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.