Thank you yuri, dnikeeb, timothy, ah clem and markx for your illuminating reasoning, heroes all.
Let's look at these again, with hindsight and the benefit of a computer! This first one was a misplay of mine.
"Should I hit him on the bar? That's a waste of a good number, I'll just play the solid 13/11(2), 6/4(2). I didn't even consider 6/4(2), 3/1*(2) but it is easily the best play, very like the position after an opening split (for White) and a 5-5. When White dances you can cash the game. You won't be too good. When he enters, well at least you have a three point board and often two or three blots to shoot at. If White enters with a 6, you can probably double and get a take, although weaker positions than this are passed every day. Any other play is a BIG blunder.
This play came from 23 years ago. White is Alan Steffen, Black is Joe Sylvester and Joe took half an hour to make his play. Joe played 10/1, 4/1. He eventually did this as the best anti-gammon play. Danny Kleinman commented that he would play to win 11/8*, 11/5, 10/7. There were almost as many other ideas as there were experts! In 1988 of course, there wasn't anybody with a laptop and a bot.
Both the best play include 21/18(2). This seems so obvious to me, because it gives White no "safe" points. If you stay back she can leave blots on the 13, 12 or 11 pts and only risk an indirect shot. After that you pick up the blot on the 10pt and play 7/4 or 4/1. The two plays are roughly equal. How did Joe's "gammonsaver" play do? It's probably fourth best, winning about 29% and losing 10 gammons. Danny's "play to win" approach wins 33% but loses 20 gammons! The winningest play is 21/18, 11/8*(2), 10/7, earning 36 wins but losing 28 gammons!
Finally this one.
It's double match point. 13/9(2) is the clear winner, putting you just one roll away from making a 6 prime. Even when White rolls a 2, you are far from dead of course. making the point 6 pips away from a straggler is always strong, so that he can't jump out with a single die. To many people's surprise I am sure, this is also the right play for money. You cash when he doesn't roll a 2 and you are still in the game when he does.
How did our brave correspondents fare? One fell nobly on his sword after feeding the positions into Gnu, another had three wrong answers, another one right, another two right and dnikeeb nailed all three. Kudos to dnikeeb of course, but equally kudos to the others for sharing their thought processes here, from which we and they can learn a lot. We only learn from mistakes. Our successes teach us nothing.
I'll find something else for you tomorrow. Don't forget to order your copy of Mochy v. Falafel, annotated and with comments from the players, the most instructive match I have seen for ages with many tough plays. dorbel(at)gmail(dot)com for PayPal and/or queries. $10.
Until next time, enjoy the game!