100
money game
Blue
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Problem 1
| 81 100 | White money game Blue |
Chuck Bower: 6/1, 6/3.
White's board is just too good to voluntarily give him direct shots.16/13, 5/1 is only four shots, but leaves a homeboard that may be hard torebuild. 6/1, 6/3 leaves ZERO shots this turn, and a board that can be cleaned up more easily than 16/13, 6/1. With cube access, one hit/fanmay be enough to give Blue a cash, even with a less-than-perfect home board.Don't give White an easy escape route. 6/1, 6/3 is my choice.
Malcolm Davis: 16/8
Reject breaking my board, therefore must choose between leaving two blots versus one(same number of shots) and duplicating 1's. Although I am not a proponent of duplication pre say, I do not deny that it sometimes is appropriate, and on the 4 extra indirect shots, I am assured of return shots, which very well could produce a gammon. Owning the cube, I would more seriously consider breaking my board to avoid leaving any shots at all, but must opt for keeping in intact and playing with 2 blots.
Ray Fogerlund: 16/11, 16/13.
I don't know, mannnnnnnn! Maybe it is right to play 16/13, 6/1hoping to hit and cover later or something. Bah, humbug. I like deterrent value, I like to provoke my opponent. I like to threaten him, and challenge him to roll a good number. I want him to worry about throwing a bad one, so maybe next game he won't be so fast to double me because it seemed sooo dangerous bringing this one home... 16/11, 16/13 does most of these things. It leaves him with 8 bad numbers that I can use to redouble him ! That's considerable compensation for the 11 numbers that he will enjoy playing, and the other 4 hits that he won't mind playing. What the heck? Sometimes they miss a shot, and if not... I was losing this game anyway, wasn't I? I'd really hate to hit a shot and still lose this game, so I am not going to compromise my board. Snowie usually doesn't either (see below to find out!) No weenie moves for me, but I do want to cut down White's "effective" shots, as much as possible.
Hal Heinrich: 16/11, 16/13.
If White had a closed board, I'd be inclined to play safe bybreaking the six point. But in this position, being hit isn't always fatal, so paying now and keeping a killer board is right.Note that White can often hold the eighteen point for anotherroll, so even if Blue plays safe now, that may not be an optionnext turn.
Ron Karr: 16/11, 16/13.
Leaving a direct shot against a 5-point board isn'tappealing, but I think wrecking the board is worse. I'm behind in therace anyway, and even hitting a shot won't guarantee winning if myboard is destroyed. This way, if I'm hit (except with 41), I'll have afew chances to come in & hit something; and if not hit, I'll have muchbetter flexibility for maintaining my position for a couple of rollswhile waiting for my well-deserved shot. :-). And if I hit it, keepingthe board means I can win immediately with the cube.
Assuming I'm leaving a shot, this play leaves no more shots than thealternatives, only 1 blot, is flexible, and blocks 66 and 33.
George Klitsas: 16/11, 16/13.
One should reject 16/8, for it leaves two vulnerable blots instead of one (thus increasing the gammon danger), with no adequate (visible) compensation. Another play, 13/5, leaves more shots than 16/11 16/13 , with no easy follow-up. The super safe play (6/1 6/3) is very bad in race terms and loses the six point, giving White a chance to reenter after being hit (along with the ace point in most variations). We are left with 16/11 16/13 and 16/13 6/1. My choice is 16/11 16/13. Blue, if not hit, has an easy follow-up. He can save his checker on the eleven point, or use it in making a point with rolls like 3-1, 4-2, 5-3, retaining in all cases his racing chances and his board intact. If White is unlucky enough to roll one of his awkward rolls immediately (6-5, 6-3, 6-2, 6-1) one can count practically these games as wins for Blue. In a sample of 36 games Blue won 21 simple and 1 gammon, White 10 simple and 4 gammons [equity=+0.28 ppg for Blue on a two-cube]. The other candidate (16/13 6/1) is not as good.Blue is severely damaging both his race chances and his inner board. If White rolls one of his seven awkward rolls that contain a six, he hits mainly from the mid (compare it to the suggested play) and even in that case, White is far from lost. Blue looks like an underdog after 16/13 6/1. In a sample of 36 games, Blue won 16, White 19 simple and 1 gammon. Breaking one's own board is seldom correct and I think it's definitely wrong here.
Laila Leonhardt: 16/11, 16/13.
White is forced to leave the barpoint on 10 6's next roll, so breaking anyof the board points would severely weaken Blues chance for winning, even ifhe hits White.The 2 remaining options are then 16/11, 16/13 and 16/8both leaving White 15 hitting numbers, but even when hit Blue will mostlyhave a return shots from the bar and a chance for gammoning White. I prefer16/11, 16/13 because it generates less gammon losses because White cannotpick up 2 checkers and still keeps a strong board and many hitting numbersif White is forced to leave with a 6.
Rob Maier: 16/11, 16/13.
Breaking the board doesn't seem to be the right idea. To many sure winsevaporate with the six point slotted instead of made. The race is alsofar from hopeless, another reason to avoid sewering checkers. Althoughthe blot gets hit 15 times, 7 of those rolls leave a direct shot and twoextra gammon producing blots. Even if White can lift the blot, Blue willstill have jokers this roll and next, and they will all *at least* win.
David Montgomery: 16/11, 16/13.
Good players hate to break their boards. With a strong boardand contact you can always win. Without a strong board, a position is less safe than it looks because the opponent can take more chances. 16/11 16/13 beats 13/5 because it leaves fewer shots and puts more pressure on the 18 point, now and in the future. It beats 16/8 becauseit only leaves one blot.
Snowie: 16/11, 16/13.
I'm not breaking up my board now -- that would make things too difficultin the future. As long as I'm willing to pay now I'll make the play whichwill give me the strongest position if the shot is missed. Let's see howhe is going to play some of his sixes after my play.
Kit Woolsey: 16/11, 16/13.
Since I am behind in the race, I don't think I can afford to break up myboard. I need to be ready when White makes his run for it. If I survivethis shot, my future plays will be comfortable.
Chris Yep: 16/11, 16/13.
Leaving two blots (16/8) is too risky with White's 5 point board (if White misses both blots he will stay on the anchor until forced off). In addition, after 16/8 many of Blue's next rolls are awkward. 16/13 6/1 gives White a chance to make a "run for it" while Blue has two inner board blots (White should run a back checker even if he rolls a 7 or 8). 6/1 6/3 might be a little better for Blue, but it still breaks down his board and leaves his next roll awkward.
16/11 16/13 and 13/5 leave only one blot and don't break up Blue's board. I prefer 16/11 16/13 to 13/5 because the blot is harder to hit (15 shots, instead of 17) and easier to safety next turn. In addition, if White is forced to run with a 6 next turn, Blue will have a double shot at White's remaining back checker. Furthermore, Blue keeps maximum contact on White (a point 6 away instead of a point 9 away), which he will be able to hold longer. In most cases, White will have to leave the barpoint before Blue has to leave the midpoint. When this happens, Blue will be 6 away, an optimum distance for hitting.
Summary: In this day and age of paying later, the panel took the sensibleview that it was necessary to prepare for the future and pay now. It is justtoo difficult to win otherwise.
Play Votes Score16/11, 16/13 10 10016/8 1 606/1, 6/3 1 6016/13, 6/1 0 4013/5 0 40
Problem 2
| 144 151 | White money game Blue |
Chuck Bower: 8/4*, 4/1*.
Magriel's "safe play vs. bold play" calls for BOLD: Blue has a betterboard, an anchor, and a race deficit. White has no anchor. 8/4* isthe start, but what is the followup? Continuing to the acepointleaves fewer shots, a blot that is in a less desirable point (for Whiteto make) and takes away all of White's roll, not just half of it. Lastly,a fan by White is much more ominous. "When in doubt, (double) hit."
Malcolm Davis: 8/4*, 4/1*.
Just can't resist hitting 2 men. If ahead in the race, would play 13/6. Usually don'tlike breaking the 8-point to hit, but elect to try it one more time. Seems like I win 9 games(9 fan numbers) right away.
Ray Fogerlund: 13/10, 8/4*
Pound and unstack. The double hit leaves meover-extended, and I want to fight for the best point. I have the security of the anchor in the event I get hit and roll the dreaded (2,6) from the bar. Don't worry, be lucky. Hit White off the 4 point and allow her to throw one of her 17 nauseating rolls. If she doesn't, then deal with it by playing like you have the better position/board/game. Slap her around and show her who is the boss!
Hal Heinrich: 8/4*, 4/1*.
It's thematic to put two of your opponents men up on the roof,and this is no exception. You have the stronger board, gettinghit back is no big deal, and the alternative merely brings abuilder into play -- QED.
Ron Karr: 13/10, 8/4*.
I'm slightly behind in the race, have a better board,and White has no anchor, so I'm hitting. Then, hitting again seems toomuch, since I'm not in position yet to go for a closeout. My goal isto make the 4 point, so I want the maximum coverage ammunition in placefor it. I could get hit twice, but even then I should be able tosurvive, because White's position is mediocre.
George klitsas: 13/10, 8/4*.
I like the pure play here (13/10 8/4*). It would be just bad (not exactly a catastrophe, though, since White's inner board is quite undeveloped and ugly - difficult to make progress) if White came back with something like a 4-6, but Blue, having spun the cube must undertake some immediate risks in order to make the crucial four point, reducing White's future recubes (a quiet play like 13/6 would permit White to make Blue's four point with an increased number of potential recubes). Another play, (8/4* 8/5), with a similar plan is not as effective - leads to a safer but unproductive position with dramatically fewer potential covers or rehits and no presence in the outfield (one could say that Blue's position is divided in three parts in that case). The last candidate (8/4*/1*) goes for the throat with only one hand (two are needed in that case and the second one is not close enough!) - Blue just lacks the ammo for the blitz. I vote for 13/10 8/4* and I think that 13/6 is a close second, if one noticesWhite's difficulty to play four's and two's (with the cube in the middle it would be a tough choice between these two plays, I think).
Laila Leonhardt: 8/4*, 4/1. Rob Maier: 13/10, 8/4*. David Montgomery: 13/10, 8/4*. Snowie: 13/10, 8/4*. Kit Woolsey: 13/10, 8/4*. Chris Yep: 13/10, 8/4*. Summary: The panel recognized that the bold hitting play is clearly calledfor here, despite the loss of the eight point. The concensus was that thedouble-hit is a bit over-extended. Problem 3 Chuck Bower: B/23, 8/4, 6/4. Malcolm Davis: B/23, 8/4, 6/4. Ray Fogerlund: Bar/23, 13/11(2), 6/4. Hal Heinrich: B/23, 13/11(2), 6/4. Ron Karr: B/23, 8/4, 6/4. George Klitsas: B/23, 8/4, 6/4. Laila Leonhardt: B/23, 8/4, 6/4. Rob Maier: B/23, 8/4, 6/4. David Montgomery: B/23, 8/4, 6/4. Snowie: B/23, 8/4, 6/4. Kit Woolsey: B/23, 8/4, 6/4. Chris Yep: B/23, 8/4, 6/4. Summary: It was clear to the panel that building the strong innerboard had priority over the flimsy outer board blocking point. Also therewas no need to move up the back checker into the jaws of death. Problem 4 Chuck Bower: 23/13(2). Malcolm Davis: 23/13(2). Ray Fogerlund: 23/18, 8/3(2), 7/2*. Hal Heinrich: 23/18(3), 7/2*. Ron Karr: 23/18, 8/3(2), 7/2*. George Klitsas: 23/13(2). Laila Leonhardt: 23/13, 23/18(2). Rob Maier: 23/18, 8/3(2), 7/2*. David Montgomery: 23/18(3), 7/2*. Snowie: 23/13(2). Kit Woolsey: 23/18(3), 7/2*. Chris Yep: 23/13, 23/18(2) Summary: In a difficult choice, re-establishing the bar point won outover the hitting plays. I can see the arguments for this, but it sure doesn'tfeel right to let White get away in one roll. Problem 5 Chuck Bower: 8/2, 6/3. Malcolm Davis: 13/4. Ray Fogerlund: 13/7, 13/10. Hal Heinrich: 7/1, 7/4. Ron Karr: 8/2, 6/3. George Klitsas: 7/1, 7/4. Laila Leonhardt: 22/13. Rob Maier: 22/13. David Montgomery: 13/7, 13/10. Snowie: 7/1, 7/4. Kit Woolsey: 7/1, 7/4. Chris Yep: 7/1, 7/4. Summary: Back on track, the panel voted to pay later. Looks like a smartmove, since the pay now plays don't necessarily work even if they survivethe first shot. Problem 6 Chuck Bower: 18/14(2). Malcolm Davis: 18/14(2). Ray Fogerlulnd: 8/4(2). Hal Heinrich: 8/4(2). Ron Karr: 13/9, 13/11(2). George Klitsas: 8/4, 6/4, 3/1*. Laila Leonhardt: 18/14(2). Rob Maier: 18/16(2), 13/9. David Montgomery: 8/4, 6/4, 3/1*. Snowie: 8/4(2). Kit Woolsey: 8/4, 6/4, 3/1*. Chris Yep: 8/4(2). Summary: The panel vote was clearly in favor of plugging the gap inthe inner board over working in the outfield. Looks right to me. Problem 7 Chuck Bower: 24/21, 13/8. Malcolm Davis: 23/15. Ray Fogerlund: 23/15. Hal Heinrich: 23/15. Ron Karr: 23/15. George Klitsas: 24/21, 13/8. Laila Leonhardt: 13/5. Rob Maier: 13/5. David Montgomery: 13/5. Snowie: 8/3*, 8/5. Kit Woolsey: 24/21, 13/8. Chris Yep: 24/21, 13/8. Summary: The panel's vote was clearly against disturbing the blockade in favor ofthe loose hit. Howver our knowledgable bot thought otherwise. Who knows. Problem 8 Chuck Bower: 24/22, 8/3. Malcolm Davis: 8/1*. Ray Fogerlund: 8/1*. Hal Heinrich: 24/22, 13/8. Ron Karr: 24/22, 9/4. George Klitsas: 24/22, 13/8. Laila Leonhardt: 9/4, 8/6. Rob Maier: 13/6. David Montgomery: 8/1*. Snowie: 13/8, 13/11. Kit Woolsey: 13/8, 13/11. Chris Yep: 24/22, 13/8. Summary: Split, build, hit? There wasn't much of a concensus on thisproblem. Very difficult.
White's homeboard is not threatening, and it is important for Blue to preventWhite from making an advanced anchor.with Blue's 3 point board, and an anchor on the 21 point to fall back on,going for a blitz
Hitting is clear. The double hit seems tough to capitalize on, there isvery little wood in the shed. 13/10 is more covers for the four point,and more chances to win the battle for the four point if the initialattempt is thwarted.
With a bigger board, an anchor, and two vulnerable blots, abigger play than 13/6 is called for. Hitting two is reasonable.But Blue very much wants to get the checkers on the midpointinto the action, and this is a perfect time to do so. After8/4* 13/10 Blue will get hit more often, but when missed Blue willbe more likely to cover and doing so will make a better point.I think it's worth it.
I have the stronger board, I have the anchor, I am behind in the race. Coulda position scream louder for a bold play? Let's go for the gusto.
With my strong board and anchor to back me up, I think the loose hit isworth the risks involved, even though I am breaking the eight point. The gains if my play works are huge, and if I let White get the anchor he isright back in the game.
Compare this problem to Problem 2 from the December 1999 quiz (see my solution in the January 2000 GOL issue at http://www.gammonline.com/members/Jan00/solutions/index.html. For all the reasons that I liked going after the 5 point in December I like going after the 4 point here. In fact the differences between this position and the December position seem to argue more toward going after the 4 point: as opposed to the December position, Blue is behind in the race and White does not have an anchor. White does have a 2 point board, but it is a weak 2 point board with the 2 point made behind Blue's anchor. Thus, 13/6 is too passive. On the other hand, 8/4* 4/1* is too much. After hitting on the ace point, Blue won't have any direct covers and his remaining men are at the moment too far away to carry out an effective blitz. I prefer 13/10 8/4* over the more passive 8/4* 8/5. Blue gives White a few more shots (2-6 hits on the 8 point; 4-4 and 4-6 double-hit instead of single-hit), but this is more than compensated for by the extra builder for the 4 point which can be used to cover if White misses or continue the attack if White should hit back from the bar. In addition it leaves the 8 point slotted, which is itself an important point to make. Play Votes Score13/10, 8/4* 8 1008/4*, 4/1* 4 708/4*, 8/5 0 5013/6 0 40
141
171
White
money game
Blue
This is a nice roll, but is far from giving Blue the upper hand. Blueis forced to leave three blots, and volunteering a fourth (with the slotof the 4-point) doesn't look prudent. Likewise starting the point Whitemost wants to make, White's 4-point, does not seem smart with no anchor(bad defense) and a weak board (bad offense). So I think it's down toeither 8/4, 6/4 or 13/11(2), 8/6.
Given that blot hitting is probable, I think improving the home board,even though it is behind White's back checkers, is the better tactic.If Blue had an anchor then 13/11(2) would have more going for it. Butif Blue is going to be on the rail struggling for survival, White won't have so much trouble pulling up anchor, and the 11-point won't carry it's usual weight. I like B/23, 8/4, 6/4.
Looks as if I am going to need my 4-point right away, and don't wish toget hit or pointed-on on my opponent's 4-point (my 21 point). It is tempting to make the11-point, as I am way behind in the race, but will stick with my original play.
Enter, make a blocking point and startthe best point. It used to be that I would make the inner board point, but Snowie has taught me to block the point 6 away from the opponent's anchor. I will be able to complete the 4 point in the future. Also, I do not want to step up to the 21 point and diversify White's hitting numbers. If she wants to come after me on her ace and deuce points, fine, but I would like to stay as far out of harm's way as I can for now.
Blue's best game plan here is to attack the men on White'stwenty point when they attempt to run home. Making the elevenpoint and starting the four point is the best way to implementthis plan. Trying for the twenty-one point is too ambitiousconsidering White's advantage in board strength combined withthe advanced anchor.
I'm not stepping up to the 21 point. White has lotsof ammunition, so I'd rather stay relatively out of harm's way and tryto improve my position before being provocative. Making the 4 pointseems like the best use of my checkers and the best way to threaten. The 11 point is nice, but I don't think it'll provide much help ifWhite gets an attack going.
I don't like striping the midpoint here (though it's relatively close) in order to make the eleven point. Making the four point with B/23 8/4 6/4 looks best, retaining a good balance of builders and strengthening the inner board which could come in handy if some hitting occurs.
Blue wants to avoid having 2 checkers hit next time. With the blot on the 14point, he doesn't want to step up to 21 point yet, but by creating a pointin his homeboard he makes it less attractive for White to leave too manyblots, and less likely White is tempted to abandon his goldenpoint anchor.
With a possible bloody battle looming, it seems reasonable to work on theboard rather than a nebulous outside prime. As for the last two, weshould be in no hurry to move up to an attractive attacking point,especially as we are behind in the race, and can use the last two toresupply the six point.
Blue shouldn't come to the 21 point. Doing so just provokesan overwhelming attack by White. Blue should prefer the 4 pointto the 11 point. Blocking White isn't a reasonable plan. Whiteis in no hurry to leave the 20 point, and Blue will have difficultyadding even a fourth blocking point. A weak blockade without a board to back it up is just weak. The four point, on the otherhand, will be valuable the rest of the game, and make any blockadeBlue holds more effective. Finally, the fourth deuce playswell after making the four point.
Backgammon is a game of inner board points. I need to get something I canfight with. Making the 11 point just strips my position.
No rush to advance to the 21 point since I am already way behind in therace. I need to build my inner board fast so I can take advantage of anyblots I happen to hit.
White has an advanced anchor and a strong 3 point board backed up by the 8 and 9 points. Blue has 3 blots, no anchor, and no progress on his side of the board. There's a cliche' that sometimes the best defense is a good offense. I think it applies here -- Blue must make the 4 point. The 11 point is a good offensive point to make, but what Blue really needs are inner board points. If Blue doesn't make the 4 point, White will have considerably stronger attacking chances. Between b/21 6/4(2) and b/23 8/4 6/4, b/23 8/4 6/4 is better. It leaves a better distribution of builders on Blue's side of the board and stays farther back from White's attackers. Play Votes ScoreB/23, 8/4, 6/4 10 100B/23, 13/11(2), 6/4 2 60B/21, 6/4(2) 0 40B/21, 13/11(2) 0 40B/23, 13/11(2), 8/6 0 40
124
168
White
money game
Blue
Another good roll. Is Kit feeling sorry for us because of all our lousyluck in the online match? :) Large rolls are good for racing and badfor timing. With this 55, I think a minimum of two checkers need tocatapult off the 23-point. So start with 23/18(2).
With Blue's current distribution, containing (priming) White'sback checker is going to be easier than closing it out, so I don't like8/3(2) here. With that decision, 7/2* is also unattractive for similarreasons.
We're down to 18/13(2) or 23/13. Both leave a 6 to close the barpoint(making the efficient 5-prime) and both leave two blots, vulnerable to5's and 1's respectively. I don't think I can logically choose betweenthe two, but holding the 5- and 13-points looks better balanced (froma coverage and playability standpoint) than holding the 5- and 7-points,which seem to duplicate coverage and restrict future safe movement. So I'm settling on remaking the midpoint, a potential long term asset. 23/13(2).
Seems right. If I get away with it (no hit), I am in pretty good shape, and if Ido get hit, I will just have to try to retaliate - I will at least have some outfield control.
This play maintains all of my options aswell as being the most direct and to the point. Make the best board and hit. Start to escape, and I am ready for any eventuality. Either White enters and hits, or she doesn't, and I don't really care which. The game will be comfortable for me to play, either way, and my two anchors are the perfect insurance policy against the dangerous nature of purely-played backgammon.
Making the three point and slashing on the two is thematic andtempting. It is wrong here because it leaves Blue's two armiestoo widely separated. After that play, Blue will be rooting tomove those men on the twenty-three point -- it is better to doit now while we have the roll to do it with. After jumping threemen out to the eighteen point, it's tempting to go to the midand aim at locking up the game by making the seven point. Thatgives White too much mileage with a five -- it hits and escapes.Better to attack by hitting in the deuce point. Note the rootnumbers this play sets up: 5-1, 5-3, and to a lesser extent 6-2.
This play builds on my strength: better boardand anchors. 23/13(2) is a more balanced play, and gives me a chanceto make the 5-prime, but White has a direct shot and then I still haveto cover, and after all that I'm still not gin. So I think theattacking play is best. Getting hit back is not a tragedy, and ifWhite fans for a while I should be able to gradually advance the backcheckers. White will also have some awkward numbers that force him toexpose more blots.
Remaking the midpoint with 23/13(2) is a golden opportunity that Blue should not pass up, as it offers him at the same time a direct road to victory (make his bar point if White does not roll a five and complete a five point prime in front of White's back checker). Other plays are not attractive. For starters, 23/13 23/18(2) with a similar idea is definitely inferior, as Blue will have difficulties disengaging from those anchors (the combination of holding one's opponent's bar point along with his five point for some reason is almost always bad). Another play, 23/18 8/3(2) 7/2* divides Blue's army in two, almost always bad in itself, too. Still, worst of all seems 23/18(3) 7/2*.
Making the 18 point makes it difficult for White to clear his 2 midpointcheckers. Blue leaves White 20 hitting numbers, and the 16 non hittingnumbers could easily turn the game around to Blue becoming the favorite.If hit, Blue still has a lot of contact and return hits and with White's 3point board only, this is a good time to take the chance to make a solid 5point prime in front of White's back checker.
The best of both worlds. We have the opportunity to make a strong fivepoint board and prime, and still have both anchors as a security blanket,and to pick off additional enemy checkers. Even if White hits on thetwo point next roll, he could still be forced to leave additional blots ifhe fails to exit immediately.
23/3 is too loose and too likely to force the backgame. 23/8 7/2*is a bit better but the forward chances aren't good enough withouta direct way to quickly get a solid five prime. 23/18 8/3(2) 7/2*is better still, but Blue just doesn't have enough offensive firepower to try this. Thus, Blue has to play two fives 23/18(2).
23/13(2) is possible, taking aim at the five prime. But if Whitehits Blue's defensive position is much weaker than if he owned the18 point. 23/18(2) 23/13 grabs the 18 point and threatens to makethe five prime, but leaves two blots and a double shot.23/18(3) 7/2* gives decent forward equity with little immediaterisk, and a strong defensive position if White hits or escapes.
I don't have enough ammunition up front to go with the offense. I badlyneed a presense in the outfield, and this is the way to get it. If Whitedoesn't hit I will have a good chance to make my bar point and get somethingout of this difficult position.
I'm not going to have a better opportunity to get those checkers off the23 point. The loose hit prevents White from escaping in one roll.
7/2* doesn't seem right with Blue's 5 back men so far away. A better approach is to try to prime White. If Blue can make the bar point, White will need a 1 and then a 6 to escape. Moving at least one checker to the midpoint seems right. I prefer the double-anchor play (23/13 23/18(2)) over remaking the midpoint. The 18-anchor puts a lot of pressure on White's midpoint, while the two anchors in tandem put some pressure on White's 10 point. In addition, the blot on the midpoint is mitigated by two factors. First if White hits it he has to break his own midpoint, usually leaving Blue a fair number of return shots from the bar. Second, if Blue rolls a 6 he will want to leave the midpoint anyway, assuming that White is still behind his prime. Play Votes Score23/13(2) 4 10023/18, 8/3(2), 7/2* 3 9023/18(3), 7/2* 3 9023/13, 23/18(2) 2 80
121
132
White
money game
Blue
What's going on here? Blue is somewhat behind in the race, has a worseanchor than White, and presently has a worse board. BUT, he owns the cube,has no checkers out of play, and has better outfield control. I wishall my takes ended up here!
Running off the anchor in this kind of situation is unlikely to succeed,even though it leaves a prettier distribution. With good rolls, White points on Blue's head. With less than that he just waits to take advantageof his race lead.
Taking one or two checkers off the midpoint gives White shots and outfieldcontrol. It also results in little immediate pressure with blots insideBlue's home board, and outside. Can we find something better? I think so.8/2, 6/3 secures the third home board point and leaves only one blot, whichwill lead to lots of return shots if hit. The bad part here is 6/3, but ifthis decision were easy it wouldn't be in the quiz. 7/4, 7/1 is harder toclean up, gives White the green light to run loosely, and is likely to endup in a less effective position, anyway. I vote for strengthening the board and keeping control in all quadrants: 8/2, 6/3.
Don't want to run off my anchor when I am behind in the race, and can't find a moredesirable alternative.
I must keep the anchor or else I will allow Whiteto choose her best game plan. I don't really want to get hit, but 7/3, 7/4 seems a bit gratuitous. So, I will just bring the builders down and go to work on building my inner points next turn. Hopefully White will have trouble breaking contact to run, or later when she is bearing in. By then my house will be ready for company.
Blue is again playing against White's anchor on the twenty point.This means building up a board while maintaining an outfieldpresense. Leaving a blot only gives White a chance to run withtempo. Breaking the seven point now, maximizes the points thatBlue can make on the next roll. It's true that this allows Whiteto run a man with a seven, but Blue doesn't have a better play.Note that running a back man to the midpoint is wrong because itaims at a slighty inferior race at the cost of giving White greatattacking chances.
I'm not leaving the anchor: White has too many attackersin place; and the 3-point game should be OK, particularly since Whitemay never make his 5 point. The safe play 7/1 7/4 is too messy andmakes it easy for White to run, which he wants to do. 8/2 6/3 has theadvantage of keeping the midpoint and making an extra home board point. It'll be very risky for White to hit and leave possibly 3 blots. Andif he just moves his checker on the midpoint, once again I'll haveoutfield control.
I don't care, here, for any play that leaves a voluntary shot. Being hit is very bad and the gain from not being hit is minimal. So, we are left with 22/13 (play a) and 7/1 7/4 (play b). I believe that with the cube in the middle, available to both rivals, these two plays are about equal. The fact that Blue owns the cube is crucial, though. Keeping the anchor (play b) permits Blue to play till the end, avoiding a number of gammons. Play a, instead, is very dangerous for Blue in gammon terms. With the cube in the middle, if Blue adopts play a and things go bad for him (for example White points on him or hits loose and Blue dances) all he loses is one point (White doubles having lost his market [by far sometimes] and Blue passes). With Blue owning the cube, if things go bad for him, he could be easily get gammoned and lose four points instead. I believe that this fact is catalytic and tips heavily the balance in favor of play b. A wonderful problem and a lesson for all of us to think always in cube terms.
The race is almost even, and making a run for it before White brings downyet another builder from the midpoint seems to be best option. Any otherplay doesn't solve any problems, or strengthen Blues position. Also, White's5 point is still open, and even if White should make his 3 point, Blueshould have some rolls to make his escape from Whites board and get fulloutfield control. This will make it very hard for White to bring his backcheckers home.
Giving up the anchor is tough to swallow, but there are no reasonablealternatives, and the race is fairly close.
Running is unattractive--Blue trails in the race and White isprepared to pounce. 7/1 7/4 is reasonable, but it leaves Blue'sboard a mess, and Blue will be have to crack another point with the next six. 13/7 13/10 gives White an immediate shot, but if Blue gets away with it he will be able to hold hisposition for a while and build up his board more more smoothly.
Why not? Getting hit in a mutual holding game when the race is close isvery costly. These are inner board points I will need, so why not slot themnow. The bar point isn't of much value.
This is not the time to leave any shots, particularly since I don't gainmuch if the shot is missed. The race is fairly close and I have my advancedanchor, so I'll just prepare to build up my board and play the mutual\holding game. The blots I leave now will soon become points.
22/13 seems like an invitation for White to attack -- White has a stronger board and advanced anchor while Blue has a blot on his 2 point. 8/2 6/3 effectively puts a checker out of play and leaves Blue with an awkward position. I think Blue should just play safe with 7/1 7/4. The three blots don't hurt Blue much -- White won't be leaving a single blot on Blue's 5 point anytime soon (except maybe if he rolls a 7). In the meantime, Blue can build up a board behind White's anchor. It looks like the right approach for Blue to let White come to him -- White is slightly ahead in the race and Blue controls the outfield. Furthermore, because of Blue's outfield presence, White will usually be frozen to his anchor. With the 2 and 4 points made and the 20-anchor not moving, White will only have 9 checkers to use to make the 5 point, so there's a good chance that he won't be able to make it, causing White some awkwardness in the waiting game that will develop. Play Votes Score7/1, 7/4 5 10013/7, 13/10 2 708/2, 6/3 2 7022/13 2 7013/4 1 6013/7, 6/3 0 40
131
122
White
money game
Blue
With a nice race lead and a chance to reduce contact, 18/14(2) looks right.A couple months back in a similar situation the vote was for staying back and maximizing gammon chances. But here White's position is comparable instrength, so the standard observation that a race lead is accompanied by atiming disadvantage seems to take precedence. Making the 4-point or tryingto keep pressure on White with 18/16(2), 13/9 looks like greed waiting fora chance to backfire. I like the simple, yet effective 18/14(2).
Am ahead in the race - Just want to get home. No other play looks feasible.
Probably too simple to be the majority pick. Butsimple and solid is a good way to play. Believe me, I have learned that the clever plays usually aren't so clever. The bar point is a threat to White's stripped position, so I would like to keep that and perhaps vacate it with a better double later if possible. Just make the best point available, with no shots and await developments. React to whatever White does. Let's see her get home without leaving a few shots.
Blue is up in the race which means that the timing of being onthe eighteen point is against Blue. So any play that gets off theeighteen needs to be looked at. Blue's home board is kind of cheesyand making the four point goes a long way to resolving that issue.On balance, the merits of making the four point outweight those ofgetting off the eighteen. Any future contact will reward making astronger home board -- and here that seems quite likely as Whitehas three stripped outfield points and a straggler that wants out.
Ahead in the race, it's tempting to play 18/14(2).However, it's not going to be easy to bring this home because of thegaps in my position. Also, it takes all the pressure off White'scheckers on the 8 point and midpoint, so he can just play freely whilewaiting for me to roll a bad number.
The attacking plays are risky and don't accomplish enough. Making the4 point is nice, but it removes a landing point. 13/9 13/11(2) is veryflexible for making points or playing safely. By staying on the barpoint anchor for now, I keep a lot of pressure on White, who is likelyto have to bury checkers or leave a shot, and also avoid catastrophe ifI should get hit.
One play looks outstanding here, namely 8/4 6/4 3/1*. Blue must realize that he has to attack sooner or later - it's the best way to bring his disjoint position home - so he is well advised to do it immediately. By postponing the attack even for one roll he is only giving the opportunity to White to make his ace point or to decrease the percentage of the time he gets gammoned . In this aspect, even the second-best move (8/4(2) ) is clearly worse than the suggested play.
Blue is leading in the race, and needs to clear the 18 point before he runsout of timing and will have to leave a double shot.White has spare checkers to play while Blue would be waiting for anotherdouble to clear with, so Blue should definitely grab the chance to clear thepoint at this first opportunity.
Very unclear to me. My style very rarely leads to my having both the twoand three points made with the four and five points open, so I almostnever consider these positions (I never have enough energy to care how myopponents play them). Still, there is one of those general principlesthat says when ahead in the race, race. I think I've heard our belovededitor mention that once or twice. So, 18/16(2) seems a good way tostart. If we followed the dictum blindly, we might continue to the 14point. However, our structure is going to lead to a lot of shots, atleast a couple sets of indirects I'd imagine. Also, it releases some ofthe pressure on White's midpoint. By staying on the 16 point, we freezeFOUR of White's checkers, which mitigates the problem of playing a holdinggame with a race lead. 13/9 brings in a builder for a badly needed newpoint. So, we make an improvement on both sides of the board, which can'tbe ALL bad :).
The four- and five-point gap in Blue's board is an eyesore. Other playslook reasonable but I can't resist filling in the four point. It looksclose between the quiet 8/6 and 3/1* with the last deuce, but I'll hitbecause of White's inner board blot.
Fiddling with the outfield checkers doesn't accomplish much. The four pointis a real point. Much as I would like to hit loose, I just don't havethe ammunition for it yet. White is at the end of his rope. Let's see howhe plays his next roll.
The outfield checkers are fine where they are. Making the four point isa big improvement. The loose hit both activates the dead checker on thethree point and puts White on the bar against my strong board. It seems tobe worth the risk of being hit.
I don't care much for 13/9 13/11(2) or 13/11(3) 3/1*. The first playstrands the back men and doesn't accomplish much offensively (suely 8/4(2) must be better). The second play also strands the back men and is the wrong hitting move. If Blue wants to hit he should do it in conjunction with making the 4 point (8/4 6/4 3/1*).
I see two conflicting themes in this position. The first is that Blue will be ahead by 17 pips after this roll, so perhaps he should be running. The second is that Blue's gap in his inner board could cause later awkwardness, so perhaps Blue should make the 4 point now. Making the 4 point is also good because White still has a back checker in Blue's inner board; Blue may want to attack this checker later in the game. The compromise play of 18/16(2) 13/9 doesn't look good at all. It strips the midpoint, leaves a blot on the 9 point, doesn't make the 4 point, and only moves the back men slightly closer to home.
Between the two plays which make the 4 point, I prefer 8/4(2). Even though White has a blot in his inner board, he still has a decent board. If Blue hits, he will only have 7s, 4-4, and 6-6 to cover. Since Blue is significantly ahead in the race, he loses a lot if he is hit back. I believe it is better to simply make the 4 point and then, if White is still there next turn, re-evaluate the position to see whether hitting is warranted. If Blue had more covering numbers (say he could move a fifth 2 (8/6)), then I think hitting on the ace point would be correct.
I slightly prefer 8/4(2) over 18/14(2). While not moving the back men will make it more difficult for Blue to play safely in the future, it will also make it more difficult for White to play safely! White has 3 stripped outfield points (admittedly the stripped 8 point is not much of a factor; White will usually be able to play both checkers into his inner board) and will have trouble finding good moves if Blue stays on the 18-anchor. Meanwhile, it's not clear whether White's back checker is an asset or a liability if it continues to stay on Blue's ace point. At the moment it appears to be an asset for White, but since Blue has a 4 point board it could soon turn into a liability as Blue brings another checker in from the midpoint. Play Votes Score8/4(2) 4 1008/4, 6/4, 3/1* 3 9018/14(2) 3 8018/16(2), 13/9 1 6013/9, 13/11(2) 1 6013/11(3), 3/1* 0 40
145
150
White
money game
Blue
Blue's strength is the broken prime. There isn't enough to gain here byeschewing it for a loose hit. In contrast to Blue's holdings, White's strength is mostly potential, so Blue needs to step carefully. Don't challenge a cornered animal. 13/8 puts a builder in a better position. 24/21 is safe, keeps pressure on White, maintains linkage between theBlue's back two checkers, and puts a checker in position to either escape or make an advanced anchor.
I don't know why. 24/21, 13/8 might very well be right. I don't like breaking the8-point to hit, and somehow or other, 23/15 looks pretty good.
24/21, 13/8 Duplicates fours and makes itdifficult for White to play any but her best numbers, but I don't know if it is the best play. I don't like the hitting plays, which don't show an appreciation for the strength of Blue's broken 6 prime. White would like to escape, and I would like to prevent that. So often have I analyzed my errors with Snowie that I am beginning to see a pattern. In difficult middle game positions, Snowie tends to just pump checkers into the outfield where they can't get pointed on inside. So, when I am in doubt, I just pump checkers into the outfield if there is not a clear cut alternative. This position is far from clear to me, so I'll switch on the pump.
White wants to escape or start building board. It seems that hittingwith 8/3* makes it easier for White to escape, so that approachgets rejected. The way to dissuade White from making points is tocover the men on the eleven -- in effect freezing them in place because White doesn't want to leave a blot. The most effective wayof doing this is 23/15. Blue doesn't mind mixing it up while Whitehas no board -- and escaping one helps a lot when White does startbuilding a home board.
My broken prime is quite strong: only 44 and 45 escape forWhite, while 43 leaves a single shot; the other 4s leave a triple shot. Therefore, attacking seems wrong since White is so unlikely to escape. If I had good closeout chances it might be worth it, but here I have along way to go, so the risk of getting hit back seems too great. WhatI'd really like to do is make my bar point. I'm not in position yet,but 23/15 gets a builder closer, compared to 13/5 which aims for thewrong point. My main worry is having White make a good position andwin the priming battle, so by running I distract him. White hits with1's and 3's, but if he does so he's not making a new point, which is whathe wants to do.
I don't care for any play involving breaking the blockade in order to hit. I don't care also for 13/5, misplacing a checker that is badly needed to complete a six-prime. Between the two remaining candidates, I slightly prefer 24/21 13/8 over 23/15. Blue's objective is to make the bar and this play is more to the (bar) point.
Blue has a verystrong position, and has no reason to slotting any forwardpoints. Blue is better off hanging back waiting for a shot than givingWhite a chance to get Blue on the bar and get back in the game. The pressureshould be put on White's remaining back checker. By bringing another builder,Blue will be able to attack White, and maybe get an early close out, with agammonish result.
With no other blots exposed, breaking the eight point to hit is not veryattractive. However, with the race close, we certainly will want toattack in the near future. So, bringing in another attacker seems to bethe right idea. The back checkers are still well placed to go after anystray blots White may leave next roll.
Attacking could be right, but I hate to rip apart my points unlessI'm confident my blitz will be overwhelming. 13/5 prepares to attacknext time when White stays put. There's no reason to move the backcheckers. Together they provide good coverage of White's side ofthe board, and because they are so far back they don't give White manyopportunities to hit.
I have by far the stronger board, and he has only one man back. Let's go forthe attack now before he can consolidate. On the other hand, I don't wantto leave too many blots strewn around in case something bad happens.This looks like a reasonable compromise.
I don't want to disturb my blockade now. One more builder into place andan advance of a back checker to a relatively safe point seems optimal.
I'm inclined not to break up Blue's perfectly good broken 5-prime. At themoment White can only escape Blue's broken 5-prime with 4-3, 4-4, and 4-5. If White gets a second checker sent back the 8 and 9 points will be valuable for Blue. Also, since the race is even, Blue loses a significant amount if hit back.
Among the 3 remaining plays, 23/15 is a possibility. It's additional outfield coverage is an illusion though -- if White runs to Blue's bar point, Blue is already a big favorite to hit; it really only helps if White runs to Blue's 10 point. Actually 23/15's strength lies in the fact that since the race is close, Blue benefits from escaping a back checker (because of this, if White next rolls 4-3 he should probably play 13/10*/6 rather than 22/15); if White's next roll misses, Blue can escape this checker completely; both sides will then only have one man back, but Blue will have a better front position - if he gets the right rolls he can fill in the bar point; if not he can probably attack.
23/15 is a reasonable move, but White is a favorite to hit (gaining 10 pips in the race and bringing another builder into action while Blue is on the bar). I think Blue should take advantage of his superior board/prime by working on both sides of the board with 24/21 13/8. This slots an advanced anchor and gives Blue more outfield coverage. At the same time it brings another builder to bear on both the bar point and 3 point. I believe this is better than 13/5 which doesn't provide a builder for the bar point and doesn't put the same pressure on White as 24/21 does. Play Votes Score24/21, 13/8 4 10023/15 4 9013/5 3 808/3*, 8/5 1 6024/21, 8/3* 0 4023/20, 8/3* 0 4013/10, 8/3* 0 409/6, 8/3* 0 40
157
146
White
money game
Blue
Isn't this just the last problem, a couple of rolls later? How'd we do?I like 24/17, but see Kit didn't list that. The 5 die looks awkward nomatter how we play this. The choices are: give up asset-A, themidpoint; or give up asset-B, the 9-point; or give up neither asset byplaying either 8/1* or 8/3, 24/22.
As in problem 7, I have an aversion for breaking up a nice prime. Andgiving up the midpoint with two checkers still deep in opp's board doesn'tfeel right either. So it's down to pure (8/3, 24/22) vs. impure (8/1*);the seventies vs. the nineties.
Not counting the loose hits with 51 and 52, 8/3 leaves 'only' 15 shots,with 33 a crusher and 22 pretty nice as well. 8/1* results in no crushers,but a checker which is inconsistently placed to complement the alreadyexisting prime. In fact, covering it is probably going to mean breakingthe prime. And if we're having mixed feelings (that is, maybe we'd ratherhave the checker sent back than left as a continuing headache on our acepoint) then maybe we should take the extra risk and leave it where it will do the most good--on the 3-point.
The kicker for leaving the blot on the 3-point is that the back checkersare (relatively safely) split which may ease timing problems and/or allowfor an advanced anchor. Maybe my ongoing re-readings of Backgammon Times (early 1980's periodical) is having an adverse affect, but I'm going forthe pure play: 8/3, 24/22.
Probably wrong, but I just can't resist. I really don't want to break my prime, and24/22, 13/8seems a little too passive. I have less confidence in my answers this time than usual.Maybe the problems are harder, or maybe it is just because I have been losing. However, if my opponent fans, or doesn't hit or bring in 2 checkers, I like my hand. Otherwise, I will just have to deal with it.
Well, it seems to me that if White is allowed 15 numbersthat make an anchor, then she will be able to build a formidable prime of her own. So, I will put a second checker up in the air for lack of a better alternative. I would really like to slot the bar point, but the best 5 would be to slot the 3 point too, and oh, by the way.......... that was not one of the options. By hitting, I can eliminate good reasoning from White's arsenal. She will be forced to depend on the dice, and I may be able to blitz her into oblivion before they can come to her rescue.
Blue's first priority is to get the back men moving, so we play24/22 and look around for a five. There aren't any good ones, but13/8 appears to be the least damaging -- it maintains the asset ofthe nine point and brings a man closer to help with the home board.
Blue needs to get the men on the twenty-three point moving, and this is the perfect roll to do it.
The first question is whether to pound away with 8/1*.My feeling is it's too committal. White gets an immediate shot, I haveno direct covers, and I still have to make the 2 and 3 points to getthe closeout (not to mention escaping the back checkers). I have agood prime, with reasonable chances to make the bar point, but I alsowant to be able to attack if White enters on the 3 point, so 24/22 9/4seems like the most flexible, as well as getting the back checkersmoving at little cost. It gives up the 9 point, but I think it's worthit for the extra builder.
The five should be obviously played from the midpoint (13/8). As for the two, the odd-looking 24/22, leaving a blot on the midpoint looks to me better than lifting the blot (13/11). I think it's more important for Blue to start activating his back checkers before it's too late, than worrying too much for a few indirect hits (1-1, 2-1 and 3-1). After bringing two down, Blue's army is visibly separated in two parts resulting in White controlling the whole outfield. After 13/8 24/22 (my choice) Blue controls the outfield with his checker on the twenty-two point and White has a number of awkward entering rolls himself, like 1-4, 2-4 etc.
Blue needs builders to continue his attack on White before he makes ananchor in Blues homeboard.Bringing in maximum number of builders might also pay off by Bluesuccessfully closing out White and winning a gammon.Blue should focus on aggressively trying to prime or close out White, beforeworrying about escaping or splitting his back checkers.Hitting at the 1 point serves no purpose for Blue, he doesn't have buildersto cover, and cannot afford to get a builder sent back. And if White shouldanchor on the 1 point, Blue is still in a good position.
A problem I can't find a clear winner for. I don't like any of the playsthat break the 9 point. Unless White gets blown off the board, the 9point will be an important piece of insurance. 8/1* seems over-ambitious,and 24/22 8/3 is trying a little too hard to keep everything. Byelimination, we are left with 13/8 for the 5. While it seems instinctiveto me to get the back checkers moving, the resulting position has too manyblots, and too much cleanup, and I have gained very little ground in theblitz department. Bringing a checker in to the 6 point has the advantageof creating a new builder for the blitz, and must be sufficient toovercome whatever benefit there is to splitting. While 13/11 eliminatesany immediate worries of being hit, there will be danger later if Whiteanchors, so we might as well do our best to prevent it by bringing the newbuilder in.
Blue would like to get his back checkers going, but splitting leaves a bad five, forcing Blue to either leave some shots or lose a point. After 8/1*, if Blue isn't hit he will have a strong attack, and even the hits aren't too bad because of Blue's strong blockade.
The bar point is the point I want the most, and my play gives me three buildersfor that point without taking any unnecessary chances. Sometimes backgammonis a simple game.
My back men aren't in great danger of being trapped. Looks right just tobring the wood down for a potential blitz.
Similar to problem 7 but now Blue is 15 pips farther ahead in the race,while White has made his 5 point, has a big stack of checkers on the midpoint, and has a stripped 8 point. These factors all seem to argue further toward moving up in White's inner board.
Since Blue is now ahead in the race he doesn't want to get stuck on the 24 point, but instead wants to split to try to obtain a more advanced anchor. Splitting now seems desirable, while White is on the bar and before White can bring down his army from the midpoint. Also, since White has made his 5 point, it is more urgent for Blue to try for an advanced anchor before it becomes too dangerous. Splitting also gives Blue more outfield coverage. White's stack of checkers on the midpoint have nowhere to go but the outfield; by splitting Blue gets at least a double indirect shot at any blots White leaves in the outfield. Finally, by splitting Blue puts pressure on White's stripped midpoint; if White uses a checker from the 8 point to make the 4 point, for example, he leaves Blue a direct shot. Thus, if it was right (in my opinion) to play 24/21 in problem 7, then it must be right to play 24/22 in this problem.
As in problem 7, I don't like destroying Blue's front position. Giving up the 9 point for more flexibility and only a chance to make the 3 point doesn't seem like a fair trade. The 9 point, as part of a broken 5-prime, is a useful point for Blue to have against two back men. I don't like 8/3 either. It gives White 15 shots (3s plus 2-1, 1-1, and 2-2) and leaves Blue with a stripped and somewhat inflexbile position. If White misses and Blue rolls a 5, he'll have to break the valuable 8 point just to cover, which defeats the purpose of slotting the 3 point in the first place.
I like the thematic 24/22 13/8. It's the best move to achieve the twin goals of splitting to a more advanced anchor and keeping the broken 5-prime in place. It leaves a blot on the midpoint, but since White is on the bar, more than half of White's entering 1s don't hit. The loss of the midpoint could be serious, but I think that the move's benefits outweigh this loss.Play Votes Score8/1* 3 10024/22, 13/8 3 9013/8, 13/11 2 8024/22, 8/3 1 7024/22, 9/4 1 7013/6 1 709/4, 8/6 1 70
Vote Summary
1 2 3 4 5 6 7 8Chuck Bower 6/1, 6/3 8/4*, 4/1* B/23, 8/4, 6/4 23/13(2) 8/2, 6/3 18/14(2) 24/21, 13/8 24/22, 8/3 Malcolm Davis 16/8 8/4*, 4/1* B/23, 8/4, 6/4 23/13(2) 13/4 18/14(2) 23/15 8/1*Ray Fogerlund 16/11, 16/13 13/10, 8/4* B/23, 13/11(2), 6/4 23/18, 8/3(2), 7/2* 13/7, 13/10 8/4(2) 23/15 8/1*Hal Heinrich 16/11, 16/13 8/4*, 4/1* B/23, 13/11(2), 6/4 23/18(3), 7/2* 7/1, 7/4 8/4(2) 23/15 24/22, 13/8Ron Karr 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/18, 8/3(2), 7/2* 8/2, 6/3 13/9, 13/11(2) 23/15 24/22, 9/4George Klitsas 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/13(2) 7/1, 7/4 8/4, 6/4, 3/1* 24/21, 13/8 24/22, 13/8Laila Leonhardt 16/11, 16/13 8/4*, 4/1* B/23, 8/4, 6/4 23/13, 23/18(2) 22/13 18/14(2) 13/5 9/4, 8/6Rob Maier 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/18, 8/3(2), 7/2* 22/13 18/16(2), 13/9 13/5 13/6David Montgomery 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/18(3), 7/2* 13/7, 13/10 8/4, 6/4, 3/1* 13/5 8/1* Snowie 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/13(2) 7/1, 7/4 8/4(2) 8/3*, 8/5 13/8, 13/11Kit Woolsey 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/18(3), 7/2* 7/1, 7/4 8/4, 6/4, 3/1* 24/21, 13/8 13/8, 13/11 Chris Yep 16/11, 16/13 13/10, 8/4* B/23, 8/4, 6/4 23/13, 23/18(2) 7/1, 7/4 8/4(2) 24/21, 13/8 24/22, 13/8
