|
|
 return to index
|
| 149 129 | White money game Blue |
Chuck Bower: 20/13.
This one looks easy, but that usually means I'm on a beeline forgetting it wrong! Blue's 20 pip race lead means White has the timing.13/7 just delays the inevitable run for cover (and decreases Blue'salready thin diversity). 13/9, 6/3? What am I going to cover theblot with, and why am I'm moving a checker which belongs on the 4- (or 5-)point past it's intended camp? 8/1* would be more attractiveif it could gain some gammons, but White has plenty of time to comein on my 5-point and then continue to hassle me, and that assumes theblot on the acepoint doesn't get sent back.
Up anchor, mates! Let's head for calm seas before the stormworsens: 20/13.
Steve Clark: 13/6.
The normal solution in this type of problem is to hold youranchor and bring your me around reasonably safely while trying to getsome diversification. This would argue for 13/6, and many players wouldmake that play without giving it much thought. I even might be one ofthem.
The question is whether there is some reason to go against the normalplay. 8/1* seems misdirected. We are not desperate enough to leave twoblots while helping White's blot to a better place. There are timeswhen it is right to hit behind an anchor, but we should not do itrandomly. 13/9, 6/3 forces one man to far foreward (to the 3 point) andleaves a blot to be hit as well. It achieves some diversfication butWhite would be happy to have a target to shoot at.
The real alternative is 20/13. We are well ahead in the race andrunning out of timing. 13/6 stacks too many men on the 6 point. 20/13gets a man away safely and we are almost certainly going to have tobreak something soon.
This all might be true but I would not do it. If we leave a single bloton the 20 point, we are creating a lot of good things that can happenfor White. Even if he rolls badly, we are unlikely to to make that blotsafe the next roll. If we play 13/6 and roll awkwardly next roll, wecan always leave a blot somewhere else.
It is always difficult to figure when to run off a back anchor, but Idon't think this is the time.
Hal Heinrich: 20/13.
Mutual holding games are characterized by cautious play -- don't leave blots; do wait for big doubles. This style of play clearly indicates 13/6, which would be my choice if Blue's racing lead weren't so commanding. As it is, this position looks like an exception because Blue is running out of time and flexibility while White's position is improving.
Ron Karr: 20/13.
This seems likethe straightforward play. I'm ahead in the race and running out ofmoves. 13/6 doesn't accomplish anything except not leaving any blots.The other plays risk losing racing equity for no particular gain.Leaving a blot on the 20 point involves some risk, but not a huge risk,and the risk could get greater if White starts improving his board.
Gearge Klitsas: 20/13.
What is an anchor? Something that you hold or something that is holding you? An anchor made is always reluctant to be broken and exerts an opposite force in your mind, every time you are considering breaking it. This instructive problem is a case in point. Should Blue break immediately his anchor on his opponent's 5 point or wait?
Play a (20/13) The danger of breaking an anchor is well-known . The opponent (White, here) will attack the (by now vulnerable) bottom half of the point of one time (a simple point is like a subatomic particle consisted of two quarks, top and bottom) and in a number of games (about 35%), his attack will go well and he will be able to claim the victory or offer a double. Many rolls, namely 5-5, 5-3, 5-1, 4-4, 3-3, 3-2, 3-1, 2-1 and 1-1, start the attack efficiently and Blue, might not enter or enter awkwardly (for example with 6-2) or with a 3 or 4 played inconveniently from the six point (consider also a sequence like White 5-3, played 8/3 8/5*, Blue 5-1, in which, because of his cramped position, if he elects to hit, he must destroy his own eight point). Still, Blue seems to be able to fight as a favorite in the rest of the games, often reaching a position with no blots, with the midpoint and the eight point, possibly with a spare on it, as his only outfield points, with a fair lead in the race, while White will have been obliged by his marginal timing to move his rearmost checker to his anchor on Blue's five point, a fact that brings Blue's position at a distance of one good roll from being cashed or worth of a strong double. In a sample of a manual rollout of 144 games, Blue's equity was +0.25 ppg.
Play b (13/6) The anchor is holding me. At the same time, �probable is what usually happens�. What will usually happen here? White will make a third point and, with an even more cramped position, Blue will be obliged to break something in the outfield in his very next rolls, unless he rolls a joker. Blue's lead in the race will have been transformed into a liability, as White will have more time and flexibility to strengthen his outfield presence and progressively deprive Blue of breathing space. Seems that play b is clearly worse than play a.
Play c (13/9, 6/3) I don't like burying checkers, still the anchor is holding me in still another variation. I like setting traps, tho. Strange as it seems, almost any number that hits Blue's newly created blot on the nine point could be played better by White by not hitting (I am sure only about the exception of 4-4 and 6-2, maybe 5-3 as well), for, if he hits, he exposes himself to complications that favor Blue. White should stick to his plan of making Blue lose the timing and flexibility battle. Given that, Blue actually plans to use the nine point as a landing spot for his own checkers, trying to make his position more compact. A roll of 6-5 by Blue, could be used to make the point, breaking his anchor. Also, if White deliberately slots in his own board, leaving perhaps even two blots there (for example if White rolls 5-1 played 8/2), Blue, in that case, could play a roll of 4-3, 13/9 13/10. There is some bad duplication for Blue, tho. The geometry of the position is such, that, a roll of 5-2, that points on White's blot on his ace point, has the good alternative of making the four point and the roll of 5-4 that makes the four point has the good alternative of bringing two down. Play c, which is creative and good, actually not much worse than play a, perhaps could be adopted against an inferior opponent, but, here, we assume that one plays against an opponent that makes no mistakes, so play a is still my preference.
Play d ( 8/1*) Since White is not obliged to be involved in a blood-bath , and if he is smart, he won't (see the comment on variation c above), let's try to complicate things by force - this is the idea behind play d. Blue is trying to exploit his temporary advantage in inner board points, win a number of games by quickly forming a four or five-point board and pray for the rest. It's not a catastrophe if Blue is hit by White on his ace point. He might hit back on White's three point or enter somewhere and retain good racing chances, regaining at the same time an amount of flexibility. There is a big liability in this plan, though. The loss of the eight point, the remaking of which is against the odds (Blue will rather play 6/1 than 13/8, if White flunks), is grave and fatal. In many games Blue will remain with only two points in the outfield, namely his anchor on the twenty point and his midpoint.
Recently a strong earthquake hit first Turkey, our neighbors, and some weeks later, Athens, where I live. The initial position is like a house, after the first quake trembler. There are visible cracks on the walls and the columns are ready to fall. Fleeing to an open space (in analogy with play a) is the best reaction in that case. (Self)weakening one of the columns (the midpoint in play b) is not recommended, since, in all probability, even a relatively weak aftershock (any non-joker) will break the house down. Trying to construct a secondary column to support the house (the nine point as in play c) is certainly meaningful, but insufficient and temporary. Removing for good (actually for no good!) the strongest column (the eight point as in variation d) is simply suicidal. Just flee. To a park, to the mountains, any open space far away from this ready to fall house will do. I vote for play a, which is based on a simple, clear, thematic idea, which is very instructive as well.
Rob Maier: 20/13.
With a large lead in the race, it's time to go race. 8/1* and13/9, 6/3 both aim to try and buy us a little time, but it's very little,with the large risk of seeing our race lead evaporate. That leaves 13/6as the only other alternative. Since we will probably have to run nexttime anyway, we should go now, while we can, and before White's board getsstronger.
David Montgomery: 20/13
Up 20 pips, with a temporarily stronger board, and having no strongalternatives, it looks like Blue should take this chance to run.8/1* looks very bad. Blue shouldn't throw checkers behind White'sanchor for such a weak attack.
Snowie: 13/6.
Don't break the crucial anchor unless it is clear to do so. I still havetime to maneuver while waiting to roll doubles.
Walter Swan: 20/13.
8/1* violates principle of hitting loose against ananchor. Blue, 20 pips ahead, should run now before White's board getsbetter. With only 112 pips (40 of which are tied up), Blue should notwait for doubles.
Kit Woolsey: 20/13.
The racing lead and stronger board argue for anchors aweigh. Bluecan stand being attacked, and if White is unable to attack Blue will run theother back checker and reduce White to a holding game. If Blue stays on theanchor, the timing is likely to go against him.
Michael Zehr: 20/13.
I don't care much to trade my eight point for my ace point if myopponent has my five point, and likewise I don't want to move achecker from the six to the three -- those builders are for making thefour point. That leaves the choice between running or waiting.Blue is going to have to run soon because of his racing lead, andwants to run before White's board is better. While it's risky to runnow, it looks riskier in a turn or two.
Summary: It sure looks like all the relevant factors argue for therunning play. What is interesting is that our resident bot, which usuallylikes to race when ahead in the race, though otherwise. Is there somethingabout this position he sees which we don't?
Play Votes Score20/13 9 10013/6 2 6013/9, 6/3 0 408/1* 0 30
Problem 2
| 141 112 | White money game Blue |
Chuck Bower: 8/4, 6/4.
Just in time for (American) football to hit full stride, we haveus a Blitz! The quarterback is scrambing and has just fumbled thecube. Don't let him pick it up. Once all our linebackers are acrossthe line of scrimmage, we can't send them back into pass coverage.Crack their helmets open like they were coconuts! 8/4, 6/4.
Steve Clark: 13/9, 5/3.
It is generally correct to play safely in these types ofpositions. 13/9, 5/3 leaves 2 rolls that hit and a well distributedposition. 8/4, 6/4 makes a 4 point board and will win a lot moregammons. It also leaves 15 rolls that hit. Whether we are hit or not,we will be short of ammo for a roll or two when we make this play.
Kent Goulding once pointed out that it is a law of backgammon that abird in the hand is worth 2 in the bush (One extra loss exactly balances2 wins that become gammons.). When your opponent owns the cube, thatbird in the hand can be worth cosiderably more than 2 in the bush. Youropponent will use the cube to covert the extra win into yet more wins.
If you do rollouts of this position and find the equities for each playare close, take the play that wins the most. Remember, not all equitiesare equal.
Hal Heinrich: 13/9, 5/3.
In casual money play, I'd just make the four point and pick up my dice. However, considering this asa problem convinces me that 13/9, 5/3 is a better play -- albeit an uglier one. White's sound structure makes return hits costly -- especially as it leaves Blue short of ammo to continue the blitz. So leaving fifteen hitting numbers for White is NOT automatic. If we make the ugly play of13/9, 5/3 we leave only two shots and wind up with a postion that's comparatively easy to win, if missed. Blue will have a huge racing lead opposed by a straggler that's more of a target than apoliceman. At gammon-hungry match scores, I'd make the four point -- but for money, the extra gammonsdon't compensate for the extra losses.
Ron Karr: 13/9, 5/3.
I don'tthink leaving 13 numbers to get hit is worth the extra point in theboard. 5/3 13/9 only leaves 2 shots, unstacks the midpoint, andprovides reasonable builders for next time anyway.
George Klitsas: 13/9, 5/3.
Play a (13/9 5/3) Leaving only the roll of 5-4 to White to hit him. A bit of an ugly play, mainly because a third checker is put on the three point, but a play that retains a lot of flexibility. There is some duplication in Blue's rolls (a roll of 4-1 could be used for making either the five or the two point) and some awkward rolls as well, like 6-3, but most rolls play conveniently for Blue. White's best plan is to enter on Blue's two point and take his chances. Blue wins a fair amount of gammons, about 25%, and in a manual rollout of 72 games, his overall equity was +0.86 ppg.
Play b (8/4 6/4) Leaving 11 simple and 2 double hits (5-3 and 3-5). This is too much . Also, Blue's position is somewhat cramped and, even if he is not hit, rolls that usually cover the blot on the five point (like 3-1 and 1-1), here don't. The rolls of 6-6, 5-5 and 6-5 fail even to lift the blot and both 6-4 and 5-4 can only do that by burying it on the ace point. If White enters on the two point, Blue cannot cover the blot without leaving another blot on the eight point with five new rolls, 6-2, 5-3 and 2-2. The roll of 6-1 cannot be played without leaving a direct shot and other covering rolls leave indirect shots . Blue must be prepared to live with that, as he will continue to leave indirect or even direct shots for awhile. A manual rollout of 72 games resulted in an equity of +0.28 ppg for Blue, so I am pretty confident that play a is the winner here.
Rob Maier: 8/4, 6/4.
This was quite a shock. I had written out a replythat supported lifting the blot, that 13 shots was too many, blah blahblah. As I looked at it some more, I decided to actually estimate thewin/gammon probabilities for the resulting positions, make the four pointand get hit, make the four point and fan, lift the blot and fan, etc. Iwon't list the numbers I used, but the surprising result I obtained wasthat making the four point was "clear". Now all I have to do is figureout how close my estimates were :)
David Montgomery: 13/9, 5/3.
Whenever you start a double five blitz you should be aware of thepossibility of switching to a running game. Because of the double fivesand hitting you will usually be ahead, and these positions become veryweak if the blitz fails while you still have checkers back. Here Bluecan lock up his big racing lead and will likely have blitzing chancesnext turn.
Snowie: 13/9, 5/3.
Making the four point would be an attempt to snatch defeat from the jaws ofvictory. I already have all I need to win this game.
Walter Swan: 13/9, 5/3.
Making the 4 point is striving for a blitz. However the 5 menon midpoint are not close enough to action to assist in the close out.
Kit Woolsey: 13/9, 5/3.
Getting hit costs Blue his great racing lead. He doesn't needto make more inner board points to keep White on the bar; he simply needsto bring his checkers home safely in order to win.
Michael Zehr: 13/9, 5/3.
Since White can't anchor the only thing that can put a halt to Blue'sattack right now is getting hit. Blue will be happy to hit loose nextturn if necessary, but White is on the bar whether Blue leaves a blotto hit or not, so why risk it?
Summary: A strong vote for picking up the blot. This makes sense. Weonly have to win the game once.
Play Votes Score13/9, 5/3 9 1008/4, 6/4 2 60
Problem 3
| 160 161 | White money game Blue |
Chuck Bower: 8/3, 6/3.
Deja vu? I'd say the probability of getting this position isabout 1/15 * 1/18 = 1/270. And who says math doesn't help at backgammon?
White is a bit inflexible, and that usually calls for NOT playinginto his hands (allowing him to point with the stripped checkers onhis 18- and 19-points). Jetison 24/21. Blue's strength is the 4-pointand he should build on this, so forget the running play.
Slotting the 5-point seems a bit impetuous since 13/8, 13/10 bringsbuilders into position with much less risk, especially with this (small)race lead. 13/5 falls by the wayside. So we're down to making the3-point or bringing two builders down. It looks close.
Are Blue's sixes next roll the key? Neither play sets up a six allthat well, and running then might be the prudent choice. In that casemaking the 3-point looks better for two reasons: White may leave ablot in the outfield (and some sixes hit that) and if Blue is breakingthe anchor and becoming vulnerable, the extra teeth in the homeboard willhelp. 8/3, 6/3.
Steve Clark: 24/21, 13/8.
An interesting aspect of this problem is that all the moveslook so attractive.
24/16? Looks good. That is what I would do with a 6-2. With thatblock on White's bar point, escaping must be big.
24/21, 13/8? Starts to escape. Brings an extra builder down. How canthis be wrong?
8/3, 6/3? Making the 3 point is as natural as a baby's smile.
13/8, 13/10? Brings builders down for the most important points, the 5and 7. This has got to be terrific.
13/5? Starts the most important point. White will not want to get in ablot hitting contest with a weaker board. This has to be a strong play.
A 5 way tie for first? Well, not quite. The weakest play seems to be13/5. This move has 3 defects. First, it makes White's 4's good in asituation where otherwise they would be weak. Second, it commits us onthe next roll to try to cover this blot. White can leave builders inhis outfield more safely than usual at a time when he will be seekingflexibility so as to extend his 3 point block.
Third, the move does not really address the primary need of theposition. This is really the key to the position. White's men on his6, 7, and 8 points are awkward for the moment, but if he is allowed todevelop undisturbed, he will be able to organize a powerful positionwithin a couple of moves. Thus it is more important than usual to getthe back men going now. This is also the weakness of the other moveswhich leave both back blots on the 24 point. Making the 3 point isperfectly natural but it does leave those two guys stuck on the 24point.
Of the two escaping plays, which is correct? White's bar point is astrong block but it is not an interior point. Further the blots he usesto hit in his own board are likely to mean the loss of the 7 or 8point. Finally it is quite valuable to bring a 3 builder to the 8point. All this adds up to favor 13/8, 24/21. 24/16 has the defect ofseparating the back men. When facing a weak board, it is usually betterto have the two back men working together.
Hal Heinrich: 24/21, 13/8.
This is as common a move-three position as you're going to come across. After stripping the eight point, making the three point loses a lot of its appeal because it breaks the eight point and leavesa blot. 24/21, 13/8 is a good, balanced play -- it starts the back men moving in a position whereBlue has a slight racing lead. It also unstacks the heavy mid-point and adds a useful spare to thestripped eight point. These factors combine to make 24/21, 13/8 clearly better than 8/3, 6/3. 24/16has the advantage of not attracting White's stack on the six point, but it gives up the chance to make the twenty-one point, and it does not unstack the midpoint. For these reasons, 24/21, 13/8 isdefinitely the way to play.
Ron Karr: 24/16.
With White'sbar point made, I need to get the back checkers moving. 24/21 13/8gives smoother distribution, but gives White some attackingpossibilities; and there's no guarantee I can make the anchor or escapenext time anyway, so I'd just as soon try to run now.
George Klitsas: 24/21, 13/8.
A rich position. Running, splitting, bringing down builders, slotting, making a point - each play in turn adopts one of these strategies. Only hitting is absent from this catalog of the early going usual terminology. Maybe it would be a good idea for Kit (but, I think, he already has adopted it) to include in each month's problem set a problem from the early going, like this one, since these problems are theoretically instructive and practically rewarding, for they occur in our games, under this or the other particular but similar setup, very often.
Play a (24/16). Running. Planning to eventually save the runner and play with only one checker back. If the runner can be hit, White must use necessarily the pre-last spare on his midpoint for this purpose, a fact that weakens his position not much, but more than one thinks (he might easily use soon the last midpoint spare for hitting again or as a part of an awkward roll). White also might elect even not to hit with a roll of 3-1, making the five point instead (the two plays are close in my opinion). Another point is that there is some unfavorable duplication for Blue here. Fours (the hitting numbers) are useful for splitting his back checkers, too. If White rolls 5-4 or 4-3, these two factors combine badly (for White) as he is obliged to immediately strip his midpoint by hitting and bringing one down. If the runner is not hit, he can be saved or even used constructively in the outfield. In that case, White usually concentrates on attacking/priming Blue's back checker. This happens in about one third of the games, in most cases successfully. In a manual rollout of 108 games, Blue's equity was found to be +0.11 ppg.
Play b (24/21 13/8) Splitting. Putting a useful spare on the stripped eight point at the same time. Blue controls the outfield better in comparison with play a, but leaves a juicy target for the waiting (lurking) White hitters, especially the spares on the six point (4-4, 3-3, 2-2, 1-1, 6-3, 6-2, 5-2, 4-3, 4-2 , 3-2, 2-1, all these rolls can be used for hitting on White's four point). If not hit, Blue covers the slot from the 24 point with any three, a number that can be used in many rolls constructively in the front battlefield. Exploiting this fact, White can split (24/20) with 5-4, 4-1, even with 6-4 or 3-1 maybe. Other than that, Blue's position is well balanced (strictly in the literal sense of the word, thinking of each checker as having a unit of maze) and pleasing to the eye, with an overall equity of +0.13 ppg for Blue in a sample of a manual rollout of 108 games.
Play c (13/10 13/8). Constructive. Fails, tho, to activate the back checkers for this and possibly next roll, since Blue will rather use his next roll to make a front point. Strips the midpoint, as well, diminishing the power of some doubles (like 44). Blue's blot can be hit with four rolls (63 and 54) and, if not hit, does not create many additional good rolls for Blue (as it surely would if we mentally moved it one pip front or one pip back from its current position). Blue's front line army is arrayed in equal distances, which in backgammon is bad (compact would be best, diversified second best). Many rolls containing an odd and an even die play badly enough to make this play much worse than the already examined alternatives, with an overall equity for Blue of -0.02 ppg in 108 trials.
Play d (13/5) Slotting. This kind of play is in general inflexible and here more so. I mean that even if White misses the slot, Blue must cover it as his first priority, which decreases his overall flexibility and freedom. White should be alert enough to exploit this fact, for example by slotting himself with rolls like 6-1 (played 13/7 6/5), 2-1 (making the five point), even 6-2 perhaps (played 13/7 6/4 !?) - in this case there is also a duplication of 3's involved in favor of the play. If Blue is not hit (14 rolls hit, by the way, which is quite bad), it is instructive to consider some subsequent rolls of Blue like 6-5 (leaving two blots [slots?]), 6-3 and 6-1 for someone to realize Blue's problems with the slotting play. In 72 games I had already a negative enough equity for Blue (-0.09 ppg) so I decided to stop, thinking that in all probability this play is the worst of the five alternatives.
Play e (8/3 6/3) Making a point (at least or at last). In the murky waters of the opening, �make a point or hit something�, is a sound rule that backgammon teachers give to their students as a rough guide. The strength of this play is based on the strength of Blue's inner board. Any time that checkers are hit and dance (or enter inconveniently), White is much more of a favorite of receiving the cube than Blue. White, respecting Blue's inner board, will be more reluctant in comparison with plays a to d to think of inventive plays which leave direct shots. The weakness, on the other hand, of play e, is that it goes a little bit far, leaving a blot on the eight point (which can be hit with any of four numbers), not much ammo in the outfield and a resulting position that is difficult to improve and improbable to form a better prime than White's one. In a rollout of 108 games Blue's equity was +0.11 ppg.
The conclusion is that I don't really know which is the best move here but I believe that it is among a, b and e (the other two are clearly worse). I pick up play b, for I like aesthetically the resulting well-balanced position (it's the typical winner, anyway!).
Rob Maier: 24/21, 13/8.
A few days after the quiz came out, Chuck Bower and Iencountered a similar position in a doubles match (We opened with 3-1rather than 4-2). I had already thought about the problem a little bit,and had narrowed it down to two choices. Naturally, Chuck, who wasrolling, played neither of them after a brief miscommunication at 2:00am.
Anyway, my top two choices were making thethree point versus splitting the back men and bringing the 5 down. 13/5and 13/10, 13/8 both aim at trying to build something, but if I want tobuild I can just make the three point, so I reject those two choices. Ifthe 3 is 24/21, then I think 5 down is better than 5 out. The spare onthe eight point is useful, as would be an advanced anchor if we can makeit. I'm fairly comfortable eliminating 24/16. As for the final choice, Isee a real danger of those back checkers being hemmed in. It may be onlya three prime now, but if able to make the 4 or 5 point in the next rollor two, White's position will be quite formidable. In addition, the threepoint comes at the expense of the eight point, which will make itdifficult to form a prime on our side of the board. For these reasons, Ithink the split is best.
David Montgomery: 24/21, 13/8.
24/21, 13/8 is the second best play with an opening 53, not too far behind8/3, 6/3. Here splitting is more motivated, because of White's bar point,and 13/8 is more worthwhile because the 8 point is stripped. 8/3, 6/3gains because a third point is better than a second, but on the otherhand it leaves 4 shots and doesn't get the back men going. 24/21, 13 8 beats24/16 because it is less dangerous and more constructive, and it beats13/8, 13/10 because splitting is important here. Slotting with 13/5 isn't calledfor - 24/21, 13/8 is a natural play that leaves a flexible position without thedanger of a direct shot.
Snowie: 24/21, 13/8.
As usual, put your checkers where they belong. The spare on the eight pointand the start of an anchor is exactly where I want my checkers.
Walter Swan: 24/21, 13/8.
13/8 24/21. Three positives. One man only on 24 pt, a spare on 8 pt,unstacks midpoint. In addition, because White has no spares on bar and his8pt, he will need to break them in order to point on 21 pt.
24/16. One positve. One man only on 24 pt. Negative, , allows White to hitfrom mid freely.
8/3 6/3. One positive.
Kit Woolsey: 24/21, 13/8.
The natural play, unstacking the heavy midpoint and gettingan important builder onto the eight point. The checker on White's four pointisn't in too much danger, since White will have to break already made pointsin order to attack this checker.
Michael Zehr: 8/3, 5/3.
White is getting a fairly static, stacked position. The simplest wayfor White to unstack is by hitting, so Blue doesn't want to offertargets. (It's true that playing 24/21 means White can't bringbuilders down safely from the midpoint, but White will happily attackon the 21.) Blue can simply build up his board so that when White hasto slot and blot to gain flexibility, Blue's hits are stronger.
Summary: The well-balanced down and split play won handily. As Snowie says,it pays to put your checkers where you want them.
Play Votes Score24/21, 13/8 8 1008/3, 6/3 2 6024/16 1 5013/10, 13/8 0 4013/5 0 40
Problem 4
| 166 148 | White money game Blue |
Chuck Bower: 8/7*, 6/1*.
Hey, I'm starting to like this month's quiz. We're actually winningin some of these positions! Last month seemed like duck-and-cover drills. I initially thougth 8/7* was sheer genius but I see ALL FOUR candidatesstart with that. With two on the rail there is no need to get conservativeso forget 20/15 and 13/8.
15/10 concentrates the builders for the better points AND doesn't leave the potential offense killing direct shot. 6/1* keeps White from anchoring with a one, but is otherwise the least desirable point to start. White's 11 roll sure plays well if Blue hits just one. In fact, any double which enters plays well with only two in the air. Often hitting on the 1-point doesn't leave enough covers but here both 4's and 6's will do the job if the blot survives. But another downside with hitting is that SEVENof Blue's checkers will remain out of range for building the board. This one is tough....
Maybe White's ownership of the cube swings things here. ANY anchorsoon will buy White some time, and maybe enough to threaten hurlingthe six-sided projectile. Often with the opponent owning the cube, thequick knockout (for gammon) is the better path. And if White anchorshigh, Blue may have enough time (especially with the THIRD White checkerin the loft) that if and when that finally happens Blue will be justabout inside the stockade. I just fell off the fence and landed in the acepoint manure. 8/7*, 6/1*.
Steve Clark: 15/10, 8/7*.
It is always a good idea in attacking positions to keep yourforces reasonably organized. You never know when your opponent willroll some nasty little double and turn the tables on you. Of course itis also important to bring builders down and get diversification to makethe key points while your brutish opponent is on the bar.
So how does this all apply to the position? I am not sure. The onemove I would not make is 8/7*, 6/1*. Of course it is bad luck to have 3men on the bar, but if our opponent does roll an ace, most (or all) ofour advantage would be dissipated. Also 6/1* does not aim at the keypoints at a time when we are rather short of builders.
Of the other plays it is rather difficult to pick among them. 20/15 isthe least disaster prone but it is quite passive for the position. 13/8is the intermediate play, bringing a builder while remaking the 8 point. There is a very good chance that next roll our main desire willbe to put all the blots together on points. Making the 8 is a goodstart in this direction.
15/10 is the most aggressive and the most risky. It maximizesdiversification, both for better and for worse. I am far from confidentbut I will go with the aggressive play. There are too many goodpossibilities to make a passive play at this point. I will play 15/10.
Hal Heinrich: 13/7*
This is the type kind of problem we all want -- how to continue the attack! Hitting with the ace is clear -- all the candidate plays contain it. In over-the-board play, it's important to physicallymove whatever is common to all your candidate plays -- it helps you to focus. 20/15 can be easilyrejected -- this is the time to attack, not defend! Hitting on the ace point feels wrong -- it's tooearly to try for a complete closeout, and White has no threats that the inside hit takes away. Thereal choice is between 15/10 which maximizes attackers for the five point and 13/8 which locks upan asset. I prefer taking the asset. While 15/10 maximizes the firepower for the most important point on the board, 13/8 allows Blue more flexibilty in choosing a game plan. Either by continuingthe attack or bringing the back men in. If Blue follows up by making the seven point, White'll have atough time creating winning chances.
Ron Karr. 8/7*, 6/1*.
All choicesare worth considering, after hitting 8/7*. 5/1* is the maximum blitzplay, putting 3 in the air and contesting the ace point. The questionis: is it worth the cost when the blitz doesn't succeed? White hassome jokers (11,22,33), after which I'm not going to enjoy having 5blots around, and other 1s could hurt. The opposite extreme is 20/15,which takes the sting out of small doubles, but is probably notaggressive enough. 15/10 and 13/8 are more positional, maximizingchances for a good prime, & still allowing a blitz if White doesn'tmake the ace point. I went back & forth a few times on this, but Ithink blitzing is probably best, because it has a lot to gain. Ifthings go well, a gammon is easy. Once in a while, White turns itaround quickly. Often, White anchors somewhere & I just try to gethome with the win.
George Klitsas: 13/7*.
Two, four, three, five. A Mensa test ? Does the number of blots left by each play in turn have any relation with their ranking in equity terms?
Play a (20/15 8/7*) Leaving the least number of blots (two). A quiet variation that fails to bring ammo for the blitz, but locks the 15 point, which, tho, will usually be the main liability of Blue's position if things calm down and Blue tries to bring his position home.
Play b (15/10 8/7*) Leaving four blots strewn around but bringing more ammo-pips (if this can be said) than play a, and a new builder for the five point. The White checker that is left back, on the twenty point (which is only in appearance neutral, away as it seems from the main action) is in fact a more-often-than-one-thinks target for White, and a nuisance for Blue (consider the immediate rolls of 3-3, 2-2, 1-1 for White, and many opportunities of tempo-gaining [distracting] loose hits in the future). Blue cannot play a priming game easily. He would rather be advised to play for the blitz, even if in some cases both plans will be available. For example , if White enters with both checkers (say with a roll of 3-2) and Blue rolls 3-1, I think that he should rather play 6/3*/2* than make the five point, since his many blots point against making quiet moves.
Play c (13/7*) Three blots, maximum ammo-pips, ammo-grains or ammo-tons (strangely enough �ammo� [ammos] means �sand� in Greek , which sounds good if you are going to �build� [bury] your opponent alive) and the eight point intact! One blot less, a crucial point kept and slightly more ammo looks to me more than enough compensation for only another builder down, so play c seems much better than play b. Nothing wrong can normally happen from this position on, which needs only a six to form a strong broken five-prime. Also, two ways to win : prime and blitz. Furthermore, and very important, in this solid and quiet variation, White will not be able to use the cube often and with maximum efficiency.
Play d (8/7* 6/1*) Five blots excited by their number alone in an all out attempt to blitz the opponent. It's not the number of blots that counts here (as a liability), not only because in general, more than three blots (four, five, six or more) is about the same, but, compared to play a, White has three men in the air here (one more). It will take some time to enter with these, and the fact that Blue has all these blots exposed will not count much, if at all. The problem with this play is not, either, that, Blue is committed to a blitz and deprives himself practically of any other plan - there are positions, when one must go blind for the close-out. Retaining other ways to win (priming, race, etc.) does not necessarily add to the overall equity of a position (it usually does, but not always, so in general it's hardly an argument by itself). By the way, this reminds me of an advertisement for Lotto, kind of State Lottery, where one has eleven (!) ways to win but his overall equity is poor. The problem with play d is the lack of adequate ammunition combined with an inadequate initial skeleton (the six and four points and the blot on the ace point) as a start for the blitz. This blot is a big liability. If hit, at any moment, Blue's blitz is slowed down dramatically and White becomes a huge favorite . Of course, with some luck, Blue will score some gammons (more than 25% of all the games, I estimate, he will be able to blitz his opponent). On the other hand, if the blitz fails, he will become an underdog, substantial, medium or slight, depending on dice. The three-point skeleton that White owns from his six to his eight point will look not like a hill, but, rather, like a mountain to Blue, as it will gradually start extracting like a compressed file from either side.
Once more, I am attracted by the aesthetic profile of a position - something, essentially, indistinguishable from what we usually call �feeling�-, along with the clear logical arguments. Feeling is still logical, but hidden (subconscious) - we can hardly explain it but in terms of abstract beauty. Feeling is also, in another interpretation, the judgment (based on patterns) of the internal neural net of our brain (in it's similarity to a computer neural net, a bot). Needless to say, I vote for play c, that leads usually to a solid, compact position, one that gives you the feeling that everything is more or less under control, that, normally, nothing can go wrong and I think that it's clearly better than the alternatives.
Rob Maier: 13/7*.
Forget about 20/15, with two on theroof, now is not the time to worry about the back checkers. The reflexiveplay (for me at least) is 15/10, giving us the maximum number of buildersfor the five point. But, what about the two and three points? If we areserious about blitzing, then we want to make whatever points White comesin on, rather than "in order." True, there already is one checker on theeight point, but the second one could easily see some business as well. In addition, remaking the eight point should provide us some comfort ifWhite refuses to cooperate with our nefarious blitzing fantasy. Whileworrying about single jokers too much is usually a mistake, FOUR of them(1-1,2-2,3-3,5-5) is probably worth taking seriously, and taking a littlebit of insurance against. The final option then is putting a thirdchecker on the roof with 6/1*. If White did not have his bar, or we hadan extra checker already in the attack zone, I could be persuaded to gofor it all. Here, however, I think the losses from being hit and sentback give White too much for too little chances of making the closeoutstick. I might change my mind at certain scores, but not here.
David Montgomery: 13/7*.
Blue is attacking and has no escape problems. Bringing another checkerinto the zone with 13/8 or 15/10 should be better than 20/15. 15/10creates a new builder. However, the builder only bears on the openfive point - if White doesn't roll a five Blue will usually be goingafter deeper points next turn. 13/8 brings the wood down but maintainsa solid position, and unstacks the heavy midpoint. Often White will bringboth checkers in next turn, so Blue doesn't want to have a position thatis too loose. I like 13/7*.
Snowie: 20/15, 8/7*.
No accidents for me. There is plenty of time to bring in the attackers.Locking up the other side of the board has first priority here.
Walter Swan: 8/7*, 6/1*.
After cubing, there are three basic ways to win. Close out,prime with none of your men back, and win non contact race. In thisposition, without seeing the roll, I would prefer to close Blue out ratherthan other option of priming. Seeing the roll, I see that putting 3 men onbar, leads me to that prefered goal.
Kit Woolsey: 13/7*.
Blue's back checkers aren't in too much danger, so coming outwith 20/15, 8/7* isn't very important. Bringing the wood down not onlylocks up the eight point in case of an accident but brings more ammunitioninto range for a potential blitz.
Michael Zehr: 15/10, 8/7*.
Blue has to carefully balance the risk of being hit with the risk ofWhite getting the ace point and having a chance. Obviously Blue'spreference is to close out three checkers, but White doesn't have goodtiming (yet) for an ace point game so Blue's game is almost as good ifWhite ends up with three on the ace point. So which 5? 20/15 looksway too passive. 13/8 doesn't add another builder. 15/10 adds abuilder. 6/1* spread Blue a little thin. Blue isn't worried aboutgetting hit so much as needing to make careful use of the eightcheckers in the attacking arena. Blue is more worried about hittingWhite off the 3 or 5 next turn than hitting White off the ace thisturn and having to cover it next turn.
Summary: The preference leaned toward aggressiveness either by bringinganother checker to the eight point or hitting the third blot. Only Snowiewas more concerned about safety.
Play Votes Score13/7* 5 1008/7*, 6/1* 3 8015/10, 8/7* 2 7020/15, 8/7* 1 60
Problem 5
| 123 142 | White money game Blue |
Chuck Bower: 24/21(2)*, 13/10(2).
Playing 3 or 5 of these (3 die) would be preferable. Blue wouldlike to use the cube next time, and thus should look for the play whichallows that occurence most often. Suppose you give White his BEST roll after each of the candidates. Which candidate move for Blue leaves the best position under these conditions? I think the best play comes tothe surface rather quickly. 24/21*(2), 13/10(2) gives Blue a strongposition regardless of White's subsequent roll. That is my choice.
Steve Clark: 24/21*, 13/10(2), 6/3.
Occasionally, like on problem 3, I feel fairly confident ofmy answer. Most of the time it is like this problem. 9 differentpossible answers, any one of which could be best, and I am supposed tomake some sensible comment while trying to not pick the worst of thealternatives.
At first all of the plays looked possible, but on further considerationI like 13/10(2). This has the advantage of making 5 parts of a primeand getting a couple of men closer to home. This leaves only theproblem of playing 24/21 or 6/3 with the final 3. For a while Icontemplated playing 24/21(2). This play leaves me safe even if my bloton the 3 point is hit. The problem with this move is that it does notrespond to the position very well. Blue will be trying to escape hisback men in the next few rolls, not playing safe. A good start on thatis to play 6/3, building as strong a board as possible and retainingBlue's racing lead.
On reflection this still seems like the best choice. 13/10(2) and 6/3make the best possible offensive assets. The 21 point is less desirablebecause of our need to get away soon anyway. Defensive assets are moreimportant when we are behind or being attacked and are less useful whenwe are trying to come home.
Hal Heinrich: 24/21*, 13/10(2), 6/3.
Hitting on the twenty-one is automatic. Suppose we cover the blot on the three point -- in that case,making the ten point seems right. The 3-3 roll swung 33 pips -- more if we count hyper-pips. So Blue is now up fourteen pips in the race, which makes anchors less important because we're expecting toabandon them first anyway. Suppose we hit and make the ten point -- now which three looks best? Making the three point works for me -- it really depends on how dangerous White's inner board attackis. The risk looks tolerable to me, especially as getting hit on the three equalizes the race. Whilehitting and making the eighteen point has appeal, priming the back men and building an inner boardtake priority.
Ron Karr: 24/21(2)*, 21/18(2).
I'd like to cover the 3 point, but not at the cost of leaving 2 otherblots. With 3 White checkers back, my 4-prime looks strong, so I justwant to advance my position naturally. If White hits, I should be ableto recirculate. Playing 13/10(2) might look strong for this move, butwill actually make it harder to escape the back checkers.
George Klitsas: 24/21(2)*, 13/10(2).
Play a (24/21(2)* 21/18(2)) Rejected easily. Going to the eighteen point is simply masochistic - Blue will need a lot of luck to disengage himself from there . Don't even bother to look for additional liabilities in Blue's position, like the blot on the three point that play a fails to cover.
Play b (24/21* 24/18 6/3) In the heart (mind ?!) of the expert there is fear, while considering this play and if one could follow the movement of his eyes he would notice that their focus is in turn on White's stack on the six point, then on White's five point and then on White's midpoint to rest there for awhile and then start over following the same time-table.
Play c (24/21* 21/15 6/3) The first play so far worth considering. The time-table just mentioned is still in effect but the level of fear is substantially lower. Being hit on the ace point with a return-shot by White is not as dangerous for Blue as being hit on the crucial four point. After play c, apart from dancing with 9 numbers, White has also four very awkward entering numbers that lose the game (6-2 and 6-1). With other entering numbers, like 4-2 or 2-1, he should slot the four point, I think, and this fact shows the difficulties he encounters in forming a menacing board. Entering and hitting on the ace point, results usually in an inner White board that is far from gin, and permits Blue to survive for awhile if being hit. The main liability of Blue's position is his rearmost checker that tries to be saved in two steps, hopefully surviving the enemy potential hits (moving to White's outfield then to Blue's outfield) or sometimes in three steps (going first in a more forward position still in White'shome board). I played 36 games (all my rolouts in this series are manual, the 36 rolls are rotated in every ply and when hits count I control them to a certain degree - so from now on I won't mention these details, for it would be an annoying repetition) for an equity of +0.39 ppg for Blue.
Play d (24/21*(2) 13/10(2)) Making White's four point will create less problems of escaping later than making White's bar point as in play a, in spite of the fact that the four point is more distant. The reason is that White here cannot unstuck the six and five points and form a strong reception committee in case of hitting something. In combination with making the ten point, which is gin and much more than one thinks, Blue will be able to activate his back checkers with a high probability of success. White just can't easily perform two tasks at the same time - closing out Blue and extracting three checkers from a broken six-prime. In a manual rollout of 108 games, the equity for Blue was +0.61 ppg, the best by far so far.
Play e (24/21*(2) 13/10 6/3) Rejected. Compared to play d leaves two blots and seeds control in the outfield in exchange for covering a worthless blot.
Play f (24/21*(2) 8/5 6/3) Obviously better than play e but still weak, since it breaks the eight point and the four-point prime at the same time, dividing Blue's army in three parts.
Play g (24/21* 13/10(2) 6/3) Worth considering. Compared to play d, makes the three point instead of the twenty-one one. White has immediately 15 numbers that lose the game (Blue doubles and White must pass) - the 9 rolls that dance and the awkward ones 6-4, 6-2 and 6-1. There is also a bad duplication for White - 1's and 2's that return-hit on the four point are entering numbers. Even if White return-hits on his four point and Blue does not return-return-hit himself, White has to fulfill the task of the two tasks mentioned above - here, tho, often Blue breaks himself his broken 6-prime, giving White plenty of sixes to play. This happens when White makes the highest four points in his inner board and Blue enters with a roll of 3-2 or 3-1, or when White enters without hitting and Blue rolls 2-2 and in other future sequences as well. White must be alert to play aggressively his awkward entering numbers that include a five (5-2, 5-1) by playing 21/16!! at a moment when both players have a 3-point board. In asample of 108 games the equity for Blue was +0.52 ppg , so I rate play g as slightly inferior to play d and I vote for play d.
Rob Maier: 24/21*, 13/10(2), 6/3.
So many choices, but only one theme. Hitting givesus a lead in the race. That's an asset worth protecting, so covering thethree point seems mandatory. While I would like to anchor, that leavesone more 3 that I'm not willing to playexcept by breaking the just madeanchor. Making the ten point with the last two 3's is solid, will helppreserve our race advantage, and leaves White some really bad numbers(1-6, 2-6, 4-6).
David Montgomery: 24/21*, 13/10(2), 6/3.
I don't see the justification for not covering the 3 point. Afterhitting and covering Blue would like to make the 21 point, but this leavesan unpalatable fourth three. Running with the last two threes takes awaysome of White's counter punches inside, but allows White to hit outside.13/10(2), further blocking White's three back men, looks better.
Snowie: 24/21*, 21/15, 6/3.
The ten point is junk. I don't need to contain White's back checkers. Also,making an anchor is the the game plan. Simply run my men home and win.
Walter Swan: 24/21(2)*, 13/10(2).
These are the best two points remaining on board to makeand allow 4 ways to get anchor home free. 1) Cube 2) Wait for White tocrack 3) Roll doubles immediately, 4) Play behind anchor and roll doubleslater. Plus 3 White men are put behind a 5 prime. The other plays restrictthe number of ways to win. As far as blot on 3 point, since Blue is behindalready, and has anchor, being hit is not a concern. In fact, it may helpBlue if White is forced to crack his board. Normally, reasoning goes, if Imnot hit, I'll cube, so one might quickly cover the 3 point to avoid beinghit.
Kit Woolsey: 24/21*, 24/18, 6/3.
Making the three point is important. Blue loses a lotof ground if that blot is hit. Since Blue is planning on racing his backcheckers around while White is scrambling to enter, making an anchor is notthe right approach. Blue's back checkers aren't in much danger now, but ifthey don't get going immediately Blue will have problems later.
Michael Zehr: 24/21(2)*, 13/10(2).
Blue should think about this from White's point of view. White has onehuge glaring problem with his game -- a stack of checkers with nothingto do except attack or make the four point. Blue should make sure hedoesn't give those checkers a purpose in life, so the last thing Bluewants is give White's checkers some targets. That leaves 24-21(2)*24-18(2); 24-21(2)* 13-10(2); and 24-21(2)* 13-10 6-3. (I don't carefor breaking the 8 point either -- why break up a nice four prime?) Iprefer 13-10(2) -- a hit behind a 5 prime isn't that worrisome, but ifBlue leaves two blots and doesn't make the 5 prime, White has aglimmer of hope after a hit.
Summary: So many choices, as is often the case with double-twos. Thesimple run and build play tied with making the 11 point, but there was plenty of support for other choices.
Play Votes Score24/21*, 13/10(2), 6/3 4 10024/21(2)*, 13/10(2) 4 9024/21*, 21/15, 6/3 1 7024/21*, 24/18, 6/3 1 7024/21(2)*, 21/18(2) 1 6024/21(2)*, 8/5, 6/3 0 5024/21(2)*, 13/10, 6/3 0 40
Problem 6
| 152 179 | White money game Blue |
Chuck Bower: 24/20.
Now this looks more like a typical GoL quiz problem--behind inthe game with a lousy roll to play. Note that odd numbers are goingto play nicely for White but even numbers aren't so hot. Thus leavinga blot on either the 9-point or the 11-point is out, since these willgive White a lot of good even numbers as well.
6/2 really looks lame, since the 2-point is one of the last oneswe want to make. 8/4 starts a decent point but at the risk of strippingthe 8-point. 24/23, 6/3 is better, but blotting in the home board,even when it doesn't leave direct shots, gives White a green light tohit loose. 24/20 is the direct approach. If Blue doesn't roll twoodd dice Blue may end up pulling this off. If there were a decentoption I might not make this play but the alternatives just look worse.
Steve Clark: 24/23, 6/3.
We need an advanced anchor in the worst way. We are waybehind in the race, and we have a weaker board. The only way to comeclose to equalizing is to get an advanced anchor. I would not considerany play that did not put that first. Thus I would not make any of theplays not moving a man off the 24 point. Normally I would play 24/20,make a mental note to myself that this duplicate opponent's 5's and 3'sand then say, "Wait, what about 6/3, 24/23?"
It could be the right play. If opponent can make the 5 point, I wouldrather not be on the bar. This distribution gives multi rolls whichmake some sort of advanced anchor. This play does have the defect ofputting an extra blot on my 3 point. I do not want loose blots aroundif I get in a hitting contest, but he is unlikely to start one. Opponent will not be enthusiastic about hitting me loose or evenpointing on me as he will be wanting to make the bar or the 5 point
Have I talked myself out of the natural play of 24/20? I guess I have,and now I am not entirely happy about it. 24/20 is the direct way to agood anchor and now I am playing something different.
Hal Heinrich: 24/20.
Blue wants to get an advanced anchor and continue the struggle from there -- playing from thetwenty-four point anchor is an unhappy prospect. Playing 24/23 and some three is a natural, conservative approach to this problem, while slotting the twenty point is a direct, in-your-facetry. In this position, the direct approach is called for -- stepping into three builders is atolerable risk, as it gives Blue improved chances to make the twenty or twenty-two point. Blue doesnot have a good three to go with 24/23 -- 6/3 is too deep, while 13/10 exposes another blot andstrips the mid. As long as Blue can't find a good three, Blue might as well reach for brass ring ofthe twenty point.
Ron Karr: 24/20.
I need to makean advanced anchor or hit something, and this play maximizes chances todo so. White can point on me with odd numbers, but those numbers alwaysmake the 5 point anyway. Better to make a move now, threatening theblot on the 15, rather than letting him bring more ammo into place.
George Klitsas: 24/20.
I remember, a long time ago, during my military service, I was reading a book over and over again, sitting on a bench in a square on an island, a day when I was on leave from my ship. This book was a classic by Paul Magriel, �Backgammon�. One of the concepts of this marvelous book, which essentially has never been outdated, was the concept of �coming under the gun�. When your opponent has at least three builders in position (say pointing on his five point) it is suicidal for you to put a slot there. A sound rule that like every rule (by definition, since a rule is less than a law) has a few exceptions. A couple of years later, I went to a bg tournament in Torrequebrada, Spain, where I watched a bg seminar by Joe Sylvester and Neil Kazaross. I was impressed when Joe gave some examples of correctly coming under the gun. In all of them the common theme was that the opponent (White, here) would make the point in any case, without breaking his points (having already spares on them), if he happened to roll the point-making numbers - the fact that his opponent (Blue, here) slotted, would not help him by much. So 24/20 is my play here, as Blue must definitely try for an advanced anchor. There is also duplication favoring Blue concerning White's pointing numbers on Blue's blots, but this is not the main issue. Other plays bury checkers or expose them in the outfield weakening some points at the same time - unnecessarily and pointlessly. I think that Paul himself would agree with 24/20!
Rob Maier: 24/23, 6/3.
Blue needs to make an advanced anchor. While one may be better than the other, at this point I'll take any ofthem. Splitting just to the twenty-three point, gives us more chances ofmaking some advanced anchor, either the three point, the bar point, or thefive point. We are also somewhat less vulnerable to an immediate attackif we stay off White's five point. Still, coming up to the five pointdoes have some merit, and I wouldn't argue if this was my partner's play. The ace is far more clear to me than the three.
David Montgomery: 24/20.
Playing off the midpoint doesn't look right. With either 13/9 or 13/10, 11/10Blue diversifies White's good numbers without accomplishing anything.(24/23 13/10 should be as good as these plays because it dupes White'sfives while trying to accomplish something.) Playing into the boardis reasonable. This keeps the risk down while going after a clearobjective, building up the board. Splitting the back men leaves Blueopen to a strong attack, but it does give Blue his best chance to graban advanced anchor, which is the best way for Blue to equalize the position.Between the two splits I prefer 24/20 because it tries for a better anchorbut doesn't seem much more risky.
Snowie: 24/23, 6/3.
If I get pointed on, it will be a point he doesn't particularly want to make.I should have no trouble making an advanced anchor next roll.
Walter Swan: 24/23, 6/3.
White is trying to make bar or 5 point. Should while make 5point, I do not want it on head so I have chance to make bar.
Kit Woolsey: 24/20.
This looks like an ideal time to fight for an advanced anchor.White doesn't have too much attack potential, and White's fives and threesare duplicated. White has an advanced anchor, so Blue needs one of his ownor he could be in trouble in a priming battle.
Michael Zehr: 13/9.
No matter what Blue does he's not going to accomplish much with thisroll. Often the hardest plays to make are when one has to selectamong a number of rather poor choices. Blue is down in the race,behind in development, and not making any progress this turn. Itmight help to think about it from White's point of view. White wantsto make her bar and five points, bottle Blue up, and then bring theback checkers home safely. White would also happily attack Blue ifBlue splits. Blue's options are to build a board behind White or putup roadblocks. 6-2 feels like it's playing too deep in Blue's board,and 8-4 duplicates 2's while removing a builder for the bar point.13-9 is the lessor of several evils.
Summary: Getting the back men moving was clearly indicated. The panelis not afraid to come under the gun if the situation warrants it.
Play Votes Score24/20 6 10024/23, 6/3 4 8013/9 1 608/4 0 506/2 0 5013/10, 11/10 0 40
Problem 7
| 134 158 | White money game Blue |
Chuck Bower: B/24, 9/7.
Most players detest making the 2-point with the opening roll, eventhough the rollouts say it is as good as the alternatives and BETTERwhen gammons pay more than 2::1 (not here). But even if you don'tlike making this play, you need to know how to defend it. My observationof JF rollouts indicate that splitting 24/x is not the optimal defense.Building your own prime/board is better. On top of that, White's strippedbarpoint becomes builders for pointing on Blue's head. For these reasonsI'm ruling out B/22.
Whenever I make a play like 6/4, my master instructor (Snowie) rapsmy knuckles, so my bruises won't allow me to do THAT any time soon. Theother two plays leave about the same number of shots, but 9/7 leavesfewer blots, starts a point we'd really like to make, and is easier toclean up. Recall that another master instructor lectures that whenholding a single checker in your board, the barpoint is as good as the5-point, so better to get half of the barpoint now than hoping for all of the 5-point next time. B/24, 9/7.
Steve Clark: B/22.
When your opponent makes his 2 point, you generally shouldbe more reluctant to split onto a higher point. She will love to hityou, particularly if she can point on your head. In this problem thereare some considerations which make splitting more desirable than usual.First is that we have made an inner point of our own so that theopponent will not be so eager to hit loose, particularly when we onlysplit up to his 3 point. Second, now that she has made her bar point,we are in greater danger of being trapped and thereby have someincentive to get moving before she improves her board further.
What about the other plays. 6/4 pushes a checker too far forward. 9/7looks totally unbalanced, leaving us with limited ways of goingforward. 13-11 looks cockeyed but it actually has real merit. We arefar behind in the race so getting hit isn't as bad as usual. It doesbring builders for the 5 point. Also White really will want to make aninner point, hitting on the 11 point is not really in her agenda. Ifshe does make an inner point, we will have 2 men aimed at her blot onour 10. If she hits us, we will be able to bring a checker to her 3 or 4point while still having an anchor on her ace point.
I really like 13/11 but is the right idea in this position? Trying toescape while you can is one of the basic concepts of backgammon. I amnot very confident here. Opponents rarely make the 2 point so I havelimited background on this type of position. Either play could be rightby quite a bit, but I will play B/22.
Hal Heinrich: B/24, 13/11.
The need to get off the twenty-four point is the driving issue here. Should Blue risk White's attack in order to avoid being trapped? At first, I thought yes, but further consideration changed my mind. Two considerations are key: Blue has good counter-play against White's back man, and White has poorer priming chances than normal. White's priming chances are worse than usual because the deuce point isalready made, and the six point still has five men on it. After retaining the twenty-four anchor, wecan reject 9/7 -- it's horrible because it lets White's back man escape while hitting, and it doesn'teven duplicate sixes! 6/4 is the conservative way, but 13/11 has the right stuff! Being hit on theeleven isn't clearly bad because a third man back helps Blue's chances to advance the anchor -- afterseeing that, the additional building chances make 13/11 the mandatory play. In short, Blue can expectto escape later and need not risk being attacked now.
Ron Karr: B/24, 13/11.
Normallysplitting 24/22 would be right, because White has made his bar pointand is threatening to escape one back checker. However, in thisposition I'm not sure it's worth the risk of getting attacked. White'sboard is awkward enough that just sitting on the ace point has merit:he may have trouble coming home even if he can escape both backcheckers. 13/11 works on building my own position, and I won't mindgetting a 3rd checker sent back.
George Klitsas: B/24, 13/11.
Play a (B/22) The weakness of this play is that it allows White to attack, unstucking the six point in many cases (consider White's rolls like 5-2 and 3-2, that hit both blots, almost all doubles, 5-4, 4-3). White has the ammunition to continue the attack, even if hit back by Blue. Invoking a blood-bath type of game is not the appropriate strategy when your opponent has made early his two point but his distribution is awkward. In a sample of 36 games Blue's equity was -0.39 ppg.
Play b (B/24 13/11) Calmly adding a builder for the five point. If hit, this checker actually will help Blue to make an advanced anchor or a phantom point in White's inner board. In fact, it's Blue's checker on his eleven point that puts pressure on White's checker that is close to him, not vice-versa. Consider a roll of 6-2 for Blue (played 24/16*) to see what I mean. See also the comments on a similar play that I chose in the August issue (Quiz solutions, problem 2), even if it was not included as an alternative (by oversight, I think). In 36 games the equity for Blue was -0.22 ppg.
Play c (B/24 9/7) The problem with this play is not that the slot might be hit, but that the resulting position has not much building potential even when the slot survives. Clearly worse than play b.
Play d (B/24 6/4) Semi-burying a checker. Without fighting spirit, hoping that somehow he will not lose, at least soon or immediately, waiting for �deus ex machina�. Unfortunately, there is no draw in backgammon.
Needless to say, my vote is for play b.
Rob Maier: B/22.
Without a moreuseful two to play, 2 back versus 1, and a slightly better board, I thinksplitting is a must.
David Montgomery: B/24, 9/7.
White's offensive checkers are numerous and awkwardly placed for makingpoints. Thus Blue should avoid B/22, which allows White to attack. 6/4is possible, but the distribution looks a bit better with both spareson the 6 point. 13/11 should be inferior to 9/7 -- if Blue is going to leavea direct shot, he might as well slot a good point. With Blue pinned backon the 24 to avoid an attack, it is important for Blue to get a goodoffense going. I like 9/7.
Snowie: B/24, 13/11.
It is vital to make the five point quickly before White escapes. Havinga third checker sent back isn't too costly since I am already behind inthe race.
Walter Swan: B/24, 6/4.
Despite putting man on 4 point before making 5 pint. I want myfull roll next time to improve Blue's offensive positon. Given a full rollI am a favorite to improve offensively, splitting I am not a favorite tomake an anchor. The other reason for splitting, covering White's outfield,doesnt stop White from bringing builders to White's 10 and 11 points,although it does retard White from moving 15-9 with a 6.
Kit Woolsey: B/24, 6/4.
Blue can't afford to come up to the 22 point. White has a pileof checkers on the six point which are looking for a home. Even thoughWhite has made his bar point, Blue is not in too much danger in a primingbattle because he has extra checkers on the midpoint and White has made thedeep two point. There doesn't appear to be any reason to leave a shot.
Michael Zehr: B/22.
Staying back takes too much pressure off White. Sure White mightattack after stepping up, but otherwise White will simply bring downbuilders and slowly choke off Blue's escape path.
Summary: Most of the panel definitely did not like splitting theback checkers against the made two point. However the choice of which twoto play was not clear.
Play Votes ScoreB/24, 13/11 4 100B/22 3 90B/24, 9/7 2 80B/24, 6/4 2 80
Problem 8
| 142 189 | White money game Blue |
Chuck Bower: B/22, 23/22.
Can Blue win this position forward? Answering that question goesa long way to deciding the best play. Here an old fashioned hand rolloutworks nicely. B/24, 13/12*, 5/4*(2) is a forward going move so I did36 (sequential dice) hand rollouts. Blue did not do so well here. Mostof Blue's wins were from backgames, which answered the question ratherconvincingly. Blue must win backward.
Blue's timing is questionable. Thus hitting White seems a mistake.With questionable timing, the 1-2 backgame is out, so grab the 22-pointwith B/24, 23/22(2). Now we are left with a single ace to play, andthere is only one which is consistent with the gameplan--24/23. Thischecker can be used subsequently to either jump the prime (assumingWhite doesn't make his 8-point) or improving from the 1-3 to 2-3 backgame.
The old cliche "the best two points for the backgame are the onesyou have" fails once again. The 22-point combines well with EVERYother possible defensive point in the opponent's home board. Grab it now and entrench! B/22, 23/22.
Steve Clark: B/24, 23/22, 13/12(2)*.
Don't play back games at any score. Particularly don'tplay 1-2 back games. You end up with all your checkers stacked up onyour (or your opponent's) ace point. One way out of the back game is tohit him twice, B/24, 13/12*, 5/4(2)*. This has the advantage ofparalyzing him while we try to escape. Maybe we can pick up his otherblots in the mean time and turn this around. The problem with thisapproach is that he will be able to come in eventually. Our back menare so badly positioned that we will have trouble making significantimprovement before he starts forward again.
What about the opposite approach of B/22, 23/22. This gets as many menup to the starting line as possible. It leaves our opponent's extrachecker on the 18 point with nowhere good to go. Unfortunately it alsoleaves him with complete flexibility on his next turn. He will be happyto have a chance of adding a 5th point to his growing prime.
I think we have to hit something here. And if we are going to hit onlyone blot, it look like it has to be on the 12. This keeps a betterboard and takes away an immediate builder. After that I suppose itcan't be right to leave blots on the 13 and 12 points. They would justinvite the super crunched back game. By process of elimination B/24,23/22, 13/12(2)* must be the right play. I suppose so but I haven't evenconvinced myself.
Hal Heinrich: B/24, 23/22, 13/12(2)*.
This is an extremely important play in a difficult position -- I don't have much confidence in theplay I've chosen. Just making the twenty-two point expresses a confidence in Blue's backgame chances that I just don't share -- let's reject this and try to win frontwards. So now we've come in from theroof and hit with 13/12* -- this is key because it removes a builder for the fifth point of White's prime. Certainly putting two men up against a three point board with 5/4(2)* merits consideration. Theprospect of catching one or both of White's dangling blots is certainly tempting. Although this playmay turn out to be right, it feels wrong. Not only do Blue's back men remain badly placed behind White's prime, but Blue is in serious danger of losing all presence in the outfield. In addition, Blueis poorly placed to continue attacking the blots that've been sent to the roof. Let's make the twelvepoint with our third ace, and hang onto our meagre outfield control. The last ace is now easy -- 23/22.This steps up to the edge of White's prime preparing to escape, anchor, or pick off White's danglingblots. The risk in breaking the twenty-three point anchor is tolerable -- White is a little short ofammo, and needs to come in from the bar first anyway.
Ron Karr: B/24, 23/22, 13/12(2)*.
Despite having 5 checkers in back of a 4-prime, I don't want to playthis as a backgame. The timing looks poor, plus I have chances to makeforward progress, with White's 4 blots as possible targets. I want tohit something for sure, to prevent White from making a 5-prime, amongother things. But if I hit 2, my back checkers could be trapped & myposition could fall apart quickly. So I think 23/22 for sure, todiversify the back checkers. Likely I can make the 22 point later ifnecessary, or hit a fly shot. Then 13/12(2)* to send that checkerback. If White can't anchor, I may be able to keep hitting; or elseI'll circulate some back checkers.
George Klitsas: B/24, 23/22, 13/12(2)*.
Play a (B/22 23/22) If Blue is trying strictly for a backgame, he lacks the timing. In reality Blue is hoping that White's difficulties to lengthen his 4-point prime and bring the rest of his checkers home, will permit him to win some games by going forward and a number of games by forcing Blue to give him a well-timed backgame. In practice, things don't work usually in White's favor and he often ends up in a hopeless backgame with a crashed inner board. Crucial is the first roll of White - when he makes his eight point forming a 5-prime, Blue should be happy to save the gammon. In 36 games Blue's equity was -0.83 ppg.
Plays b (B/24 23/22(2) 13/12*), c (B/22 13/12*) and d (B/24 23/22 13/12*(2)) From this group that hits the White blot on Blue's twelve point, I think that play d is superior, since it leaves no additional blots in the outfield in exchange for less costly losses in White's inner board. Play d is a step towards the real demands of the position - to go forward. By pointing on White's blot on the twelve point, Blue removes a most needed builder for the extension of White's four-point prime and the overall control of the outfield. By now Blue can jump in the outfield with back checkers without much fear and even make points there resulting in less times being gammoned and in more wins. Blue's equity in 36 games was -0.44 ppg.
Play e (B/24 23/22 5/4*(2)) Pointing on the inner blot instead of the outer one (in comparison with play d). One problem with this play is that it does not remove White's third builder in the outfield. Another, and more serious, that, in order to remove it in the future, Blue must break the midpoint losing control of the outfield. Blue often has to break the midpoint anyway with 3's and 4's, when he is not able to activate his back checkers. In 36 games Blue's equity was -0.64 ppg.
Play f (B/24 13/12*(2) 5/4*(2)) Pointing on both blots, in an effort to gain more time and win by going forward, but failing to put a checker on the twenty-two point. Is this (failure) crucial and to what extent? (more or less than one things at a first sight?). The answer is �more than one thinks�. Blue will usually have a hard time trying to extricate his back checkers, ending up in busted backgames or bad-timed ace-point games. His occasional wins when he scoops White's outfield blots and doubles him out, are not many in number, to make play f the winner. Actually, in 36 games that I played, Blue's equity was -0.67 ppg.
A very difficult problem, one that would be best answered by extensive human rollouts - hardly by abstract arguments of any type. Unfortunately, the kind of rollouts that in all variations are time consuming, each move's difficulty reflecting the overall difficulty of the initial position and the branch-positions a through f, as well, kind of fractal-position(s). I will vote for play d, the typical winner, according to these short rollouts of mine, with a decent probability of being correct, I guess.
Rob Maier: B/24, 13/12*, 5/4(2)*.
If it were just a question of picking the better back game, then B/22,23/22 would be best, as it requires less timing to avoid crashing our homeboard. Here, however, our timing is so bad that we should be looking totry to win going forward. With White's two ADDITIONAL blots, we shoulddefinitely hit twice first and ask questions later. White could easilyspend the next several rolls up on the bar. Don't make the mistake of"compromising" between offense and defense with B/24, 23/22(2), 13/12*.The race is too close, and White's position too strong, to expect to beable to play anything resembling a well-timed backgame, and even if Whitefans with the single checker, we will wish that the second checker werealready on the roof. Backgame? After hitting two, we could easily beWINNING the race in two rolls.
David Montgomery: B/24, 13/12*, 5/4(2)*.
If Blue hits once, it seems he should play 13/12(2)*. Blue isn't concernedwith White anchoring, and sending another checker back makes it morelikely White will ultimately have to make some concession. Hitting witha single checker 13/12* gives White too many returns with perfectdiversification. This narrows it down to three candidates: not hitting,hitting once, or hitting twice.
Of these, I like the look of hitting twice best. This play appears to meto give Blue the best chance to win going forward, while still leavingBlue good chances for a backgame if necessary.
Snowie: B/22, 23/22.
Doesn't anybody know how to play a back game? The highest priority is tomake the advanced anchor. Everything else is secondary.
Walter Swan: B/24, 23/22(2), 13/12*.
Blue with no other checkers to play cant playthis back game. This play makes best anchor available, doesn't make Blue'shome board worse, keeps White from making his 8 pt. and makes an attempt tosweep up White's 4 loose blots. In this postion, there is not , any timesoon, going to be a lets try to save gammon line of play for Blue.
Kit Woolsey: B/24, 23/22, 5/4(2)*.
Blue's timing is suspect for a back game. If hejust makes the defensive three point, White has some rolls which make thefive-prime and Blue will be in big trouble. On the other hand, Blue needs hismidpoint as a lifeline. The shifting play may gain Blue some time toget the back checkers out into the outfield, without letting White makean anchor.
Michael Zehr: B/24, 23/22(2), 13/12*
Four is more than you think, and it takes a long time to rescue fivecheckers from behind a four prime. That makes moving up to the 22 mynumber one objective. With my last ace I'll hit on the 12 to preventWhite from having a full roll to make a five prime.An attacking plan (hitting twice) still leaves Blue needing three 1'sand 2's and five 5's and 6's -- a tall order while also trying tocontain White using only ten checkers. That plan looks more likely tolead to Blue crunching than anything else.
Summary: The popular choice was to shift in the outfield and maybe try togo frontwards. I still have my doubts if the timing is adequate for thatapproach. Interesting that Snowie preferred not to hit at all, instead lockingup the 22 point anchor. Who said that bots are afraid to play back games?
Play Votes ScoreB/24, 23/22, 13/12(2)* 4 100B/22, 23/22 2 80B/24, 23/22(2), 13/12* 2 70B/24, 13/12*, 5/4(2)* 2 70B/24, 23/22, 5/4(2)* 1 60B/22, 13/12* 0 40
Vote Summary
1 2 3 4 5 6 7 8Chuck Bower 20/13 8/4, 6/4 8/3, 6/3 8/7*, 6/1* 24/21(2)* 13/10(2) 24/20 B/24, 9/7 B/22, 23/22 Steve Clark 13/6 13/9, 5/3 24/21, 13/8 15/10, 8/7* 24/21*, 13/10(2), 6/3 24/23, 6/3 B/22 B/24, 23/22, 13/12(2)*Hal Heinrich 20/13 13/9, 5/3 24/21, 13/8 13/7* 24/21*, 13/10(2), 6/3 24/20 B/24, 13/11 B/24, 23/22, 13/12(2)*Ron Karr 20/13 13/9, 5/3 24/16 8/7*, 6/1* 24/21(2)*, 21/18(2) 24/20 B/24, 13/11 B/24, 23/22, 13/12(2)*George Klitsas 20/13 13/9, 5/3 24/21, 13/8 13/7* 24/21(2)*, 13/10(2) 24/20 B/24, 13/11 B/24, 23/22, 13/12(2)* Rob Maier 20/13 8/4, 6/4 24/21, 13/8 13/7* 24/21*, 13/10(2), 6/3 24/23, 6/3 B/22 B/24, 13/12*, 5/4(2)* David Montgomery 20/13 13/9, 5/3 24/21, 13/8 13/7* 24/21*, 13/10(2), 6/3 24/20 B/24, 9/7 B/24, 13/12*, 5/4(2)*Snowie 13/6 13/9, 5/3 24/21, 13/8 20/15, 8/7* 24/21*, 21/15, 6/3 24/23, 6/3 B/24, 13/11 B/22, 23/22 Walter Swan 20/13 13/9, 5/3 24/21, 13/8 8/7*, 6/1* 24/21(2)*, 13/10(2) 24/23, 6/3 B/24, 6/4 B/24, 23/22(2), 13/12*Kit Woolsey 20/13 13/9, 5/3 24/21, 13/8 13/7* 24/21*, 24/18, 6/3 24/20 B/24, 6/4 B/24, 23/22, 5/4(2)*Michael Zehr 20/13 13/9, 5/3 8/3, 6/3 15/10, 8/7* 24/21(2)*, 13/10(2) 13/9 B/22 B/24, 23/22(2), 13/12*
