Page 1 PrimeTime Backgammon September/October 2010 To Double or Not to Double Kit Woolsey, a graduate of Oberlin College, is the author of numerous books on backgammon and bridge. He had a great tournament at the 35 th Michigan Summer Backgammon Championships, winning the Open and placing second in the Masters Jackpot; he is currently in third place in the USBGF rankings for 2010. One of the most interesting games in Kit s view was Game 3 of his semi-final Masters Jackpot match with David Rockwell, with Kit 4 and David 0 in an 11 point match. Kit Woolsey (W) vs. David Rockwell (B), Match to 11 points Game 3; Woolsey leads 4-0 1) W 61: 13/7 8/7 1) B 54: 24/20 13/8 2) W 64: 24/20 13/7 While normally one would play 24/14 or 24/18, 13/9 with an early 6-4, in this position 24/20, 13/7 isbest. The key is that the checker on the bar point is safe and is a valuable builder.
Page 2 PrimeTime Backgammon September/October 2010 2) B 41: 24/20 6/5* 3) W 61: Bar/18 Stepping out to his bar point is mandatory. He has an advanced anchor, so if I sit on his ace point with B/24, 13/7 I'm going to find myself on the wrong end of a priming battle.
3) B 61: 13/7* 6/5 4) W 41: Bar/21 24/23 Page 3 PrimeTime Backgammon September/October 2010 Once again I must split despite the increased danger. He is threatening to make a solid 4-prime, and if I stay back on his ace point my game will soon deteriorate. I must fight for an advanced anchor of my own.
4) B 52: 7/2* 6/4* Page 4 PrimeTime Backgammon September/October 2010 This is a difficult play. The double hit goes after the point he wants the most and take advantage of his stronger inner board. On the other hand, the resulting builder distribution is weak with the six point stripped. The alternative is the quiet 13/8, 7/5. This leaves better distribution, but also leaves me free to either anchor on his four point or run one of the back checkers. I believe he chose correctly. The key is the cube. After the double hit, if I roll badly from the bar he will have an efficient cube. After the quiet play, he won't have a cube whatever I roll.
5) W 41: Bar/24 Bar/21* 5) B 61: Bar/24 8/2 6) W 43: 24/21 13/9 Page 5 PrimeTime Backgammon September/October 2010 Making the anchor has clear priority over making my three point. Now I am solidly in the game whatever happens. However, I should have played 24/21, 6/2. I was thinking that if he hits after my play he will be forced to leave the anchor, but that isn't important -- he won't mind leaving the anchor when I'm on the bar against his three-point board. The problem with my play is that it strips the midpoint in a position where I'm likely to need a spare on the midpoint to swallow a bad roll in the future. If I had a fourth checker on the midpoint, my play would have been correct.
6) B 41: 24/23 20/16* Page 6 PrimeTime Backgammon September/October 2010 Slotting the bar point is wrong. The downside of being hit more than compensates for the upside of making the bar point (which he might not be able to do anyway). Whether 24/23, 20/16* or 20/16*, 16/15 is better is not clear. I probably would have played 20/16*, 16/15 to cover the nine point in his position, but advancing the back checker might be better since my eight point is stripped.
7) W 41: Bar/21 6/5* 7) B 51: Bar/20* 16/15 Page 7 PrimeTime Backgammon September/October 2010 Once again, slotting the bar point is wrong. Here, however, he definitely should have played B/20*, 23/22. The difference is that the checker on the 22 point can escape with sixes and communicates with the blot on the 16 point.
8) W 11: Bar/24 7/5* 6/5 8) B 63: Bar/16 Page 8 PrimeTime Backgammon September/October 2010 Correct, even though he is walking into a double shot. It is important for him to avoid getting stuck behind my solid 4-prime. B/22, 15/9 would allow me to hit from a point I want to hit from, while after B/16 if I hit I lose my midpoint
9) W 41: 13/9* 9/8 Page 9 PrimeTime Backgammon September/October 2010 While I would like to make my nine point, it isn't worth leaving the blot there with 13/9*, 6/5. I've got too many other things to worry about to leave another blot dangling. The spare on the eight point is valuable, since I will not want to be giving up that point.
9) B 63: Bar/22 15/9 Page 10 PrimeTime Backgammon September/October 2010 Once again, he should have played B/16 for all the same reasons as the previous move. In fact, it is now more dangerous to play B/22, 15/9, since I have the spare on the eight point which can be used to attack in my inner board. It is surprising that he made the right play last turn, but in this very similar position he went the other way.
10) W 21: 13/10 Page 11 PrimeTime Backgammon September/October 2010 I judged that the increased chances of making my four point with the help of the checker on the ten point compensated for the increased danger of being hit on my ten point.
10) B 21:23/21 22/21 Page 12 PrimeTime Backgammon September/October 2010 Grabbing this advanced anchor clearly has priority over making his bar point. Now he will be in good position to take advantage of his superior outfield control if I don't hit the blot.
11) W 11: 10/7 6/5 11) B 51: 9/3 Page 13 PrimeTime Backgammon September/October 2010 Even though he is ahead in the race, I have too much firepower for him to run with 21/16, 9/8. His slotting play puts the checker where it belongs, but he loses a lot of ground if I hit and if I don't hit he still has to roll well to cover. 13/8, 9/8 is ugly, but perhaps best here.
12) W 51: 21/15 Page 14 PrimeTime Backgammon September/October 2010 21/16, 7/6 is better on the offensive front. The spare on the six point is better than the spare on the bar point, since I'm willing to give up the bar point in order to attack but I'll never give up the six point. However, I chose 21/15 because his fours are so awful and I didn't want to give him a good four.
12) B 31: 13/10* 10/9 Page 15 PrimeTime Backgammon September/October 2010 13/10*, 3/2 is safer, but that checker does not belong on the two point. Still, getting hit can be costly here, so it might be best. 13/10*, 10/9 is the natural play. An interesting and hard to find alternative is 13/10*, 8/7, which leaves him good distribution and not many more shots as my threes and sixes are both duplicated. However, 3 blots might be too many.
13) W 62: Cannot move 13) B 66: 21/15(2) 9/3 8/2 Page 16 PrimeTime Backgammon September/October 2010 His play protects against 1-5 or 4-5, but the third checker on the two point is very ugly. 21/15, 21/3 leaves a much better structure, and would surely be correct if I owned the cube. However, since he has cube access he must think about his upcoming cube. If I flunk again, I'll have a clear pass vs. either play. What if I enter? If he judges that I would still have a pass then the safe play is correct -- leaving the jokers would be overkill. However, if he judges that I would have a take after he makes the safe play and I enter, he should play 21/15(2), 21/3.
14) W 43: Bar/21 7/4 Page 17 PrimeTime Backgammon September/October 2010 Is the back checker an asset or a liability? With his two and three points made, the back checker isn't guarding much, and it gives his spare on the two point something to do in the future. Furthermore, B/21, 24/21 lets me take full advantage of a future 5-5 or 6-6. I was thinking that the extra indirect shots from the 24 point, the possibility of making his bar point with 6-3, and the value of starting my four point made B/21, 7/4 better, but in retrospect I believe the back checker is too much of a liability and I should have played B/21, 24/21.
Page 18 PrimeTime Backgammon September/October 2010 Black doubles Now obviously he has a clear double. It is the take which is the question. I have a solid four-point holding game, with the plusses and minuses of the checker on his ace point. My offensive structure is good, and will likely only improve over the next few rolls. He has several checkers in the outfield, and I figure to get at least a couple of indirect shots as he tries to clear them. On the other hand I'm way behind in the race, so I will have to hit a shot to win. Will hitting that shot win it for me? Not clear. It will depend on when I hit the shot and the exact status of my board. The match score is a big consideration. A typical scenario is when I hit a shot with a solid 5-prime and will then be considering recubing. At an even match score I would be able to effectively recube much easier than I would at this match score. Bot rollouts indicate that the match score is the swing factor. At an even match score I would have a take, but at this match score it is a close pass due to my hampered recube vig. White takes
14) B 22: 15/11(2) Page 19 PrimeTime Backgammon September/October 2010 Making the nine point isn't right. That would just be an extra point to clear. Hemming me in isn't that important, since I have plays on my side of the board. However, he should be considering punishing me for leaving the blot on his ace point and switching with 13/11(2), 3/1*(2). That gets me out of his hair, and if I stay on the bar for a couple of rolls his gammon chances go up a lot. The switch completely kills the third checker on the two point, but it is still might be the best play.
15) W 52: 8/3 5/3 15) B 63: 11/8 11/5 16) W 32: 24/21 8/6 Page 20 PrimeTime Backgammon September/October 2010 Now I went the other way, scurrying to the safety of the 21 point in the face of the new builder. I think I should have instead played 7/6, 7/4. It isn't so much that staying back is good -- it probably isn't. What is critical is that my play leaves my important four point unmade. He is quite likely to be running one outfield checker to safety, giving me an indirect shot. If I hit that shot, I will not like having my four point slotted.
16) B 42: 8/6 5/1 17) W 61: 21/15 6/5 Page 21 PrimeTime Backgammon September/October 2010 I thought it was clear to stop on the 15 point. This gives me the potential to make the point next roll, as well as return sixes if I am hit. However, there are two extra shot numbers compared to 21/14, and perhaps that is enough to swing it.
17) B 65: 8/3 8/2 Page 22 PrimeTime Backgammon September/October 2010 This is a classic pay me now or pay me later problem. The three things to look at are: 1) If he pays now and gets away with it, will he have pretty clear sailing or will there be future problems?. 2) If he pays later, will his position be deteriorating badly? 3) If he pays later, will my position be improving or deterioriating? In this position, all three factors argue for paying now. If he isn't hit, the resulting bear-in figures to be pretty safe. After paying later, his position will be very difficult to clear. Furthermore, my position figures to improve a lot as I have the potential not only to make my four point but to make his ten point. He should have played 13/8, 13/7.
18) W 64: 21/15 8/4 18) B 42: 6/2 3/1 19) W 53: 7/2 5/2 19) B 63: 13/7 6/3 Page 23 PrimeTime Backgammon September/October 2010 This horror roll is the ultimate punishment for his failure to pay now a couple of rolls ago. It had looked like I would have to hit a shot before considering redoubling, but this changes things. What's going on? I have 23 hitting numbers. If I do hit, I'll have a good chance of winning a gammon. If I miss, he has a fair amount of cleaning up to do and I'll probably get at least one more direct shot. For money or at 0-0 in an 11-point match this would be redouble and pass -- easy. But at this match score it might well be another story. Is it a take? That's always where the analysis of a potential cube starts. In this position, it is vital to examine what happens if I roll one of my 13 misses. He would then have the potential to zing an 8-cube back at me. Should he redouble? If he does, should I take? These questions have to be answered before an intelligent analysis of my potential redouble can be made. Let's suppose I miss with 4-1 (my other misses are probably worse) and play 7/2. For money, I would have a trivial take of his recube to 8. On balance I figure to get at least a direct shot most of the time, and if I hit that shot I will have a claim or nearclaim with a recube. The gammon danger is small. It would be his redouble to 8 which would be the question. But that is for money. At this match score it is another story entirely. If I pass, we are even at 4-4. If I take and win, I win the match, gaining 50% equity compared to passing. But if I take and lose I go behind 8-4 with approximately 24% winning chances, thus losing 26% equity compared to passing. Would I win 1 time in 3? Not clear. In addition, I have to weigh in the small gammon danger as well as the possibility that I might hit a shot and still not win as I would not be able to cube him out. The bottom line is that I think I would have a pass of the 8-cube, and that is what I decided I would do at the table. Now that the fate of his potential recube to 8 is determined, we can look at his pass/take decision of my redouble. 13 times out of 36 (when I miss), he wins immediately. He will also win a small percentage of the time when I hit, since I will have to play the game to conclusion as he will be holding the cube. He will get gammoned a lot when I do hit, of course, but the gammon is far from certain -- I might not win the fight for my ace point or he might get one or two of the blots to safety if he enters quickly. Perhaps I'll win a gammon on 1/2 of my hits. Getting gammoned on a 4-cube loses the match for him, but the equity cost of the
Page 24 PrimeTime Backgammon September/October 2010 gammon isn't so large since if he loses a non-gammon he will be behind 8-0 which is pretty bad. So all things considered it appears that he has a take. Given that he has a take, should I redouble? I'm a clear favorite, and the position couldn't be more volatile since almost everything rides on whether or not I hit. Still, there are plenty of arguments against doubling: 1) If I redouble and miss, I lose outright when he turns it back to 8. If I hold the cube, I get to play to conclusion. Since I have plenty of life after death when I miss, redoubling costs a lot of equity if I roll one of the 13 misses. 2) If I do hit, I will almost certainly have a safe play-on for a gammon. I might or might not get that gammon, but I will be able to play for it, cashing only if and when the danger of losing the game exceeds my potential gain from winning a gammon. Of course it is nicer to win 8 points than 4 points, but I will still get my gammon value from waiting. 3) If I don't double and hit, I basically lock up the win. If I double and hit I have to play to conclusion and there is a small chance that I could get unlucky and lose the game. Kit Woolsey (Photo by Karen Davis) 4) If I do redouble and win a gammon, there is overage involved as that gets me to 12 points. While that would be nice, it means that the value of winning a gammon on a 4-cube is worth considerably less than normal. Redoubling would be a lot more attractive if I were ahead 3-0 and could use the full value of a gammon on a 4-cube. From the above analysis, I came to the conclusion that redoubling was probably theoretically incorrect. That meant that if I were sure he would take (and then redouble to 8 if I missed), I should hold off on doubling. But perhaps he will pass. There were several psychological reasons which might induce him to pass. 1) In the earlier position, he should have paid now with his 6-5 roll. Of course he considered the play, and his decision to pay later couldn't have worked out worse for him. I know that when I make a questionable play which blows up in my face I tend to get discouraged with the game and am more inclined to pass a cube than I should be. If the same is true with him, he may be leaning towards passing due to his 6-5 play. Most players like to be able to continue to play the match, even if they will be big underdogs, rather than take a double which they think might be a bad take and lose the match because of the take. 2) He can see that I have 23 hitting numbers. He can also see that if I do hit I have a good chance to win a gammon. How likely I am to win a gammon after hitting isn't clear, but most players tend to think gammon chances are higher than they really are in this sort of position. If he thinks that when I hit I will almost always gammon him, he will be more inclined to pass. 3) If he does take and I win a gammon, the match is over. He will be totally at the mercy of the dice. Players don't like being in that position -- they like to feel they have some control of their destiny. Most players like to be able to continue to play the match, even if they will be big underdogs, rather than take a double which they think might be a bad take and lose the match because of the take. 4) He might not see how powerful his potential recube to 8 is. It may look to him like he has a lot of cleaning up to do and will probably be leaving another shot. The fact that his recube is an immediate winner is what makes his take so strong.
Page 25 PrimeTime Backgammon September/October 2010 5) I thought a long time before redoubling, as there was a lot to think about. He might think that in my mind I was wondering if I was too strong to redouble -- that I was considering playing on for a gammon. If that is his perception, it may cause him to pass. Different players react differently when faced with a redouble behind in the match. Some will take virtually anything, preferring to shoot it out now rather than play from behind. Against that sort of player I definitely would not redouble. I judged that David was willing to pass if he thought passing was correct. He might work it through and come to the same conclusion that, like it or not, he has a take. If I knew that would be the case, I would not redouble. However, I judged there was a reasonable chance that he would pass, so I chose to redouble. extreme Gammon Analysis White redoubles Black drops; White wins two points.