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| 135 57 | White money game Blue |
Chuck Bower: 6/1*, 5/1.Starting out with a toughie! I'm sure over the table I wouldhave taken two checkers off, and that was my analysis choice forquite a while, but I kept thinking. Gammons, gammons, gammons??
I definitely don't like the in-between play (hit loose andtake one off) since it leaves liabilities now and later. Maybegetting hit on the 1-point is less damaging initially than onthe 6-point; I don't know. But I don't like the shots which maycome on the next roll (or even after that).
Pointing on the 1-point is "fairly" easy to analyze. Ifyou get hit this roll, my guess is that the game is about even,particularly since White owns the cube. Thus I give White about15% 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% ofall games will be gammon wins for Blue and that leaves about25% simple wins for Blue.
Taking two checkers off leaves White with a kind of acepointgame. Blue can still point on that checker if White fails tomake it, but doing so cleanly will be tough. Acepoint games areworth about 20% wins or so when owning the cube, I think.
I'm sure I'm not that good at estimating--can't concludethat 20% wins for White is better than 15% for the other play, but...Look at the gammons. With this pseudo-acepoint game after Bluetakes two off, White will be able to get off the gammon quite abit more frequently, I would guess. He will have only one checkerto bring in (instead of two) and will get some gammon savers withhits that don't end in wins (already counted). My guess is lessthan 50% of games will end in gammon wins for Blue. My above estimates say that White may win more games afterBlue takes two off, and probably lose less gammons. Pointinglooks like the best play. White's formidable board caused myinitial reaction to be "why leave a voluntary blot??" but afterMUCH 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 hitback. By comparison 5/0, 5/1* could leave continuous blots on the acepoint for successive turns.
5/0, 4/0 is safe for the present but subjects Blue to potential futurerisks on most rolls. In addition, making the ace point appears toincrease the gammon potential substantially. Finally paying now has theadvantage for Blue of having a good opportunity to escape if he is hit.
The benefits of playing safe are that any potential risks are postponeduntil Blue has more men off and therefore has a greater chance ofwinning when hit. Also there is a significant chance that Blue willnever have to leave a blot. These are powerful arguments for playingsafe and therefore it seems to be a close decision. If Blue had morespares to make the ace point in the next few rolls, I might go the otherway. 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, soI'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 6-6all 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 aboutit. After all, it is 2 checkers off with no shots, and I still havepretty good gammon chances. Since it's a quiz, I have to considerwhether making the ace point could be right (this must be better thanhitting loose on the ace point). And I think it is!
--If White misses, I have virtually no losing chances, and I'vemaximized my gammon chances.
--If he hits, I still have good chances, since he only has a 2-pointboard and still has to enter another one against my 5-point board, andI'm not too likely to crash further.
--If I don't make the ace point now, I'm unlikely to make it ever, soeven if White doesn't anchor, he'll have shot chances until the veryend.
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, whichshould be safer in the long run.
I would play 5/0, 4/0. It's easy to lose after getting hit. On occassionbig 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 equityand clearly increase my gammons and backgammons, while I still havereasonable chances of surviving an immediate hit.
Taking two off (5/off 4/off) gives White the potential of a real orphantom ace-point game with good hitting chances.
The in-between play (5/off 5/1*) doesn't have the upside of making the1-point, while Blue is still in some trouble if he gets hit. It lookslikethe worst choice.
Snowie: 6/1*, 5/1.Hey, gammons count double last I checked. If I get away with my play I amgin, and even if I get hit he will still have another checker on the baragainst my 5-point board. I don't want to have to face a pesky ace-pointanchor for the rest of the game.
Kit Woolsey: 5/0, 4/0.The extra gammon chances from hitting don't appear to compensatefor the increased losing chances if I am hit back. Taking two men offleaves me with excellent winning chances, and the gammon possibilities arestill pretty good.
Michael Zehr: 5/0, 4/0.I rip 2 off without worrying about it too much. While Imight have to leave a direct shot later, it's unlikely that I'llever 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'mhit, 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 thatWhite anchors and later I have to leave a shot, but that's no worsethan definitely leaving a shot this turn.
Summary: Half of the panel was willing to risk leaving the shot in orderto get increased gammon chances and prevent the ace point game. They areprobably correct. I wonder how many of us would have found this at thetable.
Play Votes Score6/1*, 5/1 5 1005/0, 4/0 5 905/1*, 5/0 0 30
Problem 2
| 128 124 | White money game Blue |
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 bigadvantage of having a direct route to the win. Escape the back man andbring 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 lucky6-2.
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 tothe 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 inthe future while waiting for a joker to escape. If I stay back, italso 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 thatleaves an awkward fourth 2. It's too awkward to do both, so you have todecide 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 checkersbehind a five prime is a lost cause.
Coming up to the 21 isn't such a priority here because your opponent's primeis stripped and his potential builders are far away. This means that youropponent can't extend his prime, and in fact he may have to weaken it. Youshould 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 primewhen 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 Iprefer 15/13 to 23/21. Coming up to the 21-point allows White to hit meoutside (very strong for him) or attack inside (also good with theace-point made). There's no hurry to escape since White's prime breakswith a lot of rolls.
Snowie: B/23, 15/11, 13/11.With five men in the outfield, there is no rush toescape the back checker. My play is safe, which is quite important. Alsomy back checker may be effective for harassment purposes.
Kit Woolsey: B/21, 13/11(2).It is important to take this opportunity to prepare toescape the back checker. The cost of leaving the extra blot doesn't appearto be too severe. I'm not afraid of being attacked on the 21 point, sinceWhite has little ammunition.
Michael Zehr: B/21, 13/11(2).I have to try to escape. Staying back and playingsafe up front gives White all sorts of safe ways of playing -- roll a 2and then break the 16, leaving only a 4/36 shot; roll a 9 or higher torun from the 5 point, etc. While moving forward means that White's 10rolls that make the 21 are a bit better, staying back doesn't turnthem 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 ScoreB/23, 15/11, 13/11 5 100B/21, 13/11(2) 5 90
Problem 3
| 153 141 | White money game Blue |
Chuck Bower: 23/15.Leaves fewer blots (2 vs. 3) and a spare on the midpoint.Furthermore the communication looks better for getting the backchecker(s) home. After making the 10-point those back two checkersappear 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 menon the 5 point and it creates more opportunities of covering the blot onthe 4 point. Even so I would not make this play. The 15 point is veryuseful and I am happy to only have one man back. Furthermore I am happyto have a spare on the 13 point.
I find it hard to define my total reasoning in this type of positionexcept to say that 23/15 leaves a position that is more "balanced". Iknow that having the proper sense of balance is important in manypositions. Unfortuately proper balance is often tantalizingly difficultto define and to determine.
Hal Heinrich: 23/15.Blue is ahead in the race and should build on this advantage by escapinga 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 bebe 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, sincethey're diversified, and if the blot on my 4 point gets hit, which isfairly likely, I'll have more numbers to make an anchor with two menback rather than one. Also, there's the option of covering 10/4 if theblot doesn't get hit. And having the 10 point will provide someblocking power against White's back checkers if things start going hisway.
I'm not too worried about having stripped outfield points, since Ishould be able to play one of the back checkers next time. If I makethe 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 andkeeps my men more connected. I play 23/15.
Snowie: 23/15.Making the ten point spreads my resources too thin. What would Ido 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 followupwould be difficult. I like having only one checker back and plenty ofwood in the outfield to help play my awkward rolls.
Michael Zehr: 23/15.Toughest choice for me yet so far. Making the 10 seemsso 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, yetI have no builders. Will it be too hard to clear the 10 later ortoo hard to clear the 15 later? In the end I choose to bring up aback checker because I want to keep my men in contact as much aspossible and keep a builder in the outfield.
Summary: A near unanimous vote. The panel clearly respects outfieldcontrol for this position.
Play Votes Score23/15 9 10015/10 13/10 1 50
Problem 4
| 123 97 | White money game Blue |
Chuck Bower: 13/6.With a centered cube, I think Blue wants to look for the quickestroute to using the cube. He must give up one of the three outsidepoints this roll. Assume no hit: which two points would Blue liketo remain? I think White has enough time to hold his midpoint.Thus Blue will be better having the 8 and 10 points remaining thaneither 8 and 13 or 10 and 13 points.
After 13/6 and White's miss, Blue should first safety the remainingchecker on the 13-point, but then probably has a double. After any otherplay with 61 (followed by a miss), Blue still has to wait quite awhile before being able to cube.
What if White hits? 15 numbers hit, but only 61 and 44 bothhit and cover. Admittedly, if Blue fans, White has a cash. Theother two plays leave fewer shots (11 and 12) which is certainlysignificant. 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 notparticularly attract because Blue is likely to be further exposed in thefuture and Blue does not clean up all the blots in his home board. Butthe merits of this move are not trivial. Blue will not like it if hegets hit on any move he makes and then has entry failure. WouldBlue have a take at that point? I think that Blue would be close enoughto a drop that it really does not matter; so perhaps it is not soimportant to Blue to close up his board. Also Blue will have a coupleof spares to play with so he probably will not have to leave anotherblot for a move or two. 10/9, 10/4 and 10/4, 2/1 both have the advantage of leaving Blue with amore flexible position when he is not hit. These moves, when consideredin sequence with 8/7, 8/2, leave progressively better positions but alsolose 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, thegame goes on. If Blue strips down the 10 point, he might have a doubleafter not being hit, but it is not a particularly strong double. Therefore such a double does not greatly affect the overall valuation ofthe position.
Suppose, however, Blue moves 13/6. If he is missed what type of doublewould he have then? With this move he would have made great progress tocoming home safely. He would seem to have a good double which somemight drop. Would it be a strong enough double to really affect thevaluation. 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 thealternative moves. I am not very confident about this plan, but I willplay 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 whereit'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 whereyou are comfortable doubling. Barring a 6-6 or 5-5 or a hit by White, Irate the position as a double and a take. The safe play of 8/7, 8/2 isjust 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, buteven if White misses there'd still be a huge amount of work to do. IfI get away with 13/6, the position is a lot easier to bring home. Infact, I may never have to clear the 8 and 10 points since I canprobably 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, inreviewing 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 youget 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 greatercube efficiency, and even if I'm wrong, then hopefully my opponent is atleast 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 anyreason 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 opponentwill probably be squeezed off the midpoint first
Kit Woolsey 8/7, 8/2.The safest play, and it has the additional advantage of lockingup the two point in case a blot-hitting contest ensues. I may be ableto 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 ifI'm hit and I don't want to break the middle of my three points. Idon't like 10/4, 10/9 because it also breaks a middle point withoutmaking 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 anddon't ask questions."
Summary: The panel was strongly in favor of simply clearing themidpoint, possibly with an efficient cube to come if the shot is missed.Could well be right, but not at all clear.
Play Votes Score13/6 8 10010/4, 10/9 1 608/7, 8/2 1 5010/4, 2/1 0 40
Problem 5
| 158 156 | White money game Blue |
Chuck Bower: 7/1, 6/3*.A typical early game decision: No points for either side andan even race. The bots have taught me that usually the right choicehere is to attack and attempt to gain a racing edge. That rulesout the passive building/splitting play of 13/7, 24/21. Blitzingdeserves consideration: 7/1 with a hit. The problem here is thateven 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 quickknockout. 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 hismost vulnerable right now. Take advantage by attacking. Witha 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 hithim. Once I have a blot on my one point, I want to cover rather thanfiddle 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 haveanything else going for himself with that play. If Blue plays 13/7, the3 plays pretty bad anywhere. 7/1 turns the blot on the ace into anasset (of sorts anyway).
After that hitting White off of the 5 point seems to be the best stepforward. 6/3* is safer and might be right but it does go after the wrongpoint. I don't believe 24/21 could be correct. With Blue having thestronger board, it is more logical to try to drive White back from the 5point.
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 beyondme! 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 mostgood. This play locks up a second inner board point and starts a hittingcontest when you have the stronger board. Hitting the man on the fifteenpoint from the twenty-four point is normally such a coup, that it'sautomatic. Here, however, only nine numbers fail to return hit and tennumbers double-hit. So hitting on the fifteen leads to an even, thoughvolatile, position. I prefer making the ace and hitting which leavesBlue 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 acomplete mess, with no assets, and is likely to cost more in the racethan it gains. 24/21, 13/7 is the pure play, making a good point andduplicating White's 2s, but still leaving a blot on the 1 point, along-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 ofa 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 than8/5*, and the 3 point is almost as good as the 5 once the ace point hasalready 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 cannow 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 getmany of my checkers sent back, which should make the game longer and givemy opponent more chances to make mistakes. But this play is probably too looseto 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 hitme and to anchor.
24/21, 13/7 looks better than 24/21, 7/1. Although it's true that once you slot the 1, yougenerally want to make it, the 7 is a better point, and leaves more of my checkersin 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 ispositionally good, but then X has no three. So I play 7/1, then look forthe best hit. 6/3* leaves the fewest returns and doesn't strip the8-point, so that's my play.
Snowie: 8/5*, 7/1.Attacking is a must, and I don't want to leave loose ends lyingaround. If I don't make the ace point now, the blot will be sitting thereto haunt me in the future. Making the ace point is not nearly as bad ashumans think.
Kit Woolsey: 8/5*, 7/1.This game figures to be an attacking contest, not a primingbattle. Thus, making the ace point could be just as valuable as makingthe bar point. In addition, I won't have to worry about the blot on theace point later in the game.
Michael Zehr: 13/7, 8/5*.I want to get a solid asset out of this other than the acepoint, hence I make the bar point. Hitting 24/15* has very lowchance 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 Ihit my opponent off the front edge of the prime. If I can cover itnext time even at the expense of being hit on the ace point I'm veryhappy.
Summary: These days experts are not afraid to commit to the ace pointif there is a potential blitz. Once the ace point is started, it mightas well be covered.
Play Votes Score8/5*, 7/1 4 1007/1, 6/3* 3 9024/21, 13/7 2 7013/7, 8/5* 1 6024/15* 0 5024/21, 7/1 0 40
Problem 6
| 145 104 | White money game Blue |
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 atleast 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. Therewill be a few good rolls next turn if he stays, but most rolls will beworse then than they are now.
Hal Heinrich: 20/14, 6/2.Breaking the anchor is thematic and clear. I wouldn't be surprised if20/10 was better than 14/4 -- and 20/10 is clearly very inferior to20/14, 6/2. White has an enormous job attacking and containing Blue'sback checker(s) while escaping his own. And if White gets hit, gammonsloom large! After 14/4, Blue is out of time and will be rooting for aleaping number which is available now! And the risk rates to increaseor remain similar.
Ron Karr: 20/14, 6/2.I think I have to go for it now, while my board is strong and White'sis weak, and his timing is better. If I play safe, then 4s and 3s cancause me to crash next time. And if I roll a single 5 or 6, it's notclear that I'll be any better off waiting til next time to run. Badthings can happen after my play, of course -- I could end up with 3exposed 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 rolledthat number this turn, you should use it. Obviously, breaking the anchor gives youropponent 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 playthe mindless 14/4.
Snowie: 14/4.There is too much ammunition aimed at the five point to justifyrunning. Also, and very important, if I play 20/14, 6/2 my next movemay be very awkward if I can't spring the back checker. That spare on thesix point is vital. Maybe next roll the atmosphere will be morefavorable 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 muchdanger, and the outfield point is a nice asset.
Michael Zehr: 20/14, 6/2.I have to run sometime, and while I hate putting achecker 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 theoutfield, with only our resident bot and one expert taking exception. Rather surprising,since usually the bots are quicker to break an anchor than humans. DoesSnowie know something we don't about this position?
Play Votes Score20/14, 6/2 8 10014/4 2 7020/10 0 30
Problem 7
| 154 158 | White money game Blue |
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 aboveaverage game. I will have his 5 point and a racing lead. He might hit back andhe might make my 5 point but even if he does both, I will pretty muchhave an equal position.
So, can I do better? B/20*, 4/3* does not particularly attract me. Thisjust seems disaster prone without trying for anything particualarlygood. 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 KGconcept of "He with the most blots wins." Particularly when he has astronger board. Could I recommend plays that maximize blots on thisproblem and maximize blots on the next? Am I losing my mind?
I guess not. Double hitting plays are attractive when there are noparticularly good alternatives. Here making White's 5 point look goodand I will take it. I can hear KG humming the Oscar Meyer weiner songin the background.
Hal Heinrich: B/20*, 4/3*.This play seems straightforward -- hit the most men and leave the fewestshots. Anchoring is not a priority here -- White doesn't have enough menpoised to attack. 6/5* is sexy if you get away with it -- but why leave80% more shots and one extra blot?
Ron Karr: B/20*, 6/5*.Attacking looks good, despite White's better board, because it putstwo men in the air. The upside is large: if White doesn't roll a 4 or5, I'm in great shape. And if I get hit back, I should have plenty oftime to enter and anchor or resume attacking. I think 6/5* is betterthan 4/3* even though it leaves more shots, because it has more to gainpositionally -- and White's 5s are good after 4/3* anyway, making the 5point.
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 isstrong 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 ordouble-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'sgood 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 ofbeing attacked, so I take this opportunity to do some damage up front.However hitting loose on the five point gives him too many returns. Hittingon 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 Idon't want to leave three or four blots with no anchor.
Summary: A tough 3-way decision, but the concensus was toconcentrate on offense without leaving too many blots.
Play Votes ScoreB/20*, 4/3* 5 100B/20*, 21/20 3 80B/20*, 6/5* 2 70
Problem 8
| 147 154 | White money game Blue |
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 inthis type of situation and it is often the controlling factor in mydecision. Here I am not so sure. The two remaining blots in theoutfield are well positioned for White to hit. With a plot on the 10point, I am not so well positioned even if the blot on the 7 point ismissed. He will hit one of the other blots if possible and I will haveless opportunity than usual for my bravery.
Well then, what about just making the 7 point? It is terrific exceptthat I am leaving 4 loose checkers floating about the board. Whitewould love to rescue them all and pull them up onto dry land.
Hitting on the ace point goes another direction altogether. It followsthree general principles of backgammon; 1. Hit if you are behind inthe race; 2. Hit if you have the stronger board; 3. Hit when youropponent has loose blolts; and 4. Hit first when he threatens to hitme. (Ok, so I can't count too well.)
I might live to regret it, but I couldn't bring myself to break so manyrules at once.
Hal Heinrich: B/21, 13/7.An interesting problem with three different approaches for Blue. I likethe priming approach because the fourth point in Blue's board is huge andthe risk is tolerable. The idea is to claim a lasting positional feature atthe cost of some short-term blitzing danger. White doesn't have great1's, 5's or 6's, so duplication is working. Blue's home board ispowerful enough to cause White to think twice about loose hits. Hittingon the ace is a common theme when you have the better board and dubiousalternatives. 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 playresults in the most wins if the game is played to the end, but hittinglooks like it must yield the most gammons, and also provide the mostcube leverage with the cube in the middle. If White fans, I don'tthink he can take a double, with an extra vulnerable blot and not agreat board. And if I get hit back, even twice, it should still be awhile 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 advantageof 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 positionwith 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 justifyhitting loose on the ace point.
Kit Woolsey: B/21, 7/1*.The key is the doubling cube. If he flunks, and that willhappen 1/4 of the time, I will have a very efficient cube. I believe thiscompensates for the cost of not making the bar point. See my "Threadingthe 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/217/1* and double if white dances, but I'm not sure the 1/4 chance ofwhite dancing is worth White's good numbers -- 11 hits on the ace plus22, 23, 24, 34, 46, 44. After locking up the bar point White's missesare still pretty bad for him and White's hits aren't as good becauseof the trapped checker. B/15 just doesn't excite me at all -- itmakes a point that I don't really want to hang on to.
Summary: Now it is the bot which is playing purely, while the humansare slashing loose on the ace point. What is this world coming to?
Play Votes ScoreB/21, 7/1* 7 100B/21, 13/7 3 80B/15 0 50
Vote Summary
1 2 3 4 5 6 7 8Chuck 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, 13/7Ron 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, 13/7Kit 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