Alan Alsop: 20/17, 18/17.Ouch, Blue is in a bit of trouble. Doubled and looking a gammon in the face, trouble looms. Mind you there is not a great deal one can do. As Blue can92t hit it only leaves tidying up to best effect. This really only leaves the above move, duplicating 5's and leaving 3's
Chuck Bower: 13/9.
Blue has decent chances at winning this game, so taking a defensivestance (for example, 20/17, 18/17) seems too pessimistic. Blueshould just maximize hits next turn. The two factors that gointo that are avoiding being hit, and positioning checkers tomaximize shots when missed, and 13/9 accomplishes both. White getsonly 1's, 5-5, 6-4, 2-2, 3-3 that hit without leaving direct returnshots, and Blue's three back checkers make it hard for White toget home safely this turn, and maybe even next turn.
Ilia Guzei: 20/17, 18/17.
Four blots scattered around is too much - getting gammoned is avoidable, so I would anchor up first. And if missed I will likely get a direct shot.
Oystein Johansen: 20/17, 18/17.
Whoops, I can't hit. I don't think this is the right time to play big. Ijust make the 17 point and save a lot of gammons. The only alternative movemust be 13/9, since this leave fewer direct shots, but I'm still praying Iwon't be hit. 20/17 18/17 must be better!
Neil Kazaross: 20/17, 18/17.
Two plays come to mind here and stay there. 13-9 or 17(2). I think 13-9wins a bit more often than 17(2) but fear that 17(2) loses more than twice as many gammons as games it costs. Once in a while a random point in the outfield in this position type can block something effectively on a later roll.
Slight preference for 17(2) for me.
George Klitsas: 13/9.
A problem that needs exact calculations, difficult and cumbersome for a human (a count of the possible two-ply shots is not enough, one must take into account a rough estimation of the probability of a gammon in each case). I think that playing as safe as possible (20/17 18/17) is not the best move, tho most players in a chouette, would first make that play and then, perhaps, realize that Blue can still lose a fair number of gammons. By instinct, I prefer 13/9 over 20/16, which is second-best (imo) and slightly better than the third-best 20/17 4/3, due to the duplication of one of White's best rolls, namely 53.
Laila Leonhardt: 13/9.
At first glance it may seem 'big' to leave 1's 3's and 5's to hit,But when you are faced with a decision look at what your opponent reallywants to do and what he would want to avoid.White would prefer hitting on the outside and would like to avoid hitting inhis home board and thereby giving you are direct hit.With 13/9 you leave the minimum outside hitting numbers and create moredirect hit scenarios for your next roll.
Snowie: 20/17, 18/17.
Blot minimizaion and outfield coverage. White has no safe landingplace for his outfield checker if he can't hit. If I move the checkeron my midpoint, this gives White some safe places to stop.
Marty Storer: 20/17, 18/17.
The shot count after this and the alternative 13/9 lookspretty close at first glance; in my head I get a differenceof some 3+% in favor of 13/9. That's close enough to makeme want to minimize blots to try to save some gammons. Iwon't set pen to paper or strain my brain any more. Countingshots over 2 ply is fine if there aren't too many alternativesfor each play; imagine opponent's reaction if you try to setand reset the checkers for each one. Here, I hit loose andleft a second blot if doing so minimized shots; Blue's cubepossession means White is in a lot of trouble after havingone blot hit, almost as much as after being hit twice. I'llleave it to others to try to work things out more exactly.
Bob Stringer: 20/17, 18/17.
I tried to spend a little bit of time over this, just to give theposition its due, but it looks like a no-brainer to me. White getsa direct shot regardless of anything I do, and if he hits it whileI have blots laying around it's gammon time. Even if he doesn'thit in the outfield right away, he'll hit loose in his board if hecan. That means I have to pick up two blots by making the 17point. No choice as I see it.
Casper van der Tak: 20/17, 18/17.
Errr... Do I have to answer this? At my first go at the problem set I skipped this, since I had no clue what to do. But I suppose I have to say something...
Blue is in big danger of losing a gammon, even if Blue does not get hit he is often gammoned in a straight race. Hence Blue needs to be realistic in this position - losing a single game is a good result from here.
Being hit is a disaster, reducing winning chances and upping the gammon losses. Open plays like 20/16 and 20/17 13/12 or 20/17 4/3 can be discarded - in too many cases White hits and continues to scoop up blots for the gammon or backgammon if we are really unlucky. Getting hit reduces Blue's hitting chances tremendously.
Remain two choices: 13/9 and 20/17 18/17. 13/9 may seem to provide Blue more hitting chances, but is that really true? After 13/9, White can play some of the missing numbers in the no-mans land behind Blue's checker on the 9 (eg 43 17/14 6/2 32 17/15 6/3), reducing the number of Blue's hits. After 20/17 18/17, White does not have this opportunity. So on misses like 21 and 31, Blue will get more shots. And from a joker-control perspective, making the 17 reduces the downside of the disaster scenarios.
20/17, 18/17 it is!
Kit Woolsey: 13/9.
Minimizes outfield shots, duplicates aces, and keep spread out to catchWhite as he comes around. Making the 17 point cleans up a couple ofblots, but I think I need to be optimistic and go all out for a shot.
Chris Yep: 20/17, 18/17.
No matter what Blue plays he has to leave a direct shot. It looks like Blue is about even money to get gammoned so safetying blots could be crucial. I like 20/17 18/17, cutting down Blue's blots from 4 to 2, while still providing decent outfield coverage.
Summary: Is it right to minimize the blots, even if there are more direct shots inthe outfield and you lose some of the double-coverage? The panel says yes.I guess I can be convinced this is right.
