The following game of Scrabble was played between John Chew and Zev Kaufman on June 15, 1997, as part of an NSA-sanctioned tournament in Toronto, Canada.
- Chew's score: 0
- Kaufman's score: 0
- Chew to play holding ACLOOPU.
- Chew plays 8d COPULA for 26 points.
COPULA leaves Kaufman fewer opportunities to exploit squares 7g and 9g, but provides more hooking options: COPULAE COPULAR COPULAS SCOPULAE SCOPULAS. The presence of many hooks makes the game more volatile, because it makes rack-emptying bonus plays easier to come by. It is generally easier to make a seven-letter word from the letters on one's rack than it is to form an eight-letter word or longer by playing through letters on the board, but a seven-letter word in one's rack can only be played if there is a hook for it.
Although it scores the same number of points as CUPOLA, Chew prefers COPULA on the grounds that it will leave more hooks, increase volatility, and therefore increase his chances of upsetting a stronger player. On a whimsical note, he retains an O and dreams about the 1/95,589 chance of drawing the letters for 8a PRECOPULATORY, scoring 119 points.
- Chew's score: 26
- Kaufman's score: 0
- Kaufman to play holding AHNNRV?.
- Kaufman plays 7g NAH for 25 points.
- Chew's score: 26
- Kaufman's score: 25
- Chew to play holding AEIJOSX.
- Chew plays 9i JO for 38 points.
Simulation pegs the value of 9i JOE as four points higher than 9i JO, one point more this turn and an average of three points more next turn. It may seem counter-intuitive to relinquish an E while holding the X, but there are good reasons for it:
- It creates a backup square for the X at 8l.
- Playing an extra tile increases the odds of drawing a blank next turn.
- Playing an extra tile increases the chance (from 29% to 40%) of drawing something which can be used in place of the S on Chew's big play next turn. For example 10h FIX would score 68 and keep the S for the following turn.
- It creates a second hook for Chew's S (JOS is no good but JOES is).
- No E's have been played, so the E is 35% likely to be replaced.
- Chew's score: 64
- Kaufman's score: 25
- Kaufman to play holding EENORV?.
- Kaufman plays e3 OVERdONE for 70 points.
- Chew's score: 64
- Kaufman's score: 95
- Chew to play holding AEEILSX.
- Chew plays f8 PAX for 55 points.
SIX and PAX are objectively equal. The ten points sacrificed this turn are balanced by greater future scoring opportunities from retaining the S and a more balanced rack. Kaufman's play after PAX averages three points more, while Chew's next play averages eleven points more, and Chew's next rack after that averages two points better: 65-55 = -3+11+2
Chew prefers PAX, not for the increased equity, but for the increased volatility. PAX gives him a 30% chance of opening up a 60-point lead by next turn compared to only 20% for SIX. Against a stronger opponent, he wants the swings as wild as possible in the middle game. Against a weaker opponent, SIX or XI would be preferable for the opposite reason. XI would close column k, and despite the immediate sacrifice of 15 points, XI simulates only two points worse than SIX because it retains the S.
- Chew's score: 119
- Kaufman's score: 95
- Kaufman to play holding AAPQRSW.
- Kaufman plays 10j WAP for 29 points.
- Chew's score: 119
- Kaufman's score: 124
- Chew to play holding EEEIILS.
- Chew plays 11i LEI for 16 points.
- Chew's score: 135
- Kaufman's score: 124
- Kaufman to play holding AELQRSU.
- Kaufman plays 5b SQUEALER for 68 points.
- Chew's score: 135
- Kaufman's score: 192
- Chew to play holding EEINOST.
- Chew plays b4 ESSONITE for 62 points.
- Chew's score: 197
- Kaufman's score: 192
- Kaufman to play holding EFIINTY
- Kaufman plays a1 TINY for 42 points.
- Chew's score: 197
- Kaufman's score: 234
- Chew to play holding BDHNTUV.
- Chew plays a7 HUB for 39 points.
- Chew's score: 236
- Kaufman's score: 234
- Kaufman to play holding AEEFILW.
- Kaufman plays 4i ALEWIFE for 80 points.
- Chew's score: 236
- Kaufman's score: 314
- Chew to play holding DEINRTV.
- Chew plays o1 INVERTED for 158 points.
- Chew's score: 394
- Kaufman's score: 314
- Kaufman to play holding MOSTTU?.
- Kaufman plays 12f UTMOSTs for 84 points.
- Chew's score: 394
- Kaufman's score: 398
- Chew to play holding DEFGIRY.
- Chew plays a11 DIRGY for 36 points.
- Kaufman challenges DIRGY. It is not acceptable.
It would appear that a11 DEIFY for 42 points is the best play, but in fact c9 DIRGE is slightly better despite scoring only 30. DIRGE blocks the scorching Z spot at c9, which otherwise contributes 10 points to Kaufman's expected final equity. (Chew doesn't know that Kaufman doesn't have the Z.) Also DIRGE blocks the -EX hook at d10, while setting up an even better 15-point hotspot for Chew's F at a11.
The important thing to realise in this situation is that with two more full copies of DIRGE unseen and excellent places to play the F and the Y, it's natural to look for ways to play DIRGE to good effect and not waste the F and the Y on a mere triple score. Note further that in simulations, DIRGE doesn't catch up to DEIFY until the third subsequent turn, since it needs time for the FY to get played off.
- Chew's score: 394
- Kaufman's score: 398
- Kaufman to play holding ACEGNOT.
- Kaufman plays a11 OCTAN for 32 points.
On the other hand, Kaufman had only three minutes left on his clock, and he spent some of that deciding whether to challenge DIRGY. After his play he has only one minute remaining. OCTAN scores reasonably well, keeps a vowel and a consonant for flexibility, and leaves the board open to make it easier to find a good move quickly, whereas GENOA would kill the top of the board, blocking in particular the K spot at h4, and keep two consonants that might end up being hard to play.
- Chew's score: 394
- Kaufman's score: 430
- Chew to play holding DEFGIRY.
- Chew plays 14a AERIFY for 40 points.
Computer simulation shows that AERIFY wins 21% of the time compared to 16% for DEIFY and 17% for RIDGY. This late in the game, it's important to run simulations all the way to the end of the game, to correctly account for issues of endgame timing, specific utility of tiles, and hotspot values.
One should also calculate and compare winning percentages rather than total expected equity, if one is interested in winning the game rather than maximising spread.
- Chew's score: 434
- Kaufman's score: 430
- Kaufman to play holding ABDEEGO.
- Kaufman plays 15f AGO for 17 points.
In unlimited-depth simulations with DG known to be on the opponent's rack, Maven favours 15f ABODE for 29 points (wins 76% of the time) over ADOBE (75%) and d8 CADGE for 32 (72%). The important issues here are endgame timing and opponent rack information.
ABODE and ADOBE are better than CADGE even though CADGE scores three more points this turn and five more next turn, because they leave one less tile in the bag, shortening the game by an average of half a play and improving the chances of playing out in two moves from 45% to 80%. This is especially important when there's a danger of running overtime: playing CADGE means a 16% chance of having to spend time finding a third move, compared to 7% for ABODE or ADOBE. If Kaufman needs to make up a ten-point time penalty, his chances of winning drop to about 60%.
On the other hand, if it isn't known that Chew still holds DG, CADGE becomes a better play because it plays off a D and a G with two more of each to come. In this case, each of ABODE, ADOBE and CADGE win about 68% of the time with no time penalty, or 61% with a ten-point penalty.
One might also consider blocking Chew's hotspot at H1 with either 3g DOGE for 18 or 3h EGAD for 19. This would be a good idea if tournament conditions punished a wide loss significantly more than a narrow loss. But if Kaufman is playing to win rather than playing to avoid a big loss, the ten-point sacrifice isn't worth the seven-point risk. There's only a 10% chance of Chew making a 70-point play at H1.
Given that he knows Chew holds DG, Kaufman might also play 15f OBE for 20 points, saving the possibility of playing CADGE on the next turn. The board doesn't merit the delay though, as after CADGE Kaufman can expect to average 36 points, compared to only 32 points after OBE
- Chew's score: 434
- Kaufman's score: 447
- Chew to play holding DDGIRRZ.
- Chew plays d10 RID for 18 points.
This was a costly error, because 3g ZIG for 32 points would win 83% of the time no matter how quickly Kaufman plays. ZIG scores best while blocking h1 plays and forcing Kaufman to keep any I's he has if he wants to play the K at h4.
RID wins only 50% of the time. The additional time pressure is not likely to compensate for the lost points. Kaufman has to go two more minutes overtime for RID's winning percentage to hit 80%.
If Chew had spent another few seconds on this play, he might have seen m3 RIGID for 18, which wins 60% of the time but only needs Kaufman to go overtime by one more minute to win close to 80% of the time. Even better is d11 RIGID, though it requires Chew to spend a few more seconds scanning the rest of the board to find it.
- Chew's score: 452
- Kaufman's score: 447
- Kaufman to play holding BDEEIIK.
- Kaufman plays 14h BIKIE for 25 points.
Note that h2 BIKE 38 or h2 DIKE 37 score better this turn but lead to longer endgames and win only 16.5/36 and 15.5/36 respectively.
- Chew's score: 452
- Kaufman's score: 472
- Chew to play holding ADGMRSZ.
- Chew plays 3c GROSZ for 50 points.
- Chew's score: 502
- Kaufman's score: 472
- Kaufman to play holding DEGO.
- Kaufman plays 15l DOGE for 29 points.
- Kaufman scores 12 points for the ADM in Chew's rack.
- Kaufman loses 10 points for overstepping time control by 1:00.
Final Position
- This article is based on an account cowritten by Toronto Scrabble Club director John Chew and 1997 World Scrabble Champion Joel Sherman, and appears here with their consent.