(Editor's note: Previously in this space, we've posted annotated game columns where I've interviewed the two players in a CoCo tournament game and compiled their thoughts on a few of the key moves. Today, we're going to do something a little different: Adam Logan, one of the top Scrabble experts in the world, has offered to take a game from the Virtual World Cup and analyze every move himself. Adam chose a matchup between David Eldar of Australia and Llewellin Jegels of South Africa, from Week 1 of the tournament. I hope you'll enjoy his deep, thoughtful analysis as much as I did. -Evans)

Llewellin: ADELRRU

8C RUDERAL +68 68

Llewellin starts the game with a bingo rack. He chooses to sacrifice 2 points to put the A on the star, avoiding placing vowels next to double letter squares. If he decides to make this sacrifice, it is slightly better to do so by playing at 8G with the U on the star, since this increases the chance that the top left part of the board will never be reached. This favours Llewellin, since he is now ahead. However, the game is long and this is a minor consideration. Simulation supports the point sacrifice, but it is very close.

David: AAAIIIZ

E5 ZAIDA +30 30

With this unappetizing rack, the obvious choice is to score 30 points and start reducing the vowels by playing ZAIDA at E5. This scores too well for exchanging to be considered, but AALII at I6 deserves some thought. Normally AIZ is about 18 points better than AII, and the J6 square is no more dangerous after AALII than F6 after ZAIDA. Perhaps surprisingly, the plays are equal in simulation: Llewellin's next turn is about the same after each play, but David's average play after AALII scores 22 more points than after ZAIDA. On the following turn Llewellin gains about 4 points if David has played AALII (presumably because he is more likely to make a long play or expose the Z) and David does about 6 points better.

It is true that the simulation often plays too openly in column J after AALII. To some extent this is relevant because David might get an opportunity with the Z on 3I that a human would not provide, but some of it has to do with plays on row 4 or even column H. So perhaps ZAIDA is marginally better, but I think this is very close.

Llewellin: ?ADGNTX

F4 TAX +62 130

Llewellin's choice of TAX is certainly correct. There is no reason to keep a fourth consonant with AX, to waste the blank with eXTEND, or to sacrifice over 30 points with GANTED (the X and the blank get in each other's way a bit).

David: AIIIILV

exchange AIIIILV +0 30

It's definitely time to exchange here. Normally keeping AL is about 2 points better than clearing the rack. The value of AL is reduced here by the duplicated A and L on 8H-I, while the bag is slightly positive with no blanks or Ss among the 22 tiles that David can see, but keeping AL still feels slightly better. Simulation agrees.

Llewellin: ?DEGNOO

9H GOODmEN +66 196

The play of GOODmEN is good but not best. It would be better to take extra points from DRONGOEs at C7 or NOODGEs at J2. The former has some positional disadvantage in that it creates a useful bingo line in column B that will be difficult to block; if the R is left open for now, another play in that column (starting or ending on C8, or placing a less convenient consonant on C7) might avoid doing this. Also, NOODGEs blocks the S-hook on RUDERAL (there is still one on ZAIDA, but it is less convenient since a bingo ending in S cannot be hooked there). Such considerations are not visible in simulation, but they are sufficient for me to say that DRONGOEs and NOODGEs are equal.

David: AEHIIQT
8L HEAT +45 75

David chooses to take the points now rather than rid himself of the Q with QUAI at D7 or the bold QI G3. The latter play keeps not only HEAT or HAET for next time, but also a leave that is very promising for bingos through the open R, D, or N.

The disadvantage of HEAT is that David is unlikely to have a play much better than QI available on his next turn. Although HEAT/HAET could be blocked if he plays QI now, he would still have the chance to use the H1 triple word square. Of course this could be lucrative for Llewellin as well, but desperate times call for desperate measures.

Llewellin: BEEILNW

M7 BEELINE +24 220

BEELINE opens too much and scores too little. The best play here is NEWB at 10G. At a different score there would be something to be said for 10J WE, but a marginal fishing play that creates a high-scoring spot is not appropriate for a player with a large lead.

David: ?EIIMQU

L11 QI +37 112

The leave of EIMU? from QI is not wonderful (aside from the blank). I would have expected it to be worth sacrificing 5 points to play QUINIE at 12J instead, saving M?. Another interesting possibility is to play MI at 10J. The leave of EIQU? is not nearly as vowel-heavy as EIMU?, because the Q needs a lot of vowels and makes the IU combination work well together - a high-scoring bingo on row 14 or column O is a live possibility. At this stage it seems like a good idea. Indeed, simulation shows that MI averages over 20 points more than the other two plays on David's next turn, making it clearly best. On the other hand, the points sacrificed by QUINIE mostly do not come back, making that play inferior to QI.

Llewellin: CEOSTVW

10B VOWS +34 254

The play of VOWS would certainly be correct if it did not create a lucrative opening in column A. As it is, the best choices are VOW at 10G (better leave and defense) and TWO at 10I (many more points, saves the V for future defensive plays on row 14). At this score, VOWS at 14J is not terrible either, but my style would be to play TWO; something decent should be available somewhere on the board next turn.

David: ?EGIIMU

10G GEUM +30 142

With a poor draw (given that the letters for INGENIUM and MISGUIDE are not available), there are no good alternatives to GEUM. Plays such as 10I UME, 10J MI, G3 MIG do not improve the leave by enough to justify the sacrifice of points.

Llewellin: BCCESTW

exchange BCCW +0 254

A difficult position, with a lot of very different plays that are comparably good. Exchanging certainly keeps a very strong leave, but of course it scores no points and does nothing to defend the board. On the other hand, WEBS at 14J scores well, but keeps the dubious CCT and creates a new bingo line. 12K CINCT opens nothing, but scores only 10 points and keeps BESW, which is useful for scoring points but not exactly bingo-prone. Nevertheless, this might be a good time to keep such a leave; ahead by over 100 points, bingoing is not an urgent necessity.

If one does exchange, the next question is what to exchange. In general CEST is slightly better than EST, but that doesn't seem to hold here. My feeling is that Llewellin's choice to exchange BCCW is about as good as anything, and simulation agrees.

David: ?AEIIIT

exchange AII +0 142

Exchanging certainly seems right here, as ITA at A8 would leave few good lines for David to play a bingo on his next turn. However, ?AET is slightly better than ?EIT in general. With the powerful A hook in front of VOWS, and no real indication that Llewellin is holding an A, the difference is quite substantial.

In simulation, ITA has about the same winning percentage as exchanging, but I am skeptical; I think that Llewellin will play more defensively than the simulation expects.

Llewellin: EFILSTY

N13 FY +21 275

This gives up too many points and keeps a leave that is good for bingos that will not play on this board and that are not efficient with such a large lead. Considerably better plays are FEISTY at 14J and WIFELY at D10, with the latter preferred after the small exchange.

This illustrates the points regarding David's last turn: Llewellin's play was more defensive than the one made by Quackle, and after ITA it would have been correct or nearly so.

David: ?AEEIRT

A6 sERIATE +82 224

Clearly David will play a bingo in column A, but which one? His choice seems best, taking the most hooks at the end and creating something of a bingo line in column B.

Llewellin: EILMRST

G3 MISE +33 308

There are two rather different types of play here: either go for points and turnover to shorten the game, or fish and try to put the game away with another bingo. If Llewellin chooses the first, he should certainly play MILTER at O10. This scores 5 more points than MISE while bringing the game 2 tiles closer to the end and keeping the S, so it is clearly better (blocking the bingo line on row 4 is a minor consideration in comparison). For fishing, the obvious choice would be MAX at 6D.

Out of 44 unseen tiles, 21 (AAABHLNNNNOOOOOPPSSTT) bingo in two spots, and another 15 (CCEEEEFIIIIUUWY) in one, leaving only 8 (DDGJKRRV) with no bingos playable. At a closer score this would be a compelling play, but here a bingo may not be necessary to win the game, and MILTER is a very strong alternative. LAX is not as good because the leave does not work as well on this board (for example, drawing an I would not give any playable bingo).

SMILAX at 6A is an interesting compromise, scoring better and playing more tiles than MAX while keeping a better leave than MILTER. It would have been quite successful on this occasion, and in fact the simulation favours it slightly over MAX.

The simulation shows MILTER winning about 1% more often than SMILAX or MAX, and 10% more often than MISE. I tend to agree.

David: CDINSTU

B1 INDUCTS +79 303

Not much to think about here.

Llewellin: LLNORTT

1A LINTOL +21 329

Llewellin's play is clearly best. On this board and at this score it does not make sense to consider a fishing play such as TILL in the same spot; a leave of NORT is not especially strong in any event.

David: DEIINOP

H1 PION +29 332

I would have played PIED, judging that the 8 additional points justified the sacrifice in rack leave (typically INO is only 3-4 points worse than DEI), and simulation agrees. There are no good plays elsewhere on the board (PIANO at N6 sacrifices far too much) so it's hard for me to come up with any reason to look beyond this.

Llewellin: ABEHPRT

I3 PEH +25 354

BAH in the same spot would certainly be better for both defense and leave. However, this area of the board does not need any urgent attention, and so the best move is APTER at O11, scoring 41 instead of 25 and keeping some high-scoring tiles that will be useful in the future.

David: ADEGINY

J2 YEDING +40 372

David's play is not only high-scoring but also quite aesthetic. Nevertheless, it is worth thinking about some alternatives. In particular, the score is very suitable for fishing, since as it stands David is not unlikely to lose a close game, whereas getting a bingo would make him a clear favourite. DEGIN is quite a strong leave, especially with the D-hook on SERIATE and a bag that is not so bad for bingos at 1H or O1. In fact, in simulation O14 AY or A3 AY both bingo almost 1/3 of the time on the next turn, as opposed to 2% for YEDING. There is also some immediate defensive advantage to blocking the O column with AY.

LYE at 10M is a sort of compromise, scoring 28 points instead of 20 or 21 but with a significantly weaker leave. It doesn't seem right to me.

Nevertheless, the 20 extra points for YEDING over AY can certainly make the difference in a close game; ahead by 18 points after his turn, David would certainly have reasonable endgame chances at least. Also, it's hard to say what to infer from PEH, but certainly I would assume that Llewellin did not keep the J (4A JUPE), the F (O13 FEH), the W (I3 PEW), and probably the K (4A PUKE). Also, with two R's he would have played PER, and with the T he probably had a better play in column O. Most of the inferences seem to argue against David fishing here, so in spite of the simulation giving 4% greater winning percentage to AY over YEDING, I'll call them equal.

Llewellin: ABCRRTU

4A CURB +22 376

If you know the word CRATUR and notice that it plays at O10, it's pretty clear that that is the best play. If you don't notice that possibility, things look pretty bad: After your play, the score will be even, your leave is not very helpful, and the endgame timing is not especially good. The situation might be desperate enough to call for BUR at K1, setting up BRACT and also hoping for a big play with the J at 4A, or something in column O. CURB is also fine, though.

David: AEKOOVW

B12 AVO +14 386

A very difficult position, with a close score, the end of the game close enough that one has to consider the endgame but not so close as to allow for a complete analysis, various openings on the board, and some difficult tiles remaining. AVO has the strong value of setting up the W, with at least EWK for 40 points available next turn if Llewellin does not play there; the S will not give a strong non-bingo, and if he has a bingo starting with S it plays at 13A (and David is probably in serious trouble anyway).

Some plays that are worth considering, aside from AVO, include:

• 2J YAKOW scores well and uses two of the difficult tiles. However, it creates a powerful spot for the J at 1M-O.

• B12 WOVE scores 11 more points than AVO. Although it appears dangerous, this is somewhat illusory; if Llewellin can score well with the J while playing enough tiles to threaten an outplay, he could likely have done the same in column O. Meanwhile the threat of placing the K on 15D is useful for David.

• 3B DOOK also scores well and leaves two in the bag instead of three. However, after Llewellin's likely play in column O, David may have few resources.

• B12 WOKE is similar to WOVE; however, the V is likely to interfere with David's plans for the future.

• Other plays such as 12A EVOKE, D10 WOVE, etc., do not seem well-founded.

So how should one play in such a position? One general question is how many tiles to play. In general, one should try to leave one or two tiles in the bag, with two being preferred in positions like this one where there are no good scoring spots for single tiles and it is easy to play longer words. This favours AVO and DOOK over the other candidate plays.

One should also try to project the likely course of the game. One might say to oneself something like: "If I play DOOK, then he will do something in column O (TAJ, AFTER, etc.) and I won't have much, so he will probably win." Having said that, the next step is to ask what can be done about it. One possibility would be OK at O14, still keeping WOVE, and in fact this seems to be a fairly strong move. Another way, as already mentioned, is to create another opening with YAKOW or WOVE. It is very likely to draw one of FST by playing four tiles (almost 75%, ignoring inferences). My thinking about YAKOW is that the likely J play at 1M-O creates another spot on row 3 and leaves me again facing two high-scoring spots, that one and the one in column O, so that is likely to be problematic and I would probably try at that point to choose between OK and WOVE. Again, OK is likely to lose if the opponent has JEAN at N6, but David is not in a dominant position regardless of his play, so that does not disqualify it.

In an actual game, I would probably settle on OK, especially if my opponent were low on time, but this may be more out of fear of the openings than for any especially good reason. Simulation puts OK and WOVE winning about 50%, with all other plays behind by 10% or more. However, I am not sure how much to believe this; Quackle's quick play in this type of position is often far from optimal, though to be sure the same is true of humans.

Llewellin: AAJORTU

A14 JA +36 412

It's hard to believe that David would have played AVO without the W, and not very likely that he won't have at least a decent play there (something like OWIE), so Llewellin presumably wants to block, and JA is the obvious way to do it (preferable to JO for undoubling the A's). If you don't want to do this, you might think of TAJ or ATUA in the O column. However, the latter of these is not really sensible, since almost certainly David will reply in the bottom left, leaving no good spots for the J.

For each of these four plays, I went through the possible endgames:

• JA wins with ES, FS, IS, KS, or RS in the bag, for 6/36. Some of these happen because there is a bingo threat that David needs to sacrifice in order to block.

• JO wins with FS or SW and ties with ES, RS, for 7/72.

• TAJ wins with ES, KW, RS, RW, or SW, for 6/36.

• ATUA always loses.
  

Since David is very likely to have kept the W for AVO, we need to demote TAJ for winning in cases where the W is in the bag, and so Llewellin's play seems best.

What about playing a single tile? It doesn't seem like a good idea. Llewellin is unlikely to have much this turn that he doesn't have next turn, unless he picks the S for JATOS/JOTAS at O11. However, David could very well outrun this by playing out in two, or neutralize the threat with FEW or something in column O.

David: EEIKOSW

O10 WEISE +20 406

It is necessary to block Llewellin's big plays in the O column (best would be FAUTOR at O10). This does so while keeping two high-scoring outplays. There is another play which does the same things but slightly better: SEI at O13 keeps AWOKE at 15A, and Llewellin has no effective block. If he blocks ineffectively, David still has WOKE at K12. In fact, SEI is 5 points better for spread.

Llewellin: AFORRTU

11F FORT +19 431

Nothing better than this.

David: KO

N6 KOAN +22 428

(ARU) +6 434

One of two winning plays, the other being WOK at D10 for 2 fewer. David gains 6 points from Llewellin's remaining tiles.

Final score: David 434, Llewellin 431.