Anatomy of a Backgame
Kit Woolsey, 2000
GammOnLine, March 2000
Kit Woolsey
Kit Woolsey
Backgames can be very interesting. Unfortunately, we don't get to see full-fledged backgames in action very often in serious play. The backgame is usually a last resort, and is generally avoided by the expert player if at all possible. It is usually too easy for a competent opponent to ruin the timing of one's backgame.

I recently played the following game on GamesGrid. It was a very long and complex backgame, which involved just about all the problems which can occur when playing or defending against a backgame. I thought it would be an intersting game to annotate so the readers can see what an expert is thinking about when playing a backgame.

I make no claim that either my plays or my analyses are accurate. These positions are extremely difficult, and the proper approach is often very unclear. Bots usually won't help us in these positions, for as well as the bots handle most ordinary positions they often do not understand the timing considerations or what the proper goals are for tricky backgames. We are on our own.

(Score is tied 2–2. Match to 5.)

Black  Kit Woolsey White  Scott Cole
1. 6-5:  24/13

Black to play 2-1.

2. 2-1:  13/11, 6/5

The popular theory used to be that it was vital to split the back checkers when your opponent has run one checker. This is correct when your opponent has run part of the way, since he is struggling to find a safe haven for the loose checker. After an opposing 6-5, however, it is not so clear. While your opponent would like to bring the builders off the heavy midpoint, it is no longer a super high priority. Putting pressure on the lone back checker can be very importnat. For a 2-1 response, the slot is as good or better than the split. It suits my style more.

2. . . . 4-2:  24/20*, 13/11
3. 6-3:  bar/22, 11/5*

White to play 6-2.

3. . . . 6-2:  bar/23, 11/5

With no productive six available, Scott slots the five point. At least this gives him something good if he gets away with it.

4. 5-4:  24/20*, 13/8

White to play 5-3.

4. . . . 5-3:  bar/20*, 8/5*

This is a good effort to make the offensive five point. Locking up the defensive anchor isn't too vital, since I have so many checkers back.

5. 3-1:  bar/22, bar/24

White to play 1-1.

5. . . . 1-1:  8/7(2), 6/5(2)

Once again Scott puts offense ahead of defense. He improves to make the bar point and diversify in front. I probably would have been happy with both five points, but his play is reasonable.

Black to play 5-4.

6. 5-4:  8/3, 8/4

Even at this early stage, I can consider the possibility of playing a backgame. I don't want to commit to one, but I want to leave the door open. The best way to keep all my options open is to slot key points in my inner board. This way if the blots are not hit I may be able to build a strong board quickly and go frontwards. If the blots are hit, I may get the necessary timing for a backgame. Of utmost importance is to keep several checkers on the midpoint while I maneuver. These checkers will give me the necessary flexibility to go either way in the future.

6. . . . 1-1:  23/22*, 6/4, 5/4

Black to play 3-2.

7. 3-2:  bar/22, 6/4

I considered more bananas plays such as bar/23, 6/3* or even bar/23, 8/5*, but decided against them. I can still go frontwards, and having the spare on the 22 point ready to spring may be valuable. A backgame is now likely, but I'm not ready for a full commitment.

5 2
Should White double?

7. . . . DOUBLE

This is a very strong double. Scott has a big board, I have five men stuck back, and my timing for a backgame is very tenuous. As usual the big question is whether or not I have a take. Is it clear? Not at all! Thus, the double must be right.


Ok, I admit it — I am a sucker for backgames or complex games. I am enough of an egomaniac to think that I can outplay my opponent in this sort of position and win more than my fair share. If I had Scott's position, I would be rooting for my opponent to take for the same reason. I want to have this game played out. I really have no idea whether or not this is a take — it probably isn't. But how could I resist? My true ego comes out here.

8. . . . 3-3:  13/7, 13/10(2)

Black to play 6-1.

9. 6-1:  22/16, 6/5*

Ideal. Springing the checker out into the outfield is potentially worth several rolls in the upcoming timing battle. The loose hit on the five point is also a big plus. I can still go frontwards if I make the five point, and if the checker is hit that may improve my timing if I can recirculate the hit checker back up to the defensive three point and then out into the outfield. So far, so good.

9. . . . 5-2:  bar/20*, 22/20
10. 4-4:  (dance)

White to play 3-2.

10. . . . 3-2:  13/8

Scott is attempting to take advantage of my vacation on the bar to extend his blockade. Making the eight point will be a big improvement which will put me under a lot of pressure for the rest of the game. Scott figures that if I hit one of his blots this will just hurt my timing for the backgame, and while Scott is squatting on my five point is is difficult for me to go frontwards. I'm not sure I agree with the approach, but it is a very reasonable concept.

11. 5-5:  (dance) 6-5:  20/14, 13/8

Black to play 4-2.

12. 4-2:  bar/23, 16/12

I don't want Scott being able to hit me on his ten point and start that while I am pinned back. My timing has improved a lot, but it is still critical. Timing is everything when it comes to backgames.

White to play 5-3.

12. . . . 5-3:  14/11, 7/2*

The theme of hitting loose on the two point in this sort of position is quite common. By making the play, Scott accomplishes two things. First, he prevents me from shifting to the 2-3 backgame, which generally is much easier to time than the 1-3 backgame. Secondly, if I am forced to hit back this will hurt my timing.

Black to play 5-3.

13. 5-3:  bar/22, 12/7

I don't mind if the blot is hit, and if it isn't hit the checker is well-placed as a builder to make the five point I will eventually need. I still have three checkers on the midpoint, and a checker poised to spring into the outfield. Things are touch and go, but the timing may well be there.

13. . . . 4-3:  20/13

Black to play 5-1.

14. 5-1:  8/3, 6/5

I would hate to see what Snowie thinks of this play. Yet, it seems logical to me. First of all, I don't like hitting. That may cost me my hard-earned timing, and trying to win frontwards with five checkers stuck behind a five-prime is a large task. Given that I'm not going to hit, why shouldn't I slot everything? I will need both the six and five points before I am ready to contain a hit checker, and it will be easier to make them both with both of them started than with the six point made and the five point open. I have no intention of hitting anything for quite a while now, so the inner board blots can't hurt me. In the worst case where I do hit something and he hits back, that can only help my timing. Of course I won't break one of the back anchors until I am really ready.

White to play 6-1.

14. . . . 6-1:  13/7, 10/9

Scott is following a common theme, slotting the edge of the prime. The idea is that I need to spring the spare on Scott's three point. If I roll the six to spring the checker and Scott isn't sitting on the nine point, I get another checker out into the outfield and will probably have sufficient timing to play my backgame. If I have to hit, Scott's checker is recirculated and he will be able to hold his five-prime longer.

15. 2-1:  13/11, 7/6

White to play 4-3.

15. . . . 4-3:  10/6, 7/4

Scott continues with the same theme. He isn't going to let me escape for free. Also, he in no rush to close his two point. His idea is that if there is some blot-hitting, he will want the two point slotted rather than closed so that I will be forced to enter with a hit and help his timing.

Black to play 6-5.

16. 6-5:  22/16*/11

The first moment of truth. It might be right for me to leave everything alone and simply make my board with 11/5, 8/3. It looks like my timing will be sufficient with two checkers on the midpoint and the spare on the 22 point poised to spring, but that is not guaranteed.

If I do hit, covering the three point doesn't look right. Trying to win frontwards while Scott has the five-prime is asking for too much. The idea is to get hit back, and have my four outfield checkers afford me the necessary timing.

The joker in the deck is the blot on Scott's two point. At the time I made my play, I didn't realize how that would figure into things. The danger is that I hit, he hits, and now I have to hit back on the two point and improve his timing. Now that the danger was made apparent to me by what happens, I believe I should have eschewed the hit and played 11/5, 8/3.

White to play 4-3.

16. . . . 4-3:  bar/22*/18

Naturally Scott does not cover the blot on the two point. He wants me to hit there.

Black to play 4-1.

17. 4-1:  bar/24, 11/7*

It looks like I will gain in the timing battle from this hit, since my partial blot prime will force him to hit something back in order to escape. Anyway, there aren't any other decent fours. Now I am completely committed to the backgame.

17. . . . 5-1:  bar/20*, 11/10

Black to play 5-1.

18. 5-1:  bar/24, 8/3

With nothing else to do, I might as well start another inner board point. Not only might this be helpful for making my board, but in the next exchange of blot-hitting I want the point slotted so Scott may be forced to hit and improve my timing.

White to play 6-5.

18. . . . 6-5:  20/14*/9

Scott is quite correct to hit. The checker on my 11 point represents more timing for me. Scott's goal is to split my army into two pieces. Also, I might be forced to enter with a two and hit, which will help Scott's timing.

19. 5-4:  (dance)

White to play 3-1.

19. . . . 3-1:  9/5

Since I have only two checkers on Scott's three point, Scott figures that keeping the nine point slotted is no longer too important. He opts instead for the smoother structure. I might have been inclined to play 10/6, but his play is fine.

Black to play 4-2.

20. 4-2:  bar/23*, 6/2

If Snowie didn't like some of my previous plays, I can imagine what it thinks of this one. Once again, I consider timing to be the utmost consideration I do not want to make my three point. The last thing I want to do is to keep Scott on the bar. I am also uncomfortable about breaking the midpoint. As long as I hold that midpoint my timing will survive, but once that goes my game may fall apart. Scott will have the opportunity to pick off these outfield blots and split my army into two pieces. Hence, my kamikazi play. I don't mind at all being hit in my inner board. That will probably only help my timing. There are many who would disagree with the play and they may well be right, but I would do it again.

White to play 4-3.

20. . . . 4-3:  bar/22*, 6/2*

Hitting loose on the two point is mandatory, of course. Scott doesn't want me to make this point without a struggle. Also if I am forced to hit back this recirculates another one of Scott's checkers and improves his timing considerably.

21. 6-5:  (dance)

White to play 4-2.

21. . . . 4-2:  22/18*, 10/8

Scott scoops up yet another checker, and brings the checker on the ten point in as a new builder for the two point. Naturally he doesn't cover the blot on the two point. He hopes to force me into hitting on the two point, then he enters and hits back, then I am forced to hit again, etc. If this plan works he will recirculate a bunch of checkers and my timing will collapse. Reasonable approach, but this may be overdoing it. If I get stuck on the bar for a while, I will win the timing battle. I would have preferred 22/20, 10/6.

22. 6-2:  bar/23*

White to play 6-3.

22. . . . 6-3:  bar/19*, 5/2*

Scott is nothing if not consistent. I would have played bar/22, 8/2*. I think he is leaving me with too many checkers on the bar.

23. 2-1:  bar/23*, bar/24

White to play 6-3.

23. . . . 6-3:  bar/22, 8/2*

Pound away. As usual, hitting loose on the two point is vital. It looks like Scott's plan to break my timing may be successful after my horrible 2-1 last turn. I have only those two checkers in the outfield to play with, and I don't even have a spare on Scott's three point. Scott, on the other hand, now has three checkers on my side of the board and will have plenty of plays available before he is forced to release his five-prime.

24. 3-2:  bar/22, bar/23*

White to play 6-4.

24. . . . 6-4:  bar/19, 18/14

Scott properly rushes to get a builder aimed at the critical nine point. It is important for him to be able to hit any checker of mine which dares to show its ugly head there. The worst scenario for Scott would be if I could make his nine point. This would establish a bridge to the outfield for me, and my timing would just about be assured.

Black to play 3-2.

25. 3-2:  bar/22, 24/22

Much as I would like to make Scott's two point, I just don't have a decent three to play. Breaking my midpoint is a last resort, and taking a checker to the ace point is also a no-no. The one thing you don't want to do when playing a super-deep backgame such as this is to make your own ace point. Once you have done that, you lose any chance of eventually trapping one of your opponent's checkers behind a blockade and forcing him to jar another checker loose.

White to play 5-4.

25. . . . 5-4:  14/9, 22/18

Scott heads right for the nine point. His idea is that if I roll a six he wants to be hit so as to recirculate the checker and improve his timing. This time, I don't think this is right. I have a bunch of checkers on Scott's three point, and if I roll a couple of sixes I can make his nine point and have virtually unbreakable timing. I believe he is better off just guarding the nine point rather than slotting it, so he can hit me if I come out.

Black to play 4-1.

26. 4-1:  24/23, 13/9

There goes the midpoint. I tried as best as I could to hang onto it, but it looks like Scott has won the timing battle. At least I finally have his two point. My army will be split into two pieces, and I have to salvage what I can.

White to play 4-1.

26. . . . 4-1:  19/15, 19/18

Scott would rather have hit my outfield checkers, or at least the one on the midpoint. Failing to do so he makes one outfield point and brings a checker to cover the blot on the nine point. Scott may not want to make this point, however. He might prefer to leave it open so my checkers get squeezed out one at a time. His ideal scenario would be for me to have seven or eight checkers buried on my ace and two points, and the rest of my checkers stuck in his board. If he can get to this position, it will be virtually impossible for me to win.

Black to play 4-2.

27. 4-2:  9/3

I am trying to prepare for the future. It is now inevitable that my army will be split in two, but I want to salvage what I can. The death knoll rings if I have to bury checkers on my ace point. If I get a checker on my six or five point, then when I roll a four or a five that checker heads to the greveyard. By moving in closer, I kill those fours and fives so I won't have to play them. Now only threes are bad. For now I can even handle an ace or a two with the spare on Scott's ace point. I don't particularly mind if the blot on the midpoint is hit — in fact, that is probably better for me. It is another checker which won't be buried.

White to play 6-6.

27. . . . 6-6:  15/9, 18/12*, 18/6

Scott's play looks like the natural play. However it might not be best. The problem is that if I roll an entering number with a six I won't have to play the six. Right now he wants to squeeze another checker of mine out, getting hit along the way. For this reason I believe he is better off not making the prime, but playing 18/12(2)*, 12/6(2).

Black to play 2-1.

28. 2-1:  bar/23, 4/3

I have plenty of checkers on Scott's three point, so I don't need any more. Stopping on Scott's two point has two advantages. First of all this gives me more flexibility in his board. In the future I can hit a shot from his two point without losing the anchor. Secondly, moving in from the four point to the three point is a plus. Now I have only one checker which has to go to the ace point if I roll a three, so I can't be forced to make my ace point. It won't be easy, but it looks like I won't be forced to crunch completely.

White to play 4-2.

28. . . . 4-2:  12/6

Once again, I think Scott should be giving more consideration to squeezing out one of my checkers and forcing me to hit. I would have played 12/8, 9/7.

29. 6-6:  (blocked)

White to play 4-2.

29. . . . 4-2:  9/5, 6/4

The right idea. If I roll a six, Scott would prefer to be hit. This way he retains his five-prime longer and perhaps I will be forced to bury more checkers. If he plays 9/7, 9/5 and I roll a six, I will be able to hold the timing which I have.

30. 6-4:  22/16*/12

White to play 2-1.

30. . . . 2-1:  bar/23*, 6/5

I don't care for this play. Every checker Scott sends back can only be of help to me, and the checker on my two point is my worst placed checker. In addition, now I don't have to play some of my bad rolls. I think he should have played bar/24, 6/4.

31. 5-5:  (dance) 4-3:  23/16
32. 5-4:  (dance) 5-4:  16/7
33. 5-3:  bar/22, 12/7 5-2:  7/5

Black to play 5-2.

34. 5-2:  7/2, 4/2

It isn't that I want to make the two point; I want to get off the four point. Now unless I roll a horror such as 2-2 I won't be forced to take any checkers to the ace point. I can reluctantly handle a two or an ace on Scott's side of the board, and larger numbers don't play. Meanwhile I escape with sixes, and will soon escape with fives when Scott is forced to break his eight point. After my timing went sour, this is about the best I could hope for.

34. . . . 6-5:  (blocked)
35. 5-4:  (blocked) 6-1:  5/4

Black to play 4-2.

36. 4-2:  24/22

I would rather have the spare on Scott's ace point, of course, but this is better than taking a checker to my ace point.

36. . . . 4-2:  8/4, 8/6
37. 3-3:  (blocked) 5-2:  6/4

Black to play 4-1.

38. 4-1:  23/22

Frustrating, but I am not going to take a checker to my ace point. The problem now is that I have no spares on the deep defensive anchors. This means that I can't hit a shot from them without breaking the anchor, and I'm not ready to do that yet. I may have to wait for a very late shot when I don't have to worry about breaking an anchor.

38. . . . 4-3:  7/4

Black to play 5-4.

39. 5-4:  22/17, 22/18*

Finally! Some fresh air. I won't be able to contain the hit checker, of course, but I will now be able to maneuver freely. The problem, of course, is that I don't have enough checkers to play with. I have the four checkers up front which can't do much, and I need to keep all my anchors for now. This only leaves me five checkers to play with in the outfield. That will not be sufficient to contain a hit checker. Eventually I will have to try to make some more inner board points, and hope to break off the anchors at a safe time. It won't be an easy job. The transition from a back game to finally winning it frontwards is very tricky, and there are plenty of pitfalls. If my four checkers in my inner board were back farther, I would be able to build a prime and achieve my goal. As it is, putting everything together is hard to do. If I had 20 checkers to play with it would be a lot easier. 15 checkers sometimes just isn't enough.

39. . . . 2-1:  bar/24, 6/4

Black to play 6-5.

40. 6-5:  22/16, 22/17

Scott's last roll was a big break for me. Now that he is off the six point, I can afford to be much freer with my plays. The question now is whether it is worth it for me to break my back anchor in order to hit the second checker. I don't think it is. That would be a very committal play. I'm simply not ready to contain anything. Once I leave the anchor I won't be able to get it back. In fact, since I have no board Scott would not mind hitting loose on his ace point and fighting for the point. If he gets it, my winning chances go down considerably. No, I think I am better off maneuvering with what I have. I will be willing to break off Scott's three point if I have to, but leaving the ace point is another matter.

40. . . . 6-2:  24/18, 6/4

Black to play 6-4.

41. 6-4:  22/16, 22/18

Not exactly clear where I am headed, but this looks to me to be the right start. I can't hold all the anchors forever — I need checkers in the outfield. Even if Scott manages to get his three point, I still have the 1-2 backgame in reserve which is fine. The blockade on his side of the board makes it almost impossible for him to get the back checker around this turn, and maybe I'll be able to get something going on the next go around.

41. . . . 6-5:  18/12
42. 2-1:  16/13* 4-4:  bar/9*

Black to play 2-1.

43. 2-1:  bar/23, 17/16*

I felt that I might as well hold the 18 point in case of boxes. Perhaps bar/24, 18/16* which keeps a spare on the 24 point is better.

White to play 5-1.

43. . . . 5-1:  bar/19

Scott can certainly consider lashing away at the blot on his three point. If he wins the fight for the point it would be a big improvement for him, while if the checker gets hit is isn't a disaster. However I would still have my 1-2 defensive structure, and I might be able to do some damage with two of his checkers to play with. I suppose his play is correct.

Black to play 3-1.

44. 3-1:  17/13

My idea at the time was that if Scott rolled 5-2 it would jar another checker loose. The problem with this is that I don't necessarily gain all that much even if this happens. In the meantime I am giving him 1-1, 2-2, or 2-1 to make the three point. I should have simply played 23/22, 16/13 and waited. This is not the time to rush things.

44. . . . 5-2:  19/14, 5/3*
45. 2-1:  bar/22*

White to play 6-5.

45. . . . 6-5:  bar/19, 14/9*

Bar/14 is also a possibility, but Scott's choice is probably better. He will be happy just to get one checker home safely, and this is his best chance to do so.

Black to play 4-1.

46. 4-1:  bar/24, 23/19

It looks best to spread them out completely. I need maximum outfield coverage.

46. . . . 1-1:  4/3*(4)
47. 5-2:  bar/23, 24/19 6-1:  9/3, 4/3

Black to play 4-1.

48. 4-1:  23/18

I felt that my outfield coverage was already sufficient. I wanted to hold the 18 point and guard against the various jokers.

48. . . . 6-5:  19/8

Black to play 6-3.

49. 6-3:  23/17*, 18/15

I'm not happy about leaving the anchor on Scott's two point, but it looks right to take the shot now that I have it. The plan will be to get the other checker on his two point out of there, and use these nine checkers to slowly build up a board. I will have to work to keep hitting Scott's checker as it continues to enter and move around until I have built up my board. When I am ready I will move the two back checkers, but for now they have to stay where they are as a final chance to hit a shot if Scott escapes.

49. . . . 1-1:  bar/24, 3/2*(3)
50. 5-3:  (dance) 4-1:  24/19

Black to play 2-1.

51. 2-1:  bar/24, 17/15

My coverage of the board looks to be sufficient. I don't want to get hit by any fly shots now.

51. . . . 5-2:  19/14, 4/2
52. 3-1:  15/11* 5-4:  bar/16

Black to play 6-3.

53. 6-3:  18/9*

I decided it was worth paying off to boxes in order to have an extra checker aiming to cover my blot on the nine point. That point would be a nice stepping stone to own.

White to play 5-2.

53. . . . 5-2:  bar/18

It isn't so attractive for me to hit on my bar point, so Scott doesn't mind coming out there. Also, he might need those spares on the four and five points much more later on.

Black to play 6-4.

54. 6-4:  11/5, 9/5

I have to start building my inner board sometime, and this looks like a good time with Scott's checker a long ways from home. As long as Scott doesn't hit an indirect shot now I will probably be able to hit him next turn and perhaps start to make some real progress.

54. . . . 4-3:  18/11

Black to play 5-1.

55. 5-1:  19/14*, 18/17

My play gives me great coverage of my outer board, as well as avoiding being hit by 4-4 and 6-6 jokers. It is a slow process, but things are starting to shape up.

55. . . . 2-1:  bar/24, 4/2

Black to play 6-3.

56. 6-3:  24/18, 19/16

Let's see him get by this army of blots!

56. . . . 3-2:  24/19

Black to play 6-6.

57. 6-6:  18/6*, 13/7(2)

I'm going to have to take some chances sometime, and this looks like the best time. The loose hit stops him from scrambling away next roll, and if I can snag my six point I will be making real progrss. If I get hit back I may at least have one roll with which to recover. However, it doesn't seem right to spread a bunch of blots out in my outer board in order to have maximum coverage for the six point. I need some kind of damage control if I am hit. Also, the bar point could come in handy in the future, particularly if he enters with an ace.

57. . . . 4-3:  bar/21, 5/2
58. 2-1:  7/6, 7/5 6-3:  21/12

5 2
Should Black
redouble to 4?

What should my cube thoughts be? It may seem that I have a double here; in fact that maybe I should have been doubling all along. The idea behind this is that in the variations where I lose I am very likely to be gammoned, so why not turn the cube since if I get gammoned it won't matter whether the cube is on 2 or 4. The answer is very simple. I have yet to get to a position where on the next exchange (I rolls, he rolls) Scott would have a pass. As long as it is impossible for me to lose my market on the next exchange, it is never correct for me to double. Doubling would have everything to lose and nothing to gain. While it is unlikely that I will lose the game and not get gammoned, it is possible.

In the actual position, I am a huge favorite to hit the shot — everything except 5-5 and 6-6 hits. If I hit and he flunks, will he then have a pass? Nah. My four point is still open, I still have two men back, and his board is as strong as mine. I might be the favorite, but nowhere near a 3 to 1 favorite. Since he won't have a pass after my best scenario, it can't be right to double. Maybe next turn, but that is a problem to be considered next turn. For now, not good enough.

Black to play 5-2.

59. 5-2:  17/12, 15/13*

While I would like to make my four point, I shouldn't be rushing into things. The key now is outfield coverage. I don't want his checker to have a chance to slip away, and I definitely can't afford to be hit. The four point can wait until I am better prepared. Ideally I would like to organize my checkers to make my ten point. Then I could bear down on the four point and the other points in my outer board where Scott might escape without any risk.

White to play 2-1.

59. . . . 2-1:  bar/24, 4/2

Note how Scott has needed every one of those spares on the five and four points. If he had squandered one of them prematurely, he would be in trouble with this roll.

5 2
Should Black
redouble to 4?

Can I turn the cube now? If Scott rolls something like 4-2 or 5-2 next turn he jars another checker loose. If that happens, will I have lost my market? Maybe. But if I do lose my market that way, it won't be by much. I won't mind at all if that happens, I double, and Scott drops. I would be far from a lock to win the game. Otherwise, I will still have my work cut out. In addition, it is now possible to envision scenarios where Scott gets his back checker away and I don't hit any more shots but I still scramble off the gammon. If that happens, I would have thrown away the match by redoubling. Still right to wait.

Black to play 4-2.

60. 4-2:  16/12, 13/11

Making the 10 point is better. This leaves a shot only on the crushing 6-6, gives me peerfectly adequate outfield coverage, and as discussed the ten point puts long term pressure on the four point. Why didn't I make my ten point? Because I didn't see the play! Yes, this happens to everybody. The most common cause of checker play error isn't choice of the wrong candidate, but failure to see the best play in the first place. This is true of players of all levels, including top experts.

60. . . . 6-5:  24/18

Black to play 6-2.

61. 6-2:  11/3

Ouch! Just as it looks like I am closing in for the kill, I miss a key double-shot. This illustrates just how difficult it can be to win this sort of backgame where your checkers are divided. Now all I can do is hang as far back as possible and pray.

61. . . . 3-3:  18/6
62. 4-2:  12/6

White to play 2-2.

62. . . . 2-2:  6/4, 2/off(3)

This might be the safer play anyway, and taking the extra checker off is big. The gammon race could be quite close.

Black to play 3-1.

63. 3-1:  12/9, 5/4

I'm willing to waste a pip or two in the gammon race in order to make my four point. In a couple of rolls it may not be clear whether or not to run one back checker anyway. Running a back checker may save pips, but it risks getting pointed on with low numbers. Since there figures to be a tradeoff anyway, it looks more prudent to concentrate on making the four point. This game is still quite winnable, but not without the four point.

63. . . . 4-3:  4/off, 3/off

Black to play 1-1.

64. 1-1:  14/12, 6/4

Once again, two pips seems to me to be a fair exchange for the made four point.

64. . . . 3-2:  5/2, 5/3

Black to play 5-4.

65. 5-4:  12/7, 9/5

Another pip wasted, but the anchor is retained another roll. This way I don't get blown away on small doubles or 2-1, and it he rolls a large number with a three I not only get a shot but will be able to stick around for another shot if I miss. This illustrates the tradeoff I had talked about earlier when I discussed wasting a few pips in order to make the four point. If I hadn't done so I would have been running a checker by now, but it isn't clear that this would be desirable.

65. . . . 5-2:  4/off, 4/2
66. 3-3:  24/12

White to play 2-1.

66. . . . 2-1:  3/1*, 2/1

A good case could be made for the aggressive 2/1*, 1/off. This would leave Scott with only eight checkers, so if he doesn't roll an ace later it would save him a full roll in the gammon race. Since the gammon race figures to be very close, it might well be correct. Scott's safer play gains by keeping me on the bar if I roll 1-1, 1-2, or 1-3. It also ensures the win. However for the aggressive play to cost the game, a lot would have to happen. First, I would have to roll an ace, 3-3, 2-2, or 3-2. Second, he would have to roll a deuce. Third, I would have to hit the shot. And fourth, I would have to win the game, which would be far from certain since he would have 7 or 8 checkers off. Using rough estimates, we get:

a) I will roll an ace or stay on the bar about 1/2 the time.
b) He will leave a shot about 1/3 of the time.
c) I will hit the shot about 1/3 of the time.
d) I will then win the game about 1/2 of the time.

Thus, the probability of Scott losing the game after the aggressive play is approximately 1/2 × 1/3 × 1/3 × 1/2 which is about 1/36. Therefore, if the aggressive play gets him a gammon he wouldn't have gotten otherwise 1/18 of the time, he should go for it. I'm pretty sure that with the gammon race this close the aggressive play will get that extra gammon more than 1/18 of the time, so I believe he should have played 3/1*, 1/off.

67. 4-1:  bar/21, 7/6 2-1:  2/off, 1/off
68. 6-2:  21/19, 12/6 6-1:  3/off, 1/off

Black to play 3-1.

69. 3-1:  19/15

It might have been right for me to play 19/16, 2/1. It depends on what I roll next turn whether or not I want the ace point slotted. I'm not sure. 19/16, 2/1 is probably the best play to get off in two rolls. However there might not be those two rolls. Scott could roll doubles either this turn or next, and then I will have to be off in one roll. After my play, 3-3 does the job. I believe this possibility is sufficient to make my play the winner.

69. . . . 5-3:  3/off, 2/off

Black to play 5-2.

70. 5-2:  15/10, 3/1

Now it is easy to calculate. My play is superior if I roll 4-1, 5-1, or 6-1 next turn. 15/8 is superior if I roll 3-2 or 1-1 next turn. Otherwise, it doesn't matter which play I make. Not a contest.

70. . . . 3-1:  2/off, 2/1
71. 6-5:  10/5, 6/off

Single game
2 points

More articles by Kit Woolsey

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Backgammon Galore