market" (that is, after the next you
roll he rolls sequence your opponent now has a take), then it is probably
correct to play for a gammon. This thought process should be applied for
any position where you are considering playing for a gammon. It may be
correct to play on even with a low gammon probability, if your chances of
gaining your market are zero or very small.

In this case, your opponent's take point is not the usual 25% but 50%!
This creates the unusual situation that if you are almost certain to be
the favorite after the next exchange, it is correct to play on for the
gammon. Of course the situation will have to be reassessed after every
roll (which is always the case when playing for a gammon), but it is
quite possibly correct to play on.

I have done some study of the sequence you roll 3-1, he rolls 6-2
(probably the most favorable start for the player winning the opening
roll). My studies have shown that it is very unlikely for you to be the
underdog after the next exchange (and if you are the underdog it is
usually by a very small amount so you won't have cost much equity by
waiting). Since gammons are possible and it is certainly reasonable to
get one (and remain strong enough all the way through to continue to
justify playing on), it appears that it is correct to wait. My guess
would be that in Igor's example it is also correct to wait.

This is all in theory. In practice it is almost certainly correct to
double anyway. The reason is that your opponent may not fully understand
the free drop concept, so he may make a mistake and take. Only if I were
sure my opponent would not take the double would I even consider
waiting. Note that this is consistent with normal playing for the gammon
decisions -- if there is any possibility that your opponent might take it
is definitely correct to double rather than play for the gammon.

Kit