Your chance of winning from 19-20 down is about 28% (2 in a row is obviously 25%, but you have to factor in the chance of getting a gammon in the next game).
Your chance of winning this game is probably about 28% as well (or thereabouts), so not much you could do to improve your odds (except for hoping he doesn't double!)
Maybe someone could run it through a computer and give us the results? I think it's ok since the double is already rejected.
(hide) If you are waiting for your turn, click on "change" next to the "refresh" on the main page, then set refresh the page to 30 seconds to get your turn to move displayed faster. (Servant) (show all tips)