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| 148 120 | White money game Blue |
Chuck Bower: 8/2, 6/2.
Since White owns the cube, Blue can't use that route to winthe game. Gammons are looking juicy! White's board is reasonableenough, however, to offer a strong defense. Certainly hitting looseon the 1-point gives White the least chance of anchoring this nextroll. However, I don't think that is enough to make this play better.If Blue hits and then is hit back, note that Blue will no longerhave sufficient checkers on his side for the closeout. While Blueis bringing the 12th checker around, White gets lots of rolls toenter (and possibly anchor).
A second drawback of the loose hit is that now Blue is concentratingon the less valuable 1-point instead of the 2-point. If White is going to anchor, Blue definitely wants it to be on the 1-point, not the 2-point.
8/2, 6/2 grabs the solid asset. Now going after the blot withthe remaining two free checkers is efficient. And if White anchors, Blue can still win some gammons. If Blue had more checkers with which to attack, I would be more tempted to hit loose on the 1-point. With only twelve checkers, efficiency appears to be the key. Don't look a giftroll in the mouth. My vote is for 8/2, 6/2.
Steve Clark: 8/2, 6/2.
This is not a straightforward problem of going for thegammon vs. playing safely for the win. Rather the issues of safety andaggressiveness are formed into a more complex web. 8/2, 6/2 wouldclearly be the more desirable (and safer) play were it not for theproblem of trying to escape Blue's rear checkers. I will go for thischoice anyway. If White comes in, Blue still has sufficientflexibility so that he should have more than one chance to escape safelywhile White would still be trapped behind a 5 point board. If youcompare White's aces after the alternative plays, you will see thatBlue is much happier when he has made the 2 point.
Hal Heinrich: 8/2, 6/2.
This play is so clear, that I don't see it as a problem!Just continue the closeout, and don't invent 'clever' alternatives.
Ron Karr: 8/2 6/2.
Making the 2 point is solid and puts White under a lot of pressureto enter. If he makes the anchor, I'm still in good shape, and if he doesn't Imay be able to close him out. 5/1* 21/15 might be right if I were desperate toescape, but here I'm not. Getting hit back now would hurt; also I'm duplicatingmy own 5s to hit the other blot and cover the 1 point.
Worst case, if White enters and I don't roll another 6 for a while, I'll have tobreak the bar point anchor, but even there the burden is on him to prime me andout-time me.
George Klitsas: 8/2, 6/2.
Play A (21/15, 5/1*) Blue tries to squelch any resistance. Having given the cube away, this is theoretically a sound idea, but not here. The problem is Blue's marginal ammunition for this plan to succeed, combined with the strength of White's broken but dynamic blockage which, with no men out of play and many builders in position, extends surprisingly easily. So, instead of cutting off White'spotential redoubles , Blue only manages to create (for White) one-point games, two-point games , even higher anchor-games (when Blue breaks a point for switch purposes) with lots of cube equity for White, something which is much limited in play b , as we will see. Furthermore, Blue has very difficult decisions in many typical situations that arise. For example, when to hit and leave two blots of his own in his inner board, when to split his 8 point in order to diversify the numbers that hit, risking not to ever remake it , when to cover his ace point with a 5 instead of hitting White's blot on his 10 point trying for a priming game, when to switch points in his inner board, when to cover with an ace (2/1) instead of covering the two point and leaving the ace point slotted, when to complete a 5-prime with double aces by playing 8/7(2) instead of switching or even hitting lose (6/2*). All these questions that are hardly answered correctly always even by experts (on the table) make play a unattractive. If we are going to be practical -especially in money game- I think that a less-than-expert player would be well advised not to adopt play a, even if it was theoretically slightly better than play b. But, according to a controlled rollout of mine (36 games in each variation) and my overall feeling of the position during this rollout, play a is inferior to play b. In this small rollout , which is hardly adequate but merely indicative, I grouped out the games as follows:
*In 19 games Blue closed out 3 White men �the gammon was naturally by far the most common result here.
*In 7 games White made Blue's one point. In 3 of them this happened early, which gave him blockage and even race potential! The other 4 games were typical ace-point games , two badly-timed and two well-timed.
*In 8 games White made Blue's two point. In 3 of them this happened early with plenty of game and ways to win with the outfield as the main battlefield. The rest were typical 2-point games, 4 well timed (a significant point) and one badly-timed.
*In the other 2 games, Blue was committed to a blitz which failed. Redouble-pass.
The equity of play a for Blue in this sample of 36 games was +2.34 points per game. A final subtle point: Sometimes in order to maximize the ammunition for completing a blitz of some type, Blue leaves (correctly or mistakenly) a man behind White's semi-blockage. Then this checker may create problems by not being able to escape in time.
Play B (8/2 6/2) Blue secures the 2-point, depriving White of a potential 2-point game. Blue's subsequent rolls play quite easily-his plan is simple enough, repeatedly hit on his ace-point until someone makes it. I grouped a 36 games rollout as follows:
*In 17 games Blue closed out White hitting all 3 blots, which almost always resulted in a gammon.
*In 8 games White anchored, but his third checker was sent back.
*In 4 more games White anchored saving his third blot.
*In the other 7 games Blue was hit and put back behind White's partial blockage. Blue encountered great difficulties and in most cases ended up giving up or taking a powerful redouble.
Net equity=+2.5 points per game.
Laila Leonhardt: 8/2, 6/2.
Making it more likely for White to dance and to create a 5 pointprime seems to outweigh any other plays by far. Even if White should enterwith a 1 next time, the strong board would be an asset throughout the rest ofthe game.
Rob Maier: 8/2, 6/2.
Making the two point gets us much closer to closing Whiteout than the alternative. If White rolls an ace, it's far from clear thatthe alternative play puts us in a better position. Meanwhile, if Whitedoesn't roll an ace, 21 numbers continue the attack on the ace point,while 6 more hit the blot on the ten point. If you look at it too long,hitting and leaping can seem tempting, but I don't think this one isclose.
David Montgomery: 8/2, 6/2.
When the opponent's already on the roof, it's usually better tomake a new point in your board rather than hit loose, unless your attack isvery likely to be overwhelming, or you can accomplish something very goodwith the other die. Here 21/15 is pretty good, but I still prefer thepoint.
Bill Robertie: 21/15, 5/1*
Blitz situations where you have a four-point board and a choice betweenmaking the fifth point in your board or hitting loose are among the mostinteresting of blitz checker play problems. (I have a whole problem setdevoted to just this tactic.) The basic idea is this: Consider theposition after you make the fifth point and your opponent enters. If thatposition is a pretty easy win for you, then make the fifth point.Otherwise hit loose.
If Blue plays 8/2 6/2 and White rolls a one, Blue's in considerabledifficulties. White's men are all active and Blue has to get through theoutfield quickly. It's not a clear win, so Blue should play 5/1* 21/15.
Snowie: 21/15, 5/1*.
When they're down, keep them down. No easy anchors forthe bad guy. Springing the back checker is nice also.
Kit Woolsey: 21/15, 5/1*.
Making the two point looks nice. The problem is thatthe followup may be difficult. If Blue doesn't roll an immediate threeor six he will have to break off the enemy bar point, which leaveshimself open to an accident. In addition, if White rolls an ace nowsuddenly White has a lot of play. Blue's back checker could be introuble.
21/15, 5/1* solves most of these problems. The back checker is liberatedfor good, and it can hunt White's other blot. Even if White hits backBlue will be in decent shape since White will probably have anotherchecker on the bar. Also White is prevented from anchoring.
Summary: A strong vote for simply making the two point. Could be right,but springing the back checker combined with the loose hit does two goodthings so it is quite tempting.
Play Votes Score8/2, 6/2 8 10021/15, 5/1* 3 70
Problem 2
| 110 144 | White money game Blue |
Chuck Bower: 24/20, 8/3.
With such a large racing deficit, Blue needs a hit (and containment).A 1 or 3 this turn would have helped, but... White is getting close toa double, but his rather inflexible checker distribution may be enough ofa liability to keep the cube centered.
Blue wants to keep the pressure on White. Coming off the 24-pointis a must! So 24/20 is half the move. Now the 5 can be played either20/15 or 8/3. Both plays have their drawbacks. For 20/15, if Bluecan't hit on the next roll then the Blue checkers are unlinked, andneither can stand on its own. White will have a strong double(and Blue probably must pass). 8/3 is lame. That checker BELONGS onthe 5-point or 7-point.
Leaving the back checkers on the 24- and 20-points this turn canlead to two good things for Blue. 1) It keeps pressure on White forthis roll and probably a few more rolls. 2) If unmolested, a 4 diemakes the golden point--a sufficient asset to give Blue an easy take,and probably good enough to fend off the double. Even though the 8/3move here should turn one's stomach, there are still three directbuilders for the 5-point remaining. Owning the 5-point will do nogood if Blue can't accept the cube. Stopping on the 20-point is likelyto be a thorn in White's side for several rolls. 24/20, 8/3 is my play.
Steve Clark: 11/7, 11/6.
Here Blue is well behind in the race and White is about toescape. 24/15 seems to make it easier for White to hit or playrelatively safely. This attempt to escape a blot is misplaced whenBlue is so far behind in the race.
I don't see the value in 11/2. If this is the best move, someone elsewill have to explain it to me.
Normally in these situation Blue tries to split by such moves as 24/20,8/3. This gives Blue the opportunity of establishing the 20 as a highanchor while covering the outfield in case White has to leave a shotthere. Is there anything about this position that argues against thisplay? Actually there is. White's position is quite awkward and ratherstripped. White is likely to have difficulty playing safely whilecoming in. If Blue makes the 20 point, White will be able to playbehind him. Also the split itself makes many of White's rolls safer orbetter; e.g. 4,1 or 5,2. Is this enough to go against the normalplay? I am not confident about this, but I will play 11/7, 11/6.
Hal Heinrich: 11/2.
Playing 8/3, 6/2 is worth considering even though it's notgiven as a candidate play. Breaking the 24 point is anti-thematic andbad. White is well ahead in the race with an awkward position -- atypical wretching ostrich attack. The problem with breaking the 24anchor is the extra options it gives White. Just hang back, build yourboard, and wait for your shot. It'd be nice to hang onto the elevenpoint, but the best way of doing that, 8/3, 6/2 is too ugly. Getting hitdoesn't hurt Blue and might help -- with hitting a shot and preservingtiming. So 11/2 gets the nod because it's the best board-building play.
Ron Karr: 11/2.
I changed my mind after thinking about this for a while. The normalplay is to split when the opponent is on the verge of escaping both backcheckers, so the default play would be 24/20 8/3. This gives maximum coverage,and prevents him from dropping his blot in the outfield to create a new builder.8/3 is a bit deep, but the position is still reasonably flexible.
On the other hand, there are definite advantages to staying back on the anchor.First, it avoids getting crushed with numbers like 33 and 55. Second, White'sposition is too far advanced, and he doesn't have a lot of good numbers, so it'snot so urgent to split. Most of his 5s and 6s either leave a shot anyway orelse play very awkwardly. Third, staying on the ace point keeps me in the gametil the end, while even if I end up making the 5-point anchor (and I may not beable to), that may make it easier for White to get home and win the race.
My original thought was that I would stay on the ace point in a 1-point match,because I don't have to worry about getting doubled, but I'd split in a moneygame, because if he does manage to safety the blot and make a new point, then Iwouldn't be able to take a cube. However, I'm now thinking I'd stay backanyway, because there's enough gain in the next few rolls to make it worthwhile.
That being the case, it might be right to play 11/2 rather than 11/7 11/6. Thatway, if White rolls 31 or 42, he'd be reluctant to make an inner point since hewould have to leave a double shot instead of a single. And if I get hit, it mayactually help me--I'm already far behind in the race, and it would give me moreflexibility in White's board.
George Klitsas: 24/20, 11/6:
Being 25 pips behind after moving, Blue must try to hit something in thenear future or in the remote future by forming an advanced anchor and waiting for a shot in a holding game. Blue must definitely contest the outfield by moving 24/something. Otherwise White will flood the outfield with builders in his very next roll and obtain a crushing advantage. The best point to land his rear checker is definitely the 20 point. If White does not make any progress in his next rolls (he has difficulty playing some numbers, especially fours and the more he is obliged to stack the more awkward his upcoming rolls become) , Blue may consider even not to anchor with a four for a while -still the long term plan is to make the 20 point and play from there. Going all the way to the 15 point is weak . This checker does not control the outfield since it is there, being subject to enemy hits as well and at the same time isolating his fellow on the 24 point. Under the light of this preliminary analysis, I rate the various plays as follows:
Play A (24/15) Weak as already told. In a controlled manual rollout of 36 games, the net equity for Blue was -1.28 points per game.
Play B (24/20, 8/3) To be frank, I would not even consider, I would not even have thought of this play. Of course 24/20 is sound and thematic, but the second part (8/3) is unthinkable. If the race was closer I might think of burring (or �burning� as we like to say in Greece) the checker, not only for general positional reasons but for a specific reason as well. Blue's plan is to hit a checker to even the race (among other considerations). Having hit the checker, he must be able to contain it, attack it, prevent it from recirculating easily . It will be a pity if this checker escapes while White has still the upper hand in the race. Here comes the hidden flaw in this play. Blue must make soon both his 5 and 7-points and form a strong �reception committee� in case of hitting something. By burring his checker, Blue considerably weakens this plan. Still, if not 8/3 then what?
Play C (11/7,11/6) Fails to split the rear men.
Play D (11/2) Same as above.
Play E (not included) (24/20, 11/6 !) Retaining all builders in position. One might reject this move because it leaves the blot on Blue's 11 point , a blot which is hit with any ace. But lets go closer and lets go specific. With 61, the blot can be hit, but, in doing so, White increases the numbers that make Blue's anchor on the 20 point and/or a second �phantom� point ( losing more ground in the race is not very important here) . Probably White should hit regardless, but the two plays are close, there are + and - in each one. With 51, White can hit and leave indirect hits from the bar. Admittedly, hitting is much better here for White. With 41, White can hit and leave an indirect shot, but he has another good alternative, 6/5*/1*. With 31, pointing on his 5-point is much better than hitting the outfield blot and with 21, 15/14* 8/6 looks quite unattractive and something like 6/5* 3/1* is to be preferred. Finally, double aces is simply an overkill. In a controlled manual rollout of 36 games, the net equity for Blue was only -0.56 points per game. Play e is my choice.
Laila Leonhardt: 24/20, 8/3.
Blue is trailing a lot in the race but has a stronger home board than White,so the obvious strategy is to make it difficult for White to bring hischeckers home. By moving forward to the 20 point Blue is covering all thequadrants of the board and thereby making it almost impossible for White toclear without leaving direct shots. Note that Blue is not interested inmaking the 20 point next roll, but wants to keep his control.
Rob Maier: 24/20, 8/3.
When White rolls poorly, we want his outfield checkerunder the gun from more than an indirect shot. 1-2, 1-4, 1-5, 2-4, 2-6,3-5, 4-6 and 5-6 now all leave direct shots. We will usually still haveseveral shots, even if we are pointed on. If we stay back, and eitherbreak or clear the eleven point, we give White too much extra freedom,perhaps the one extra roll they need to consolidate their position.
David Montgomery: 24/20, 8/3.
Usually when your opponent has escaped you want to split toprevent him from consolidating. Here it's not so clear because splittingmay just give him a chance to attack you. Nonetheless, my guess is 24/20, 8/3.
Bill Robertie: 11/2.
Ugh. Nothing looks great here. White's game is very awkward and stacked,so I'll keep the anchor on the 24-point for now. That narrows my choicesto 11/6 11/7 or 11/2. Getting hit with an ace doesn't appear to hurt meat all (I'm a mile behind in the race and White's aces are mostly goodshots anyway) so 11/2 is my play.
Snowie: 11/7, 11/6.
When behind in the race, don't race. I've got plenty of time tobuild up my board and wait.
Kit Woolsey: 11/7, 11/6.
Blue is so far behind in the race that even if he makesan advanced anchor that won't be so good. I think he is better ofsitting on the 24 point and waiting. Plays which move a back checkerask to be attacked. My play is the best for making the needed five point.
Summary: Close. A bare majority of the panel preferred to hold theanchor, but the plurality vote went to splitting and bringing a checker insafely.
Play Votes Score24/20, 8/3 4 10011/7, 11/6 3 9011/2 3 9024/20, 11/6 1 5024/15 0 40
Problem 3
| 153 167 | White money game Blue |
Chuck Bower: B/24, 7/2
May I be on White's side for once? :) I think the 1 is forced.Playing purely (13/8) seems to give White just too many good rolls.A hit anywhere probably gives White a double next time. Come to thinkof it, White probably has a double THIS turn. 7/2 leaves the fewest shots. Taking away half of White's roll by hitting loose on the 1-point isn't worth the extra 10 shots (some of which are double hits).Another checker sent back is probably fatal. The simple, if ugly, 7/2gives Blue the best chance of survival.
Steve Clark: B/24, 13/8.
I would not play B/24, 7/2. The checker is misplaced on thedeuce point and still is an exposed blot. Hits on the ace point arevaluable when Blue is desperate or when he is trying to keep White frommaking a valuable point. This play could be right but Blue's positionwould be weaker than usual when such hit's are made because of the extrablot on the 7 point. Instead I would play 13/8 and hope for the best.
Hal Heinrich: B/24, 7/2.
I could be persuaded by B/24, 6/1*.Blue has a bad position and the task at hand is damage control. B/24,13/8 can be rejected because it gives White a double-shot with thestronger home board, and free rein to develop the position. Hitting onthe ace impairs White's board-building ability at the cost of extrashots and blots. Slotting the deuce is the safest play, but it starts adeep point and gives White lots of flexibility -- but that's how I'd tryto rescue this position.
Ron Karr: B/24 13/8.
This leaves more shots than the other options, but it leaves amore flexible distribution of checkers. If I play 7/2 or 6/1*, I haven'taccomplished much if he doesn't hit me; it'll be tough to put a winning positiontogether. After 13/8, White can hit or he can make a new point, but not both(except with doubles). So if he misses, I have a better position to work with,and if he hits, I'm no worse off than with any other of the other plays.
George Klitsas: B/24, 6/1*
Play A (b/24, 13/8) Positionally attractive, but leaves the initiative to White. There is some duplication of 6's and 4's, but that's all. A passive play that might work if Blue survives next roll, which is against the odds, though.
Play B (b/24, 7/2) Leaves only 11 hit numbers but is not at all constructive, it is even more passive than play a. A liability ( the 2-point), a stack ( the 6-point) and the stripped 8-point can hardly extend to a menacing Blue structure in the near future.
Play C (b/24, 6/1*) My choice. An aggressive play that takes off White's half roll, unstacking at the same time the 6-point (Blue is not particularly sad if this checker is eventually recirculated). Blue hopes to make soon his bar-point with a six and put some pressure on White's back checkers.
Laila Leonhardt: B/24, 6/1*.
Not a pretty play, but it is important to look ahead. White's position is verystrong, and it will be hard for Blue to take the cube with any other play.By hitting on the 1 point, it instantly makes most 6's very unattractive forWhite and gives Blue a chance to get back in the game.
Rob Maier: B/24, 13/8.
What stands out in this position is the lack of a spareon the eight point. Since we rolled a 5, we ought to put one there. NoBlue checker belongs on the deuce point, and this isn't the time to slashon the ace point. Sometimes White even misses the blot on the bar.
David Montgomery: B/24, 6/1*.
Hitting doesn't leave that many more shots, it unstacks the sixpoint, and it usually prevents White from making an offensive point.
Bill Robertie: B/24, 13/8.
After the forced Bar/24 I have three choices with the 5. 7/2looks like the weakest -- I still have to leave a blot but my checker ison the wrong point. 6/1* is the sort of wacky gonzo play we all used tomake in the 70s, thinking we were being "active". Two blots for the priceof one. 13/8 is my play. I leave the blot where it belongs and put aspare on the 8-point, unstacking in the process.
Snowie: B/24, 13/8.
I put my checkers where I want them. The bulilder onthe eight point will be important in the future. Other plays aren't safeanyway, and they are too ugly for words.
Kit Woolsey: B/24, 7/2.
This looks like a simple case of shot minimization. Bluedoes not want to have a third checker sent back now.
Summary: The concensus was purity over safety. Could easily be right.
Play Votes ScoreB/24, 13/8 5 100B/24, 7/2 3 80B/24, 6/1* 3 70
Problem 4
| 111 81 | White money game Blue |
Chuck Bower: 14/11*, 4/3
Given the weakness of White's board, Blue should have no fear. Goall out for the gammon. Hitting the checker on the 11-point NOW iscalled for. This may be the only chance to snare it. Start with 14/11*.
After that, Blue's next goal is to close the 3-point.Usually voluntarilly slotting a home board point while opponent ison the bar is a mistake--wait for him to enter (on that point) andthen hit loose. Here the combination of White's weak board, Blue'sTWO spares on the 4-point and no 5's or 6's available to help buildthe 3-point naturally combine to make the slot attractive. If thisplan fails go back to the conventional thinking. But in this case Ilike gambling with 4/3.
Steve Clark: 14/11*, 11/10.
I see 14/11*, 4/3 as 3rd choice. Slotting can be right whenyou are starting to overrun a point you need to have but that is not thecase here.
Having a 4th man back would be very valuable for the gammon. Bluestill has plenty of chances to make the 3 point. White's board iscruchola so getting hit is not too dangerous. I have talked myself in14/11*, 11/10. I might even be right.
Hal Heinrich: 14/11*, 4/3.
Blue has a commanding position, and should try for thegammon by hitting. Slotting the three point is less clear, but lookslike the percentage play. It starts a point that Blue really wants -- ina flexible, well-distributed way with an acceptable level of risk. Theproblem with not slotting the three is that Blue might overrun theposition and never make the three -- that's not a disaster, but it mightcost the gammon.
Ron Karr: 14/11* 4/3.
For pure winning chances, making the 6-prime seems best: itshould hardly matter whether there are 3 or 4 checkers back. On the other hand,hitting will increase my gammon chances. If I can hit and still close the 3point, I think gammon chances go up by 20% or more. If I hit but can't make the3 point, they're probably still at least as great as if I hadn't hit. And mylosing chances have to be negligible anyway.
So assuming I hit, could it be right to just slot the 3 point immediately? Itcertainly gains in the 23/36 times he doesn't hit back (64%), since I'm a hugefavorite to cover. If he does hit, I'll lose in some variations, but, forexample, if he rolls a 32 and makes the point, it's not going to make muchdifference. And if I don't slot and he rolls a 3, then part of the time I haveto hit loose anyway, which gives pretty much the same position. So it looks tome like slotting is worth it.
George Klitsas: 14/11*, 11/10
I would be very surprised if making or slotting the 3 point is the winning play here. I thing that by not hitting, Blue only significantly reduces his gammon equity. In a lesser extend, the same danger is present if he chooses to slot. In my opinion, slotting is not urgent here. Blue can make naturally the 3-point or choose to slot later. In most similar positions and in most backgammon positions in general one waits to slot by hitting something existent (a blot) instead of something non-existent. So, play a (14/11*, 11/10) is my choice.
Laila Leonhardt: 14/11*, 4/3.
A good solid position for Blue with nothing to lose. The gammon gains byhitting the blot are big, and the slot on the 3 point is no risk for Blue.
Rob Maier: 14/11*, 4/3.
With gammons counting, 4 checkers back must be betterthan 3. We want to avoid getting hit after we have begun bearing off.With White's weak board, we can afford to get hit now, as we still willhave strong chances to make the three point and trap 4 checkers. Once westart bearing off with an empty three point, we are more likely to gethit, and not score the gammon. Since we are increasing our gammonchances, and have extremely small losing chances, the slot seems clear.
David Montgomery: 14/11*, 11/10.
Four back will win many more gammons than three, if you cansubsequently make the 3 point. It looks worth trying for. You may beable to trap White off the 22 point even if he makes it. It seems to methat it's worth a roll to try to make the 3 point naturally. If it doesn'tcome, next turn may be the time to slot it.
Bill Robertie: 14/11*, 11/10.
Not hitting is hopeless, surrendering a lot of gammons, So14/11*, then what's the best ace? I'd play 4/3 if I were a little moreawkward, but here it looks like I'll make the point half the time nextturn anyway, and if not I can slot then. So 11/10.
Snowie: 14/11*, 4/3.
The hit is a must for the gammon. Why not slot? White can't do muchdamage, and I will need the three point. If I don't slot now, I maynever get it.
Kit Woolsey: 14/11*, 11/10.
Picking up the fourth checker is big for the gammon.Blue has plenty of time, so it doesn't seem necessary to slot the threepoint now.
Summary: Everybody agrees about hitting for the increased gammon chances. Whileslotting the three point is unusual, White's weak board may well make it correct.
Play Votes Score14/11*, 4/3 6 10014/11*, 11/10 5 906/3, 4/3 0 40
Problem 5
| 138 130 | White money game Blue |
Chuck Bower: 18/14(2), 15/7
After playing 44, Blue will have a 24 pip race lead with Whiteon roll. I see no reason to risk this now by leaving the blot andthus I start out with 15/7.
Blue should now want to break contact, but that won'tbe easy. Hitting White might prove to be the best course to gettingcheckers around. Still there must be a balance, and Blue shouldn'tmake moves which prevent him from blasting home with big doubles,should they fortuitously arrive.
13/9(2) keeps maximum pressure on White's midpoint but allowsWhite to sneak into the outfield with the spare on Blue's 5-point witheither a 5 or a 6. This spare is White's main timing asset soBlue doesn't want White to easily move it.
18/14(2) puts less pressure on White's midpoint, but Blue wouldactually like White to give up that point, anyway. In fact, if Whitedoes give up the midpoint Blue can probably double him out. MeanwhileWhite's spare on Blue's 5-point must either get an exact 7 to reach themidpoint or 10 or more to hop Blue's back checkers.
Usually with a good race lead you want to bring your back checkersforward. I see no reason to deviate from that here. 18/14(2), 15/7appears to be Blue's best chance to turn this into a race and win withthe cube.
Steve Clark: 18/14(2), 15/7.
Someone said, "When you are ahead in the race, race." This involvesescaping the back men as best you can. 18/14(2), 15/7 is as close as Ican get to the race. 18/10(2) leaves a better position except for theblot, but the improvement is not sufficient to justify the blot. Hanging back with 15/7, 13/9(2) is the wrong idea for the position.
Hal Heinrich: 18/14(2), 15/7.
This is the way to proceed in this position. White's threeand a half point board is too strong for Blue to leave a direct shot --though if I was going to leave a shot, I'd play 18/14(2), 13/9(2). Afterplaying 15/7, 18/14(2) is natural. You move the men from the back so asnot to strand them. Blue may fail in bringing the four back men home,but it's a better bet than leaving two on the eighteen. White looks tohave at least as much trouble moving checkers as Blue. Note the positionof cube -- Blue has a powerful racing lead and can expect a profitabledouble. This is a strong, additional reason to lift the blot.
Ron Karr: 15/7 13/9(2).
A good roll, putting me ahead in the race, so I want to race(see Kit's article "When in Rome"). 18/10(2) tries to reduce contact, but itleaves a shot. White's board is decent, so I don't think it's worth it, so I'mplaying 15/7 for sure. 18/14(2) moves the rearmost point, which is normallywhat you want to do, but the problem is that it leaves 2 adjacent points thatneed to be cleared, which is kind of awkward. I'll probably need 2 sets ofdoubles to clear them without leaving a shot. Failing that, I'll have to playfrom my bar point.
On the other hand, 13/9(2), while leaving my rearmost point further from home,has some advantages. For one, it keeps pressure on the blot on White's 8 point.If he rolls a 7 (or 10 or more) he'd like to play the spare off his anchor, butthen I'd be shooting at 1 or 2 blots. Also, it gives me more time waiting fordoubles. I might be able to safely play the checkers from the 9 point ifnecessary.
George Klitsas: 15/7, 13/9(2)
Play A (18/10(2)) Leaving the blot is not justified here. If not hit, Blue is the favorite but not good enough to offer a double. The blot might not find a friendly landing spot next roll. I performed a 36-game rollout and the net equity for Blue was +0.06 points per game.
Play B (18/14(2), 15/7) As usually, I performed a 36-games rollout , mainly to see what types of positions arise. The results:
*In 6 games Blue was obliged to break his board before clearing any of the 13 and 14-points.
*In 9 games Blue rolled big doubles (like 44) and was able to claim the point or offer a very strong double.
*In 3 games White moved to the outfield with 33 or 44 and played from there.
*In 10 games both opponents rolled big doubles resulting in no-contact races.
*In 3 games Blue was obliged to leave an indirect shot on the 13 or 14 point.
*In 2 games White was obliged to leave a shot first.
*In 3 games Blue took his chances by voluntarily leaving a shot.
The net equity for Blue was +0.47 points per game.
Play C (13/9(2), 15/7) In comparison with play b, Blue has more difficulties here (although the 9-point gives him additional timing for a number of rolls) but White's difficulties increase even more . White must play carefully, leaving the blot on his 8-point in most variations, in order to remake the point. Below is a report of the types of positions that arose in a sample of 36-games:
*In 14 games White was obliged to leave a shot first.
*In 10 games Blue was obliged to leave a shot first.
*In 8 games after big doubles by both sides the issue was decided in a no-contact race.
*In 3 cases Blue rolled suitable big doubles (typically 44) and claimed.
*In one game Blue took his chances by voluntarily leaving a shot.
The net equity for Blue was +0.44 points per game.
The relevant equities of plays b and c are close, the sample is small anyway, and I will give the edge to play c, mostly because of the difficulties it creates for White in his effort to put his checkers where they should go. It is just a feeling and I would not be surprised If play b, after all, was shown to be better.
Laila Leonhardt: 18/14(2), 15/7.
Blue is up in the race, so no need to complicate the position. Plain safe play.
Rob Maier: 18/14(2), 15/7.
This doesn't seem like the time to leave shots. Evenif we are missed, the position is hardly gin. White may not be able tosafely spring a back checker, forcing them to leave the midpoint. If westay back on the bar, White has an easier time of springing a checker, andwe are up 24 pips, so its time to start heading home. Blue has a fewspares to play, and may be able to get away with just leaving an indirectshot, or no shot at all. With Blue's racing lead, we may also be able touse the cube to avoid leaving a shot. Incidently, if I were going toleave the shot, I would play 18/14(2), 13/9(2), which wasn't a choice. Atthe expensive of one more shot, the nine point is easier to clear than theten, and White has to roll better to get one of his spares on the fivepoint safely out.
David Montgomery: 18/14(2), 15/7.
With this roll the position changes from a mutual holding gameto a one-sided holding game. It is usually wrong to volunteer in a holdinggame, and not safetying the blot is essentially the same thing. Save theblot.Having to clear the 14 and 13 points isn't as much of a problem as you mightthink - most of the rolls that would clear the midpoint by itself will workalmost as well to clear the two points simultaneously.
Bill Robertie: 18/14(2), 15/7.
I'm ahead in the race, so it's time to run: 18/14(2) and 15/7is safe and leaves me 24 pips ahead. Must be good. Leaving a shotdoesn't look right since it doesn't buy me a gin position when I'm missed.
Snowie: 18/14(2), 15/7.
When ahead in the race, race. I should be able tobring this one home safely. No need to complicate the issue.
Kit Woolsey: 15/7, 13/9(2).
It is not necessary to volunteer a shot. Blue hasa comfortable position anyway. By staying back on the bar point Bluemakes it difficult for White to find decent plays.
Summary: The popular choice was the simple racing play. Certainlyreasonable, although staying back does have its attractions.
Play Votes Score18/14(2), 15/7 8 10015/7, 13/9(2) 3 7018/10(2) 0 40
Problem 6
| 165 156 | White money game Blue |
Chuck Bower: B/24, 16/13.
How many blots do you want to leave? 1, 3, 4, or 6?!! Bothplayers have added exactly one point to their starting positions--the valuable 5-points. Each player has three back. After this move, Blue will (at least temporarily) have a small race lead--about 9 pips (13 raw minus 4 because it's White's roll). White has every reason to attack. Why should Blue cooperate? A checker saved is a checker earned.B/24, 16/13.
Steve Clark: B/22, 8/7*.
B/22, 8/7* must be right. With 6 blots around the board, what can gowrong? Well White could roll doubles and hit 3 or 4 of them. But herea closer examination reveals that White's doubles play better when he isnot hit (except for 4,4).
Actually I don't believe that the hit has to be right but I would playit. If Blue does not hit, White has too many ways to makeimprovements.
Hal Heinrich: B/22, 8/7*.
I don't feel strongly about this andit's hard to articulate why. I dislike leaving six blots, despiteGoulding's blot rule! I've seen several rollouts that support breakingthe eight to hit on the bar -- if there's an additional blot in theoutfield. Perhaps the way to veiw this position is as a blot-hittingcontest where you have a chance to strike first. Of the non-hittingplays, B/24, 16/13 is best because it minimizes blots and shots. If Bluehad a bigger racing lead, I'd favour tightening up and trying to bringthe position home. But as it is, I'll take my chances by slugging itout.
Ron Karr: B/22 9/8.
White is threatening to making my bar point, so B/22 8/7*attempts to prevent that. However, leaving 6 blots and giving up the useful 8point, when ahead in the race, is not a good plan. At the other extreme, B/2416/13 is "safest" in that it leaves the fewest blots and shots. But it leavesthe rear checkers too far back, with no coverage of White's outfield, as well asleaving White a good 2 to hit.
B/22 9/8 gives good communication between my checkers. It's looser, but thisseems like a good time to try for a better position, rather than waiting tilWhite has a better board and/or an anchor. If White hits me, I may be able tohit back or make the 22 point. (6/5 is a similar idea, but unnecessarilyrisky--the spare on the 8 point is valuable, without leaving an extra blot.)
George Klitsas: B/22, 9/8.
play A (b/24, 16/13) A solid passive play that leads usually to quiet games. Its main flaw is that abandons White's outfield. White can anchor or hit the blot having the upper hand in both cases.In 36 games the net equity for Blue was -0.22 points per game.
Play B (b/22, 9/8) Better than play A, since it contests the outfield by splitting the back checkers connecting for re-hitting purposes the two blots and leaving a less costing (if hit) checker , the one in White's 9-point instead of the one in Blue's 9-point. Dangerous, though, are the White rolls that hit two checkers, like 54 or 52. In 36 games the net equity for Blue was -0.12 points per game.
Play C (b/22, 8/7) Suddenly one enters in terra incognita . Because one seldom decides to hit in a similar position, If he performs a rollout (as I did) is greatly surprised by the great number of backgames that suddenly, out of the blue, emerge. Backgames that are often of marginal or suspect timing , with the cube practically useful only to White for a long period of time. Blue is not always lucky to be in a backgame -sometimes he finds himself with 3 checkers behind a strong blockage- sometimes he is not lucky enough to make any anchor. The lesson is well-known - one must not leave 6 (six) blots if there is a playable alternative. Even If White simply anchors with a quiet roll like 32, Blue can only look in despair at the scattered body of his position. In 36 games the net equity for Blue was -0.49 points per game.
Play D (b/22, 6/5) Worse than play B, in my opinion, since failing to safety the blot is more important (costly) in this position than putting a builder on the 5-point. Needless to say, my preference is for play B.
Laila Leonhardt: B/21.
A loose position with many blots and many choices. Blue should seek a way toduplicate trying to get only 1 checker hit and try for an advanced anchor.My choice is unfortunately not on the list B/21 (duplicating all 2's and4's, and trying for a 4 point anchor) My second choice must therefore beBar/22 8/7* with the same idea of only getting one blot hit next time,even though this move creates 6 blots instead.
Rob Maier: B/24, 16/13.
At least we didn't fan. Hitting looks hopeless. Let'sjust leave one blot, put a spare on the midpoint, make an anchor, and seewhat happens. When you put it that way, it doesn't even seem so bad.
David Montgomery: B/22, 9/8.
White already has an advanced anchor slotted, so Blue should comein on the 22. Blue doesn't want to be stuck back on the 24 point if Whitemakes the 18 point. 8/7* loses the 8 point and leaves too many shots andblots.6/5 is the pretty ace, but the gain doesn't seem enough to offset theadditionalrisk with no anchor and three blots on the other side of the board. 9/8 issolidand flexible enough.
Bill Robertie: B/22, 9/8.
The choices here are Bar/22 9/8 (connectivity) and Bar/2416/13 (safety). Bar/22 8/7* is bad, leaving 6 blots strung out.
Bar/24 16/13 has a bad look to it. I can see White connecting on the barpoint, then I have to get my back men moving pronto. I'll opt for Bar/229/8, taking my risk now to keep my army together.
Snowie: B/22, 9/8.
Not worth losing the eight point and leaving five blotsstrewn around in order to hit. My play splits the back checkers andgets the front blot safe and to a good place.
Kit Woolsey: B/22, 8/7*.
Leaves a lot of return shots, but Blue's board is asstrong as White's. Other plays give White an easy advanced anchor, andthey aren't safe anyway. My play has possible big gains if it works,and the risks aren't too great.
Summary: The panel decided that hitting was too risky. Probably a wisedecision.
Play Votes ScoreB/22, 9/8 5 100B/22, 8/7* 3 80B/24, 16/13 2 70B/21 1 60B/22, 6/5 0 50
Problem 7
| 159 157 | White money game Blue |
Chuck Bower: 6/5(2), 3/2(2)*.
It's early in the game. The race is close. After using halfthe roll to make the 5-point, Blue has a stronger board. Whitehas two blots and one of them can go for a ride now. 3/2(2)*gives Blue a chance to take control of the game. All indicatorspoint toward the hit. Offense wins championships.
Steve Clark: 6/5(2), 3/2(2)*
The hit interferes with White's attemptsto make progress. I would be more attracted to the alternative if thepoint to be made was more attractive than the 22 point. 6-5(2), 24-22appears to to leave White with a well balanced position. In my ownpositions I try to achieve such "balance". It is valuable to preventthis balance in your opponent's position. If you put your opponent onthe bar against a 3 point board, he is not balanced.
Hal Heinrich: 6/5(2), 3/2(2)*
This is clear. Switching and hitting cripples White'spoint-making chances and gains in the race. It also leaves Blue's mensplit which makes it easier to escape and hit blots in White's outfield.
Ron Karr: 6/5(2) 3/2(2)*.
After making the 5 point, shifting points to hit seemsright. Sure, the 2 point isn't quite as good as the 3 point, but I'm notplaying a priming game, since White already owns my bar point. And putting achecker in the air is valuable. It prevents White from making a new point, andgives me a chance to get his other blot. Having the back checkers split isactually better than having them together, giving me more numbers to hit,escape, or make a more advanced anchor.
George Klitsas: 6/5(2), 3/2(2)*
Play A (24/22, 6/5(2)) A positional play, which retains the possibility of a future prime or blockade from the 3 to the 8 point. Unfortunately, this prime/blockade is almost never formed. Blue has another task to perform, a task that is by itself very difficult to be achieved, namely to escape with his rear checkers. In about 40% of the games Blue dies anchored on the 22-point and dies with the cube. But , even if one gave him some rolls after his death (pass and continue) it would be doubtful if he could form soon a strong front position. Blue's position is cramped. His only spares are at the midpoint. Certain rolls are very awkward (like 61, 51) and most of the rest (like 42, 21, 31 etc. ) leave blots or bury checkers (like 64). It is not of much practical importance but very amusing the fact that, If White slots his 5-point, Blue cannot think of hitting from the 22-point if he rolls 21!! In the meantime Whites' rolls play themselves filling gaps, running, hitting. In a 36-game rollout Blue's equity was -0.17 points per game .
Play B (6/5(2), 3/2(2)*) This looks much better. 25% of the time White will dance and then Blue can go forward, hopefully scooping Whites' other blot on the way home. If White enters, the best thing to do with the other half of his roll is usually to lift a blot. Blue is slightly better in the race, has the stronger board in case of early hits and his drawbacks are his 2 men back in comparison with Whites' one and his slightly overextended position. Performing a 36-game rollout I found out that the commonest type of game was a bar-point holding game by White (20% of the time) , then mutual bar -point games , 5-point (Blue) bar-point (White) and so on. Blue's equity was +0.08 points per game . I am pretty sure that play b is the winner here.
Laila Leonhardt: 6/5(2), 3/2(2)*.
The 3 point is not a preferred anchor and Whites building power is big.Better to put White on the bar and take away half a roll from him(preventing him to make the bar or 5 point) and if he dances Blue will gaineven more than the very passive 24/22.
Rob Maier: 6/5(2), 3/2(2)*.
This is a good time to switch points. Keeps Whitefrom building anything, and gives us some time to escape a back checker orhit White's other blot. Now's not the time to button up.
David Montgomery: 6/5(2), 3/2(2)*.
It's good to put your opponent up against a three pointboard. Even more so when he is poised to do something constructive. Theanchor would be nice, but putting White on the roof also protects you fromattack.
Bill Robertie: 6/5(2), 3/2(2)*.
This looks like a no-brainer. 6/5(2) and then putting Whiteon the bar with 3/2*(2) must be right. The 22-point certainly isn't worthgiving White his whole roll.
Snowie: 6/5(2), 3/2(2)*.
Never give your opponent an easy roll if you canhelp it. White has too many good numbers which make a good point ifhe is left alone to play his full roll. I have the bigger board, solet's take advantage of it.
Kit Woolsey: 24/22 6/5(2).
Blue doesn't have the ammunition to carry out a blitz.The anchor could come in handy, and the gains from putting White on thebar may not be sufficient compensation for going too deep and making thetwo point.
Summary: A strong vote in favor of the shift which keeps White off-balance.The panel doesn't consider making the anchor very important in this position.
Play Votes Score6/5(2), 3/2(2)* 10 10024/22, 6/5(2) 1 50
Problem 8
| 152 115 | White money game Blue |
Chuck Bower: 7/1.
So, Kit "saved the best for last". I had to resort to the lostart of hand rollouts to find an answer here. Although it is usuallyimpossible to do enough of these to get statistically significantresults, they help a lot in giving an indication of the differentpaths a position might follow. I did 36 trials of each using sequential dice for White's initial reply roll. The cube was limitedto cashing for White (similar to using a "settlement limit" withthe robot rollouts). In all cases I went for the closeout untilthat became impossible (i.e. White anchored). Here is what I found:
11/5*
The plan with this move is to keep White from making an advanced anchorat all costs. Unfortunately the second blot (on the 1-point) is currently a liability for three reasons:
1) If hit, Blue loses half a roll.
2) By hitting, Blue starts White's 1-point. (Surprisingly, even this anchor gives Blue a lot of headaches here.)
3) If hit, a big chunk of Blue's racing lead is sacrificed.
Adding up all this downside shows that leaving two blots with a four point board is just too much to give up in an all out attempt to keepWhite from the advanced anchor.
6/5*, 6/1.
This move goes for the blitz full bore. It leaves Blue'soutfield checkers nicely placed to cover. It leaves as many home board points as 11/5* and one fewer home board blot. The downside is that it leaves White with two points to turn into high anchor, and morethan half the time White anchors it is on Blue's 6-point, which iseven better (for White) than Blue's 5-point.
7/1.
At first it looks like Blue is giving White too many chancesto anchor with this play--11/36 of the time White throws a 5. Oneinteresting result of my hand rollout was that even when White anchorshe is far from out of the woods. Blue's racing lead is so large andthe disparity in home boards so great that while White is tiptoingaround avoiding leaving shots, Blue is bringing the troops to homesoil. Blue can even sustain a hit/recirculate and still maintain a nicerace lead. With the other candidates, if White anchors it is usuallyafter Blue gets some of his race lead blasted away. And maybe equallysurprising is that Blue won as many (or more) gammons as with the all-out blitz play.
Here is my hand rollout summary:
Blue wins White wins Blue's unit cube equity simple gammon bg simple gammon (std. dev. in parentheses)7/1 8 18 1 9 0 1.056 (0.211)6/1*,6/5 9 16 0 10 1 0.806 (0.222)11/5* 7 13 0 16 0 0.472 (0.227)
Even though there are insufficient statistics, I don'tsee a good reason to try and second guess these results. 7/1 definitely"felt" like the best play during the rollouts so that is my choice.
Steve Clark: 7/1.
In general 5 point boards are stronger than 4 point boards. Imight be inclined to risk more but Blue is a little short of ammo. Most likely the blot on the 5 point will be still be available fortarget practice on Blue's next roll.
Hal Heinrich: 7/1.
This is the benchmark play against which the other two plays aremeasured. Typically, making the slotted point is the correct play -- itlocks up assets and fuels the blitz should White not anchor. Here,however, White'll be in reasonable shape after anchoring -- Blue has tocome to White and White can decide whether to hit or build a home board.Of the hitting plays, breaking the six seems better because it onlyleaves one blot -- but even that isn't clear. I don't know what's righthere, but I'd lock up the fifth point because that's usually right.
Ron Karr: 7/1.
When blitzing, if given the choice of making a new point or hittingloose, it's usually right to make the point (I've blown some matches by notfollowing this principle). I don't think this is an exception: just make thestrong 5-point board and hope he fans. It would be nice to prevent him frommaking the 5 point if he rolls a 5 next time, but it's just not realistic. Whenyou're short on ammo, you can't have everything. In this case, making the 1point is solid, no matter what happens. Then I have 22 numbers to hit next timeif he fans. And if he enters, I'm still way ahead in the race, with a 5-pointboard. On the other hand, if I hit loose with only a 4-point board, simplygetting hit back costs me a lot, and even if he doesn't hit back I have somework to do to finish the job.
By the way, if I play 7/1 and he rolls a 5, it's important to try to break fromhis anchor at the first reasonable opportunity, taking advantage of my strongboard to survive any hits, rather than hanging back and allowing the timing togo against me.
George Klitsas: 7/1.
Play A (11/5*) Trying to squelch any resistance, as in a similar play in problem 1. The similarity of play(s) a in positions 1 and 8 is far from obvious, but I think that the lack of ammunition for this plan to succeed and the difficulties created by Blue's rear checkers are present and common in both problems. In problem 8, if any Blue slot is hit (especially the one on the 5-point), Blue's game is considerably slowed down . In a sample of 36 games, Blue was able to win outright 15 gammons closing out both White blots, White saving the gammon in another and winning still another by hitting an early blot as Blue was bearing off. In 10 games White anchored on the 5-point managing to win 6 of them . The rest were mainly ace-point games ,early and late ones with various results. In this set, White was able to redouble 11 times.Blue's equity was +1.84 points per game.
Play B (7/1) This variation is the most quiet of the three. Blue's subsequent plays are relatively easy - his plan simple with two sub-variations. If White anchors, then Blue plays aggressively taking his chances while White's board is undeveloped. If White fails to anchor, then Blue repeatedly hits on his 5-point leaving the slot there ( only in some late positions he may consider lifting it, when he does not necessarily need the 5-point in order to win a gammon). A good reason for an intermediate player to adopt play b (as in problem 1). In a sample of 36 games, Blue won 16 gammons closing out White and losing one, when he was hit while bearing-off. In 17 games White anchored but Blue was able to win 12 of them. Only in 6/36 games White was able to offer a redouble, a significant point and a lesson about thinking in cube-terms. Blue's equity was +2.22 points per game.
Play C (6/5*, 6/1) In about half of the games, Blue wins an easy gammon closing out the two blots - the occasional saved gammon is theoretically canceled by the occasional loss of a triple game. When White anchors, it is almost always on the 6-point. Then Blue must struggle to bring his position home, being usually well ahead in the race. White's position is not easy to develop since he cannot slot freely - if Blue is alert he immediately takes his chances playing aggressively in the outfield . In this variation (White anchors) Blue managed to bring his position home in 10 out of 14 cases. The last variation is when White repeatedly hits Blue's slots making him adopt a kind of back/holding game. White is usually the favorite in this case. A final point : in only 7 out of 36 games the cube was used efficiently by White .In this sample of 36 games Blue's equity was +2.16 points per game.
Its more a feeling than anything else, but , all things considered, I am inclined to vote for play B.
Laila Leonhardt: 7/1.
Put yourself in White's position and you'll know the answer to this one veryquickly. A 5 point board is very strong, and if White fails to enter Blue is afavorite to hit the second blot on the 5 point with great potential ofclosing out White and winning a gammon.
Rob Maier: 7/1.
There's a lot to be said for making that fifth point, even if itis the ace point. Again, we're getting closer to the close-out. While Iwon't like Blue anchoring on the 5 point, I won't like being hit thereeither. One of the big pluses of this position, besides the high gammonrate, is my big race lead. I'd rather White anchor down 40 pips and down5 points to 1 than anchor even or down 20 and down 4 points to 1. Ialready have big close-out chances, I don't want to give up my otheradvantages for just slightly higher chances, if in fact they are higher.The 5/9 of the time I get hit would seem to take a big chunk out of myclose-out percentage.
David Montgomery: 11/5*.
Usually you should prefer the point to hitting loose, but hereWhite'sanchoring fives look so strong that I am going to hit. Blue should have afairly easy game if White anchors on the one point, but when White anchorson the twenty Blue will have a lot of problems, and win far fewer gammons.
Bill Robertie: 6/5*, 6/1.
Same principle as problem 1. If I play 7/1 and White rolls a5, I'm in big trouble. So I hit with 6/5*, and then 6/1 gives fewestreturns.
Snowie: 6/5*, 6/1.
It's a blitz, so all inner board points count almostequally. Letting White anchor would be a disaster. Hit him whilehe is down, and don't let him get up.
Kit Woolsey: 6/5*, 6/1.
Blue just can't afford to let White anchor. This shiftingplay minimizes White's good rolls, and gives Blue plenty of chancesto complete the fifth inner board point.
Summary: A bird in the hand is worth two in the bush, say the majorityof the panel. Thematic, but I'd sure hate to see White anchor on my five point.
Play Votes Score7/1 7 1006/5*, 5/1 3 7011/5* 1 50
Vote Summary
1 2 3 4 5 6 7 8Chuck Bower 8/2, 6/2 24/20, 8/3 B/24, 7/2 14/11*, 4/3 18/14(2), 15/7 B/24, 16/13 6/5(2), 3/2(2)* 7/1Steve Clark 8/2, 6/2 11/7, 11/6 B/24, 13/8 14/11*, 11/10 18/14(2), 15/7 B/22, 8/7* 6/5(2), 3/2(2)* 7/1Hal Heinrich 8/2, 6/2 11/2 B/24, 7/2 14/11*, 4/3 18/14(2), 15/7 B/22, 8/7* 6/5(2), 3/2(2)* 7/1 Ron Karr 8/2, 6/2 11/2 B/24, 13/8 14/11*, 4/3 15/7, 13/9(2) B/22, 9/8 6/5(2), 3/2(2)* 7/1George Klitsas 8/2, 6/2 24/20, 11/6 B/24, 6/1* 14/11*, 11/10 15/7, 13/9(2) B/22, 9/8 6/5(2), 3/2(2)* 7/1Laila Leonhardt 8/2, 6/2 24/20, 8/3 B/24, 6/1* 14/11*, 4/3 18/14(2), 15/7 B/21 6/5(2), 3/2(2)* 7/1Rob Maier 8/2, 6/2 24/20, 8/3 B/24, 13/8 14/11*, 4/3 18/14(2), 15/7 B/24, 16/13 6/5(2), 3/2(2)* 7/1David Montgomery8/2, 6/2 24/20, 8/3 B/24, 6/1* 14/11*, 11/10 18/14(2), 15/7 B/22, 9/8 6/5(2), 3/2(2)* 11/5*Bill Robertie 21/15, 5/1* 11/2 B/24, 13/8 14/11*, 11/10 18/14(2), 15/7 B/22, 9/8 6/5(2), 3/2(2)* 6/5*, 6/1Snowie 21/15, 5/1* 11/7, 11/6 B/24, 13/8 14/11*, 4/3 18/14(2), 15/7 B/22, 9/8 6/5(2), 3/2(2)* 6/5*, 6/1Kit Woolsey 21/15, 5/1* 11/7, 11/6 B/24, 7/2 14/11*, 11/10 15/7, 13/9(2) B/22, 8/7* 24/22, 6/5(2) 6/5*, 6/1
