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Quiz Solutions

Normally the solutions will be for the previous month's quiz, so the readers will have the opportunity to send in their answers. For this demo issue, I am including both the quiz problems and the solutions so the reader can see what they will look like.

The scores for the solutions will be based largely on the votes of the expert panel, not on rollout results of neural network computer programs. This is only fair, as otherwise everybody would be able to get a perfect score simply by feeding the position to their bot. The experts on the panel made their selections without the aid of neural networks, just as they would have to do over the board. Of course Snowie does get to put his two cents in along with everybody else, but Snowie's vote is just another opinion.

Problem 1





money game


Chuck Bower: 6/1*, 5/1. Starting out with a toughie! I'm sure over the table I would have taken two checkers off, and that was my analysis choice for quite a while, but I kept thinking. Gammons, gammons, gammons??
I definitely don't like the in-between play (hit loose and take one off) since it leaves liabilities now and later. Maybe getting hit on the 1-point is less damaging initially than on the 6-point; I don't know. But I don't like the shots which may come on the next roll (or even after that).
Pointing on the 1-point is "fairly" easy to analyze. If you get hit this roll, my guess is that the game is about even, particularly since White owns the cube. Thus I give White about 15% wins (half of the 30% hits). If White doesn't hit this roll, Blue can pretty much chalk up a gammon. I'd say about 60% of all games will be gammon wins for Blue and that leaves about 25% simple wins for Blue.
Taking two checkers off leaves White with a kind of acepoint game. Blue can still point on that checker if White fails to make it, but doing so cleanly will be tough. Acepoint games are worth about 20% wins or so when owning the cube, I think.
I'm sure I'm not that good at estimating--can't conclude that 20% wins for White is better than 15% for the other play, but... Look at the gammons. With this pseudo-acepoint game after Blue takes two off, White will be able to get off the gammon quite a bit more frequently, I would guess. He will have only one checker to bring in (instead of two) and will get some gammon savers with hits that don't end in wins (already counted). My guess is less than 50% of games will end in gammon wins for Blue. My above estimates say that White may win more games after Blue takes two off, and probably lose less gammons. Pointing looks like the best play. White's formidable board caused my initial reaction to be "why leave a voluntary blot??" but after MUCH thought it looks like the right play to me.

Steve Clark: 6/1*, 5/1. Of the two possible hitting plays, 6/1*, 5/1 has the advantage of solving all problems if Blue is not hit back. By comparison 5/0, 5/1* could leave continuous blots on the ace point for successive turns.
5/0, 4/0 is safe for the present but subjects Blue to potential future risks on most rolls. In addition, making the ace point appears to increase the gammon potential substantially. Finally paying now has the advantage for Blue of having a good opportunity to escape if he is hit.
The benefits of playing safe are that any potential risks are postponed until Blue has more men off and therefore has a greater chance of winning when hit. Also there is a significant chance that Blue will never have to leave a blot. These are powerful arguments for playing safe and therefore it seems to be a close decision. If Blue had more spares to make the ace point in the next few rolls, I might go the other way. But for the present I would make the ace point.

Hal Heinrich: 5/0, 4/0. Blue is well on the way to a gammon without taking extra measures, so I'd play safe. After 6/1*, 5/1 any six by Blue is enough to make the position pick 'em. After 5/1*, 5/0 and an ace by Blue, White's board breaks immediately with 5-1, 5-2, and 5-3 with lots of additional cracking sequences. And if White misses, 6-1, 6-2, 6-3, 6-4, and 6-6 all leave repeat shots. White's board is too strong and Blue's gammon chances are too good to justify a direct shot.

Ron Karr: 6/1*, 5/1. At the table, I'd have taken 2 checkers off without thinking much about it. After all, it is 2 checkers off with no shots, and I still have pretty good gammon chances. Since it's a quiz, I have to consider whether making the ace point could be right (this must be better than hitting loose on the ace point). And I think it is!
--If White misses, I have virtually no losing chances, and I've maximized my gammon chances.
--If he hits, I still have good chances, since he only has a 2-point board and still has to enter another one against my 5-point board, and I'm not too likely to crash further.
--If I don't make the ace point now, I'm unlikely to make it ever, so even if White doesn't anchor, he'll have shot chances until the very end.

Laila Leonhardt: 5/0, 4/0. Getting hit here could jeopardize the whole position due to White's threatening 4 point prime and White owning the cube. Trying to bear off without leaving a shot, maybe point or switch if White fails to make the 1 point seems to be the preferred strategy. Blue might leave a shot later on, but could have enough checkers off to hold off the recube if hit. The gammon gain simply isn't big enough compared to the losses.

David Montgomery: 5/0, 4/0. Among the hitting plays 6/1*, 5/1 looks right. Unlike 5/1*, 5/0 it leaves the gap higher, which should be safer in the long run.
I would play 5/0, 4/0. It's easy to lose after getting hit. On occassion big plays like 6/1*, 5/1 outperform the "obvious" safe bearoff plays, but when they do, it is usually by a small amount. When the big play is wrong, it can be hugely wrong. So when in doubt, I make the small play.

Bill Robertie: 6/1*, 5/1. I extinguish all White's long-term equity and clearly increase my gammons and backgammons, while I still have reasonable chances of surviving an immediate hit.
Taking two off (5/off 4/off) gives White the potential of a real or phantom ace-point game with good hitting chances.
The in-between play (5/off 5/1*) doesn't have the upside of making the 1-point, while Blue is still in some trouble if he gets hit. It looks like the worst choice.

Snowie: 6/1*, 5/1. Hey, gammons count double last I checked. If I get away with my play I am gin, and even if I get hit he will still have another checker on the bar against my 5-point board. I don't want to have to face a pesky ace-point anchor for the rest of the game.

Kit Woolsey: 5/0, 4/0. The extra gammon chances from hitting don't appear to compensate for the increased losing chances if I am hit back. Taking two men off leaves me with excellent winning chances, and the gammon possibilities are still pretty good.

Michael Zehr: 5/0, 4/0. I rip 2 off without worrying about it too much. While I might have to leave a direct shot later, it's unlikely that I'll ever leave a double-direct, and at least I'll have a couple more off. White's position isn't so bad that I can guarantee escaping if I'm hit, and I win a lot of gammons even if I don't hit. Another way of looking at it -- the worst case if I don't hit is that White anchors and later I have to leave a shot, but that's no worse than definitely leaving a shot this turn.

Summary: Half of the panel was willing to risk leaving the shot in order to get increased gammon chances and prevent the ace point game. They are probably correct. I wonder how many of us would have found this at the table.

   Play                 Votes   Score

6/1*, 5/1                 5      100
5/0, 4/0                  5       90
5/1*, 5/0                 0       30

Problem 2





money game


Chuck Bower: B/23, 15/11, 13/11. This was the toughest for me (meaning I spent the most time on it). I'm still very unsure. I looked at White's next 36 rolls after both plays. It was too close to call. Then I went back to "principles" I use over the table.
a) "If your opp has an inflexible position, don't give him/her easy ways to remedy it." Moving to the 21 point gives White some good pointing numbers and a few flyshots. Staying back on the 23 point seems to give White fewer "cleanup" rolls. However, it leaves Blue in an unflexible position as well, so may this 'rule' shouldn't be applied.
b) (I credit this one to Robertie.) "If you own the cube, you don't have to win the game on the next roll. You can afford to wait and let your opponent come to you." This also argues for keeping the checker on the 23-point. The game is going to last a while. Wait for your opportunity. You don't have to jump the prime immediately.

Steve Clark: B/21, 13/11(2). This play has the big advantage of having a direct route to the win. Escape the back man and bring them all home. If Blue leaves the checker back on the 23 point, then White has the direct route home and Blue has to root for the lucky 6-2.

Hal Heinrich: B/23, 15/11, 13/11. The key to this problem is looking at it from White's point of view -- White's position is stripped and Blue has a strong inner board. In addition, White has given up the cube so that any bad sequence raises the spectre of a recube. Blue should play against White's three back men by minimizing White's chances of attacking. Blue doesn't need to escape the back man right away -- just reach a position that's good enough to redouble.

Ron Karr: B/21, 13/11(2). I need to escape to win, so I won't pass up this chance to advance to the edge of the prime. This leaves a few more shots, but so what? If I make the "safe" play, I'm likely to have trouble playing safely in the future while waiting for a joker to escape. If I stay back, it also allows White to break his 9 point to get more builders.

Laila Leonhardt: B/21, 13/11(2). This play gives Blue better flexibility and moves him to the edge of the prime, forcing White to break or hit next time.

David Montgomery: B/23, 15/11, 13/11. You would like to come up to the 21 and saftey the blot on the 15, but that leaves an awkward fourth 2. It's too awkward to do both, so you have to decide which is more important. Here, it's safetying the blot. If you leave the blot and come up to the 21, seven shots whack you on the 15, and many other rolls attack you on the 21, leaving the 15 point blot subject to future attack. One checker behind a five prime is a problem. Two checkers behind a five prime is a lost cause.
Coming up to the 21 isn't such a priority here because your opponent's prime is stripped and his potential builders are far away. This means that your opponent can't extend his prime, and in fact he may have to weaken it. You should have good chances to escape later: 1) you may roll a two later, when it plays to the 21 more conveniently; 2) you may be able to escape while your opponent is on the roof (you hope to attack his blot(s) on your side of the board); and 3) your opponent's five prime may soon become a four prime.
In general you should be wary of coming up under a stripped outside prime when immediate escape isn't a priority, because doing so turns the outer points into builders.

Bill Robertie: B/23, 15/11, 13/11. Three deuces are forced: Bar/23 13/11(2). With the last deuce I prefer 15/13 to 23/21. Coming up to the 21-point allows White to hit me outside (very strong for him) or attack inside (also good with the ace-point made). There's no hurry to escape since White's prime breaks with a lot of rolls.

Snowie: B/23, 15/11, 13/11. With five men in the outfield, there is no rush to escape the back checker. My play is safe, which is quite important. Also my back checker may be effective for harassment purposes.

Kit Woolsey: B/21, 13/11(2). It is important to take this opportunity to prepare to escape the back checker. The cost of leaving the extra blot doesn't appear to be too severe. I'm not afraid of being attacked on the 21 point, since White has little ammunition.

Michael Zehr: B/21, 13/11(2). I have to try to escape. Staying back and playing safe up front gives White all sorts of safe ways of playing -- roll a 2 and then break the 16, leaving only a 4/36 shot; roll a 9 or higher to run from the 5 point, etc. While moving forward means that White's 10 rolls that make the 21 are a bit better, staying back doesn't turn them into horrible rolls either.

Summary: Getting to the edge of the blockade looks natural. However the arguments for hanging back are quite convincing.

   Play                 Votes   Score

B/23, 15/11, 13/11        5      100
B/21, 13/11(2)            5       90

Problem 3





money game


Chuck Bower: 23/15. Leaves fewer blots (2 vs. 3) and a spare on the midpoint. Furthermore the communication looks better for getting the back checker(s) home. After making the 10-point those back two checkers appear particularly lonely.
This may be one of those positions which isn't easily rationalized. 23/15 just "looks" better!

Steve Clark: 23/15. I can see the merits of 15/10, 13/10. It blocks White's men on the 5 point and it creates more opportunities of covering the blot on the 4 point. Even so I would not make this play. The 15 point is very useful and I am happy to only have one man back. Furthermore I am happy to have a spare on the 13 point.
I find it hard to define my total reasoning in this type of position except to say that 23/15 leaves a position that is more "balanced". I know that having the proper sense of balance is important in many positions. Unfortuately proper balance is often tantalizingly difficult to define and to determine.

Hal Heinrich: 23/15. Blue is ahead in the race and should build on this advantage by escaping a back man. This principle suggests 23/15 immediately, and other secondary considerations do not change this. 15/10, 13/10 does make it easier to cover the four point -- though probably at the cost of an outside blot. The ten point also constrains White's back men more effectively than the fifteen point. But staying back attracts White's spares on the six and eight points -- and running from the back may be be possible next time. Run now and play with one man back.

Ron Karr: 15/10, 13/10. I don't see any big urgency in escaping one of the back checkers, since they're diversified, and if the blot on my 4 point gets hit, which is fairly likely, I'll have more numbers to make an anchor with two men back rather than one. Also, there's the option of covering 10/4 if the blot doesn't get hit. And having the 10 point will provide some blocking power against White's back checkers if things start going his way.
I'm not too worried about having stripped outfield points, since I should be able to play one of the back checkers next time. If I make the 15 point, I'm going to have to clear it fairly soon anyway.

Laila Leonhardt: 23/15. Even if Blue's checker gets hit on the 4 point next time, it will still be difficult for White to come around the outfield with Blue owning the 15 point. Blue should not leave 2 blots stranded back in White's home board with the prospect of getting another checker back.

David Montgomery: 23/15. Most of the time, when you are even or ahead in the race, escaping back checkers is a good thing. Making an outfield point is also a good thing. Overall, the 10 point is probably a better point than the 15, but the combination of making the fifteen and escaping a back checker should be better. When in doubt, pump 'em out.

Bill Robertie: 23/15. The 10-point has some merit, but the 15-point escapes a checker and keeps my men more connected. I play 23/15.

Snowie: 23/15. Making the ten point spreads my resources too thin. What would I do for an encore? I need a strong presence in the outfield.

Kit Woolsey: 23/15. Making the ten point doesn't gain all that much, and the followup would be difficult. I like having only one checker back and plenty of wood in the outfield to help play my awkward rolls.

Michael Zehr: 23/15. Toughest choice for me yet so far. Making the 10 seems so static and I have no flexibility, yet I want to make the 4 point. Making the 15 cleans up 2 blots and maybe frees me up to attack, yet I have no builders. Will it be too hard to clear the 10 later or too hard to clear the 15 later? In the end I choose to bring up a back checker because I want to keep my men in contact as much as possible and keep a builder in the outfield.

Summary: A near unanimous vote. The panel clearly respects outfield control for this position.

   Play                 Votes   Score

23/15                     9      100
15/10 13/10               1       50

Problem 4





money game


Chuck Bower: 13/6. With a centered cube, I think Blue wants to look for the quickest route to using the cube. He must give up one of the three outside points this roll. Assume no hit: which two points would Blue like to remain? I think White has enough time to hold his midpoint. Thus Blue will be better having the 8 and 10 points remaining than either 8 and 13 or 10 and 13 points.
After 13/6 and White's miss, Blue should first safety the remaining checker on the 13-point, but then probably has a double. After any other play with 61 (followed by a miss), Blue still has to wait quite a while before being able to cube.
What if White hits? 15 numbers hit, but only 61 and 44 both hit and cover. Admittedly, if Blue fans, White has a cash. The other two plays leave fewer shots (11 and 12) which is certainly significant. Still, with Blue leading already I think that last "oomph" to get to the cube-turning zone is worth the risk.

Steve Clark: 13/6. The safest play is 8/7, 8/2. This play does not particularly attract because Blue is likely to be further exposed in the future and Blue does not clean up all the blots in his home board. But the merits of this move are not trivial. Blue will not like it if he gets hit on any move he makes and then has entry failure. Would Blue have a take at that point? I think that Blue would be close enough to a drop that it really does not matter; so perhaps it is not so important to Blue to close up his board. Also Blue will have a couple of spares to play with so he probably will not have to leave another blot for a move or two. 10/9, 10/4 and 10/4, 2/1 both have the advantage of leaving Blue with a more flexible position when he is not hit. These moves, when considered in sequence with 8/7, 8/2, leave progressively better positions but also lose progressively more games from being hit by White and then flunking. As a result their relative merits are very difficult to evaluate.
All of these moves suffer from the defect that if Blue is not hit, the game goes on. If Blue strips down the 10 point, he might have a double after not being hit, but it is not a particularly strong double. Therefore such a double does not greatly affect the overall valuation of the position.
Suppose, however, Blue moves 13/6. If he is missed what type of double would he have then? With this move he would have made great progress to coming home safely. He would seem to have a good double which some might drop. Would it be a strong enough double to really affect the valuation. I am not sure but I think it might be.
13/6 also leaves fewer shots than 10/4,2/1, the best positioned of the alternative moves. I am not very confident about this plan, but I will play 13/6 and then toss him the cube if he misses me.

Hal Heinrich: 13/6. Tough decision -- but if you're going to leave a blot, leave it where it'll do the most good if missed. And that's the midpoint -- from there you can double immediately or work on improving the position to where you are comfortable doubling. Barring a 6-6 or 5-5 or a hit by White, I rate the position as a double and a take. The safe play of 8/7, 8/2 is just too likely to lead to more dangerous repeat shots -- and White's position rates to improve quickly. Future safety and the ability to use the cube are cheap at the cost of four extra shots now. And after being hit, Blue still has a chance to roll a three.

Ron Karr: 13/6. 8/7 8/2 minimizes shots, as well as covering a home board point, but even if White misses there'd still be a huge amount of work to do. If I get away with 13/6, the position is a lot easier to bring home. In fact, I may never have to clear the 8 and 10 points since I can probably win with the cube.

Laila Leonhardt: 13/6. White has timing enough to wait around even if he misses the first shot. Better to pay now and clear the midpoint and cube if missed.

David Montgomery: 13/6. I'm liable to pick any of 13/6, 10/9 10/4, and 10/4 2/1 on different days. In fact, in reviewing this quiz at different times, I have. Usually, when forced to leave a shot while bearing in against a holding game, you want to break the hardest point to clear, even at the cost of several extra shots. Usually the hardest point to clear is the rearmost point. These heuristics would argue for playing 13/6. Here, however, the ten point is also likely to be difficult to clear, and breaking the ten point allows you to clean up your inner board. The stronger inner board could make a big difference after getting hit, which argues for 10/4, 10/1; however, 10/4, 10/9 leaves three fewer shots, which is a big plus for it.
I think the cube position argues for 13/6. After breaking the 10 point, if you get missed, the position is a clear and easy take. If you break the midpoint, the take/pass looks unclear to me. If I'm right, then 13/6 should give greater cube efficiency, and even if I'm wrong, then hopefully my opponent is at least more likely to make a mistake on the cube decision after 13/6. 8/7, 8/2 isn't a candidate. Giving one extra shot with 10/9, 10/4 has to be better.

Bill Robertie: 13/6. White has plenty of time to hold his position, so I don't see any reason to avoid the traditional 13/6, breaking from the back.

Snowie: 10/4, 10/9. Only 12 shot numbers, and my followup plays will be comfortable. If I don't get hit, I will have enough spares to play with so my opponent will probably be squeezed off the midpoint first

Kit Woolsey 8/7, 8/2. The safest play, and it has the additional advantage of locking up the two point in case a blot-hitting contest ensues. I may be able to outwait him in the battle of who gets squeezed off the midpoint first.

Michael Zehr 13/6. I don't like breaking the 8 because it duplicates my 1's and 3's if I'm hit and I don't want to break the middle of my three points. I don't like 10/4, 10/9 because it also breaks a middle point without making the 4th inner board point, and again duplicates 1's and 3's. So without thinking about it too much more I "clear from the rear and don't ask questions."

Summary: The panel was strongly in favor of simply clearing the midpoint, possibly with an efficient cube to come if the shot is missed. Could well be right, but not at all clear.

   Play                 Votes   Score
13/6                      8      100
10/4, 10/9                1       60
8/7, 8/2                  1       50
10/4, 2/1                 0       40

Problem 5





money game


Chuck Bower: 7/1, 6/3*. A typical early game decision: No points for either side and an even race. The bots have taught me that usually the right choice here is to attack and attempt to gain a racing edge. That rules out the passive building/splitting play of 13/7, 24/21. Blitzing deserves consideration: 7/1 with a hit. The problem here is that even with a fan, Blue may not be quite good enough to double. 24/15 is wide open and works well if there are no return hits, but that doesn't happen very often!
Another thing the bots have taught is: go for the quick knockout. 7/1, 6/3* leaves a better distribution of builders. Since in a blitz , "how many" is usually more important than "how pretty", I like 6/3* better than 8/5*. White is at his most vulnerable right now. Take advantage by attacking. With a bit of luck the cube can be used soon (and hopefully by Blue! ;)

Steve Clark: 8/5*, 7/1. I will make the stronger board and hit him. Once I have a blot on my one point, I want to cover rather than fiddle around by playing with 14 checkers and an extra blot.
24/15* might work well if White rolls 6-2 or 6-6 but Blue doesn't have anything else going for himself with that play. If Blue plays 13/7, the 3 plays pretty bad anywhere. 7/1 turns the blot on the ace into an asset (of sorts anyway).
After that hitting White off of the 5 point seems to be the best step forward. 6/3* is safer and might be right but it does go after the wrong point. I don't believe 24/21 could be correct. With Blue having the stronger board, it is more logical to try to drive White back from the 5 point.

Hal Heinrich: 8/5*, 7/1. Yikes! Standard play by both sides led to this position 1. 6-3 24/15 6-5 13/7*, 6/1* 2. 5-3 bar/22, bar/20 6-3 ? which makes this a mainline position. The weighing of the pros and cons of this position are beyond me! Making the ace point after starting it is thematic, so I'd do that. And then I'd hit on the five point. Hitting on the three is reasonable, but if you're going to leave a shot, leave it where it'll do the most good. This play locks up a second inner board point and starts a hitting contest when you have the stronger board. Hitting the man on the fifteen point from the twenty-four point is normally such a coup, that it's automatic. Here, however, only nine numbers fail to return hit and ten numbers double-hit. So hitting on the fifteen leads to an even, though volatile, position. I prefer making the ace and hitting which leaves Blue with a small, but definite advantage.

Ron Karr: 7/1, 6/3* The "normal" play in the early game is to hit 24/15*, but this leaves a complete mess, with no assets, and is likely to cost more in the race than it gains. 24/21, 13/7 is the pure play, making a good point and duplicating White's 2s, but still leaving a blot on the 1 point, a long-term liability, and giving White freedom to play.
Covering the 1 point and hitting is surprisingly attractive:
--Blue gets a better board, and the blot turns into an asset instead of a liability.
--White can't make any new points.
--White's other blots continue to be targets.
Given that, I'd play 7/1, 6/3*, since there are fewer return shots than 8/5*, and the 3 point is almost as good as the 5 once the ace point has already been made. If White doesn't hit back, I may be able to blitz, and if he does, his board is still wide open with plenty of play left.

Laila Leonhardt: 24/21, 13/7. Making the bar point and creating a 3 point prime will put some pressure on White to either anchor or attack, (which is duplicated). If White rolls a number that makes an inner board point, or a priming point, White will still have to leave 2 blots in Blue's home board and Blue can now attack or anchor next time. Note that Blue would rather have the blot on the 1 point hit, than cover it. The ace point can not be undone and those valuable prime builders would be stuck until last checker is off.

David Montgomery: 24/21, 13/7. No matter what you do, your opponent will have tremendous options -- most plays leave many shots, and the non-hitting plays give your opponent complete flexibility to make a good point somewhere, possibly pointing on your head.
Against many players I would play 24/15*. This kind of play will tend to get many of my checkers sent back, which should make the game longer and give my opponent more chances to make mistakes. But this play is probably too loose to be the "right" play.
I don't care much for 8/5*, 7/1 and 7/1, 6/3*. I don't like starting a blitz this way -- with only a two-point board, and my opponent having direct numbers both to hit me and to anchor.
24/21, 13/7 looks better than 24/21, 7/1. Although it's true that once you slot the 1, you generally want to make it, the 7 is a better point, and leaves more of my checkers in front of my opponent. I guess I'll play 24/21, 13/7.

Bill Robertie: 7/1, 6/3*. Hitting with 24/15* leaves a zillion returns. Playing 13/7 is positionally good, but then X has no three. So I play 7/1, then look for the best hit. 6/3* leaves the fewest returns and doesn't strip the 8-point, so that's my play.

Snowie: 8/5*, 7/1. Attacking is a must, and I don't want to leave loose ends lying around. If I don't make the ace point now, the blot will be sitting there to haunt me in the future. Making the ace point is not nearly as bad as humans think.

Kit Woolsey: 8/5*, 7/1. This game figures to be an attacking contest, not a priming battle. Thus, making the ace point could be just as valuable as making the bar point. In addition, I won't have to worry about the blot on the ace point later in the game.

Michael Zehr: 13/7, 8/5*. I want to get a solid asset out of this other than the ace point, hence I make the bar point. Hitting 24/15* has very low chance of gaining in the race because there are so many return shots, so I don't see the pips gained in the race as a solid asset. Then I hit my opponent off the front edge of the prime. If I can cover it next time even at the expense of being hit on the ace point I'm very happy.

Summary: These days experts are not afraid to commit to the ace point if there is a potential blitz. Once the ace point is started, it might as well be covered.

   Play                 Votes   Score

8/5*, 7/1                 4      100
7/1, 6/3*                 3       90
24/21, 13/7               2       70
13/7, 8/5*                1       60
24/15*                    0       50
24/21, 7/1                0       40

Problem 6





money game


Chuck Bower: 20/14, 6/2. (Do they ever get easy?!?!?!) "Play up to your strength and into your opponent's weakness." Blue's strength is his/her board. 14/4 sees it breaking next roll with some bad numbers. White's board isn't too much of a threat yet. 20/14, 6/2 is my choice. Yes, I may be leaving three blots sometime in the future, but I'm counting on my board to pull me through. 20/10 is worth considering, but it leaves way too many shots.

Steve Clark: 20/14, 6/2. It is getaway day. He might nail me with double 3's but at least I won't have to fall on my sword if I roll the 3's.
More seriously, Blue is about busted if he does not leave now. There will be a few good rolls next turn if he stays, but most rolls will be worse then than they are now.

Hal Heinrich: 20/14, 6/2. Breaking the anchor is thematic and clear. I wouldn't be surprised if 20/10 was better than 14/4 -- and 20/10 is clearly very inferior to 20/14, 6/2. White has an enormous job attacking and containing Blue's back checker(s) while escaping his own. And if White gets hit, gammons loom large! After 14/4, Blue is out of time and will be rooting for a leaping number which is available now! And the risk rates to increase or remain similar.

Ron Karr: 20/14, 6/2. I think I have to go for it now, while my board is strong and White's is weak, and his timing is better. If I play safe, then 4s and 3s can cause me to crash next time. And if I roll a single 5 or 6, it's not clear that I'll be any better off waiting til next time to run. Bad things can happen after my play, of course -- I could end up with 3 exposed blots -- but I think it's worth it.

Laila Leonhardt: 20/14, 6/2. Leaving 2 checkers behind a 4 point prime is not solving any problems and is just creating a risk of busting by not being able to leap over the prime, or get both checkers hit and sent even further behind the prime. White's board is still weak and Blue has good timing with the extra two checkers in the outfield even if he would get pointed on. Optionally one could consider moving 20/10. Blue has a strong board and prime, and White could get in serious gammon jeopardy from being hit.

David Montgomery: 20/14, 6/2. You are well ahead in the race and will have to break the anchor eventually. Your opponent will probably be able to hold his blockade for several turns, meanwhile working toward developing a better board. If you play 14/4, you put yourself under immediate pressure to roll a 5 or 6. Since you have rolled that number this turn, you should use it. Obviously, breaking the anchor gives your opponent some attacking chances against the straggler on the 20 point, but your chances in a tactical battle will never be better than they are right now.

Bill Robertie: 14/4. 20/14 6/2 looks clever but leaves Blue badly stripped. If White makes the 20-point, many of Blue's entering numbers are disasters. I play the mindless 14/4.

Snowie: 14/4. There is too much ammunition aimed at the five point to justify running. Also, and very important, if I play 20/14, 6/2 my next move may be very awkward if I can't spring the back checker. That spare on the six point is vital. Maybe next roll the atmosphere will be more favorable for running.

Kit Woolsey: 20/14, 6/2. If I stall with 14/4 it looks like things will just get worse, and I may be forced to crunch my board. My back checker is not in too much danger, and the outfield point is a nice asset.

Michael Zehr: 20/14, 6/2. I have to run sometime, and while I hate putting a checker on the 2 point, putting a second on the 4 isn't much better, especially with a 16/36 chance of having to bury checkers deeper.

Summary: A strong vote for escaping and grabbing the foothold in the outfield, with only our resident bot and one expert taking exception. Rather surprising, since usually the bots are quicker to break an anchor than humans. Does Snowie know something we don't about this position?

   Play                 Votes   Score

20/14, 6/2                8      100
14/4                      2       70
20/10			  0       30

Problem 7





money game


Chuck Bower: B/20*, 4/3*. The bots have taught me to attack in this kind of position. Yes, the 20 point is a good safety valve, but White isn't threatening so much and making the 20 point still gives White 11/36 to take the race lead. Two on the rail is worth a lot. I see a centered cube and want to be the first one to touch it! B/20, 4/3*. (Why leave the 9 or so extra shots playing for the golden point with 6/5*? When you cash it doesn't matter which home board point(s) you have.)

Steve Clark: B/20*, 21/20. Making the 20 point clearly gives me a slightly above average game. I will have his 5 point and a racing lead. He might hit back and he might make my 5 point but even if he does both, I will pretty much have an equal position.
So, can I do better? B/20*, 4/3* does not particularly attract me. This just seems disaster prone without trying for anything particualarly good. Even if he misses my blot on the 3 and fails to make my 5 point, I will have too disorganized a position to take real advantage.
B/20*, 6/5* is more intriguing. I have never been a great fan of the KG concept of "He with the most blots wins." Particularly when he has a stronger board. Could I recommend plays that maximize blots on this problem and maximize blots on the next? Am I losing my mind?
I guess not. Double hitting plays are attractive when there are no particularly good alternatives. Here making White's 5 point look good and I will take it. I can hear KG humming the Oscar Meyer weiner song in the background.

Hal Heinrich: B/20*, 4/3*. This play seems straightforward -- hit the most men and leave the fewest shots. Anchoring is not a priority here -- White doesn't have enough men poised to attack. 6/5* is sexy if you get away with it -- but why leave 80% more shots and one extra blot?

Ron Karr: B/20*, 6/5*. Attacking looks good, despite White's better board, because it puts two men in the air. The upside is large: if White doesn't roll a 4 or 5, I'm in great shape. And if I get hit back, I should have plenty of time to enter and anchor or resume attacking. I think 6/5* is better than 4/3* even though it leaves more shots, because it has more to gain positionally -- and White's 5s are good after 4/3* anyway, making the 5 point.

Laila Leonhardt: B/20*, 21/20. Hitting lose on either the 5 (leaving 4 blots) or 3 point (leaving 3 blots) putting two checkers on the bar doesn't seem to have a good effect when the opponent owns more points in their home board. Being hit back could be costly if you fail to anchor, and you will have to face a cube. Owning an advanced anchor when your opponent has a point behind you is strong and even if you should get an additional checker sent back, the game is still very even.

David Montgomery: B/20*, 6/5*. Anchoring doesn't look like a priority here. White only has seven checkers in the zone, with no 6 point spare, so you shouldn't be too afraid of an attack. And with both the 20 and 21 points slotted, you will have a good chance to grab an advanced anchor if you get hit.
B/20*, 6/5* looks better than B/20*, 4/3* to me. B/20, 6/5* leaves a lot more shots, but when not hit it has a lot more developmental promise. One way to look at it is that if you knew your opponent was going to roll a 5, you would only slightly prefer B/20, 4/3*. On the other hand, if you knew that he would not roll a five, B/20*, 6/5* looks clear. Also, after B/20*, 6/5* and a hit, you will usually have many rolls that come in and make the other point; after B/20*, 4/3* and a hit, you will generally not be able to make an offensive point.

Bill Robertie: B/20*, 4/3*. Bar/20* sure looks right, then the question is : button up or double-hit. I vote for the double-hit, 4/3*.

Snowie: B/20*, 4/3*. The key is to make progress while cutting down on my opponent's good rolls. The hit on the three point is the way to achieve these goals.

Kit Woolsey: B/20*, 4/3*. Offense before defense. My back men are not in much danger of being attacked, so I take this opportunity to do some damage up front. However hitting loose on the five point gives him too many returns. Hitting on the three point looks like the right compromise of aggression and caution.

Michael Zehr: B/20*, 21/20. B/20*, 21/20. White has one more inner board point than I do so I don't want to leave three or four blots with no anchor.

Summary: A tough 3-way decision, but the concensus was to concentrate on offense without leaving too many blots.

   Play                 Votes   Score

B/20*, 4/3*               5      100
B/20*, 21/20              3       80
B/20*, 6/5*               2       70

Problem 8





money game


Chuck Bower: B/21, 7/1*. A similar bot lesson: "When you have the better board and opp is vulnerable, attack!" You can either put White on the bar or expect to be there yourself. B/21, 7/1* is my play. Does White have a take with the 9 fan rolls? I'd like my opponent to have to answer that one.

Steve Clark: B/21, 7/1*. Leaves the least number of blots. I count blots in this type of situation and it is often the controlling factor in my decision. Here I am not so sure. The two remaining blots in the outfield are well positioned for White to hit. With a plot on the 10 point, I am not so well positioned even if the blot on the 7 point is missed. He will hit one of the other blots if possible and I will have less opportunity than usual for my bravery.
Well then, what about just making the 7 point? It is terrific except that I am leaving 4 loose checkers floating about the board. White would love to rescue them all and pull them up onto dry land.
Hitting on the ace point goes another direction altogether. It follows three general principles of backgammon; 1. Hit if you are behind in the race; 2. Hit if you have the stronger board; 3. Hit when your opponent has loose blolts; and 4. Hit first when he threatens to hit me. (Ok, so I can't count too well.)
I might live to regret it, but I couldn't bring myself to break so many rules at once.

Hal Heinrich: B/21, 13/7. An interesting problem with three different approaches for Blue. I like the priming approach because the fourth point in Blue's board is huge and the risk is tolerable. The idea is to claim a lasting positional feature at the cost of some short-term blitzing danger. White doesn't have great 1's, 5's or 6's, so duplication is working. Blue's home board is powerful enough to cause White to think twice about loose hits. Hitting on the ace is a common theme when you have the better board and dubious alternatives. Blue is in great shape if White dances -- I see the position as a double and take. But the volatility works both ways here. Blue has better all around chances by making the prime. Making the fifteen point is worth a look, but can be quickly discarded because of White's 6's which simultaneouly hit Blue's slot and escape White's last back man.

Ron Karr: B/21, 7/1*. All plays leave a bunch of return shots. I'm not clear which play results in the most wins if the game is played to the end, but hitting looks like it must yield the most gammons, and also provide the most cube leverage with the cube in the middle. If White fans, I don't think he can take a double, with an extra vulnerable blot and not a great board. And if I get hit back, even twice, it should still be a while before White can double.

Laila Leonhardt: B/21, 7/1*. Many blots and no duplication available. White is going to attack, maybe even hit 2 checkers or point on Blue next time. This is not the time to be defensive and give White the change to strengthen his position. Blue's advantage is having more points in his home board, and by hitting he can cash instantly on White's 9 dancing numbers and have a strong position in those situations where White fails to hit and will have a good deal of return hits from the bar if he does get hit.

David Montgomery: B/21, 7/1*. You have to leave shots no matter what you do, so take advantage of your big board by putting your opponent on the roof. B/15 looks clearly wrong -- if you want to grab a point, you should make the 7 point, which leaves a pretty position with a strong offense.

Bill Robertie: B/21, 7/1*. Better board and blots floating around argues for the hit play: Bar/21 7/1*.

Snowie: B/21, 13/7. Assets are everything. My position is too strung out to justify hitting loose on the ace point.

Kit Woolsey: B/21, 7/1*. The key is the doubling cube. If he flunks, and that will happen 1/4 of the time, I will have a very efficient cube. I believe this compensates for the cost of not making the bar point. See my "Threading the Needle" article for a discussion of this and other similar positions.

Michael Zehr: B/21, 13/7. Lock up another asset. I'm really tempted to play B/21 7/1* and double if white dances, but I'm not sure the 1/4 chance of white dancing is worth White's good numbers -- 11 hits on the ace plus 22, 23, 24, 34, 46, 44. After locking up the bar point White's misses are still pretty bad for him and White's hits aren't as good because of the trapped checker. B/15 just doesn't excite me at all -- it makes a point that I don't really want to hang on to.

Summary: Now it is the bot which is playing purely, while the humans are slashing loose on the ace point. What is this world coming to?

   Play                 Votes   Score

B/21, 7/1*                7      100
B/21, 13/7                3       80
B/15                      0       50

Vote Summary

                  1               2                    3               4               5               6               7               8

Chuck Bower      6/1*, 5/1       B/23, 15/11, 13/11   23/15           13/6            7/1, 6/3*       20/14, 6/2      B/20*, 4/3*     B/21, 7/1*
Steve Clark      6/1*, 5/1       B/21, 13/11(2)       23/15           13/6            8/5*, 7/1       20/14, 6/2      B/20*, 21/20    B/21, 7/1*               
Hal Heinrich     5/0, 4/0        B/23, 15/11, 13/11   23/15           13/6            8/5*, 7/1       20/14, 6/2      B/20*, 4/3*     B/21, 13/7
Ron Karr         6/1*, 5/1       B/21, 13/11(2)       15/10, 13/10    13/6            7/1, 6/3*       20/14, 6/2      B/20*, 6/5*     B/21, 7/1*
Laila Leonhardt  5/0, 4/0        B/21, 13/11(2)       23/15           13/6            24/21, 13/7     20/14, 6/2      B/20*, 21/20    B/21, 7/1*           
David Montgomery 5/0, 4/0        B/23, 15/11, 13/11   23/15           13/6            24/21, 13/7     20/14, 6/2      B/20*, 6/5*     B/21, 7/1*
Bill Robertie    6/1*, 5/1       B/23, 15/11, 13/11   23/15           13/6            7/1, 6/3*       14/4            B/20*, 4/3*     B/21, 7/1*
Snowie           6/1*, 5/1       B/23, 15/11, 13/11   23/15           10/9, 10/4      8/5*, 7/1       14/4            B/20*, 4/3*     B/21, 13/7
Kit Woolsey      5/0, 4/0        B/21, 13/11(2)       23/15           8/7, 8/2        8/5*, 7/1       20/14, 6/2      B/20*, 4/3*     B/21, 7/1*
Michael Zehr     5/0, 4/0        B/21, 13/11(2)       23/15           13/6            13/7, 8/5*      20/14, 6/2      B/20*, 21/20    B/21, 13/7

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