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Chew vs Kaufman

On Sunday, June 15th, 1997, in Toronto (Canada), John Chew and Zev Kaufman played the following game as part of an NSA-sanctioned tournament directed by Mike Wise, to set a world record.

Analysis by John Chew

Additional comments by Joel Sherman
1. JC: [ACLOOPU] COPULA 8D +26 = 26
COPULA and CUPOLA simulate within a quarter point of each other over 5000 iterations. COPULA exposes a little less at 7G and 9G, but is better against a stronger opponent because of its hooking options: COPULAE COPULAR COPULAS SCOPULAE SCOPULAS are all good, giving an 88% chance of drawing a hooking tile or about one chance in three to draw a front hook after opponent hooks the end. Keeping the O also lets Chew dream about the 1/95,589 chance of drawing PRE-COPULA-TORY 8A 119.
Joel: "The argument for COPULA is valid only if the weaker player actually knows the hooks."
... ZK: [AHNNRV?] NAH 7G +25 = 25
NAH 9G sims one point better, because it keeps the back hooks to COPULA open for the blank. Using the hook now to make VAR J6 25 and killing the front hook sims one point worse.
Joel: "NAH 9G also sets up a hook at 7I for the N or R."
2. JC: [AEIJOSX] JO 9I +38 = 64
Keeping SIX for a 65-point play at 10H is important, or else we might consider JIAO 9I 40 for rack balance. Should the E be played for one more point? Simulation favours JOE 9I 39 by about four points: setting up one more big scoring opportunity for the X at 8L doesn't give opponent any points but adds three points to the expected score of our next play and improves our median lead next turn by nine points.
Joel: "JOE makes double-doubles easier but shifts an easier 10-13 point hook into a second good place for our S. The first E is 35% likely to be replaced, we get one more crack at a blank, and a 40% chance instead of 29% to draw a front hook for -IX that lets us keep the S."
... ZK: [EENORV?] OVER(D)ONE E3 +70 = 95
Kaufman looks for double-doubles but misses simple doubles in column K. One of OVERMEN OVERNEW REWOVEN VENOMER hooking JO is best, but which? A long simulation shows OVERNEW K4 78 beats other plays by at least half a point. Next best are REWOVEN K8 78 and OVERMEN K4 78.
3. JC: [AEEILSX] PAX F8 +55 = 119
If Kaufman had played REWOVEN K8, Chew would now have played ALEXINES 13F 98. As it is, he can choose among SIX 10H 65, PAX F8 55 and XI 10J 50. SIX and PAX have equivalent expected equity: Kaufman's play after PAX averages three points more, while Chew's next play averages 11 points more, and Chew's next rack averages two points better. 65-55=11+2-3. But PAX is the more volatile play, giving a 30% chance of opening up a 60-point lead by next turn compared to 20% for SIX, and is the best choice facing a stronger player. XI sacrifices the openness of column K and too many points, simulating two points worse than SIX.
... ZK: [AAPQRSW] WAP 10J +29 = 124
One of WAP, WARP or WRAP is called for at 10J or K9. Which? An extra tile turned over improves the chances that the Q can be played next turn, and the K9 plays set up two separate hooks for the S, while WRAP is better than WARP because it doesn't leave a hot-spot, even if it does take a T. Best play then is WRAP K9 31, which sims three points better than WAP 10J.
4. JC: [EEEIILS] LEI 11I +16 = 135
Chew misses LIEVE 4B 16, which sims one point better than LEI 11J 20 and five points better than LEI 11I. LEI 11J sets up a second S hook but keeps too many vowels; rack balance is more important here: Chew's next play after LIEVE averages 9 more points than after LEI 11J.
... ZK: [AELQRSU] SQUEALER 5B +68 = 192
5. JC: [EEINOST] ESSONITE B4 +62 = 197
Sims one point better than ESSONITE B3 62.
... ZK: [EFIINTY] TINY A1 +42 = 234
Kaufman misses FINITE C9 39, which sims four points better despite sacrificing three points this turn. With EEEEEIIIIIF still unseen, keeping EIF is a bad idea, while keeping the Y for A4 and turning over six tiles looking for SS? gives an average of seven more points next turn.
6. JC: [BDHNTUV] HUB A7 +39 = 236
Chew weighs HUB vs BUNDT A11 31 and loses two points of simulated equity. Given a reasonable draw, the H and V will play well at D10 or H4; but unless the board opens up, keeping DNTV is risky.
... ZK: [AEEFILW] ALEWIFE 4I +80 = 314
7. JC: [DEINRTV] INVERTED O1 +158 = 394
... ZK: [MOSTTU?] UTMOST(S) 12F +84 = 398
Better than TIMEOUTS M3 81 and TETOTUMS 1A 80 by at least four points.
8. JC: [DEFGIRY] DIRGY A11 +0 = 394
Chew did think this was a word, and should spend less time reading unabridged dictionaries. DEIFY A11 42 is an obvious best play here, but Joel points out that DIRGE C9 30 is a slightly better one. DIRGE blocks the scorching Z spot at C9 (which otherwise contributes 10 points to opp's expected final equity) and the lesser -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 (to paraphrase Joel) 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.
... ZK: [ACEGNOT] OCTAN A11 +32 = 430
GENOA 3I 35 sims about three points better, using James Cherry's ACBot simulator that takes into account the fact that opponent is known to hold DGIRY. It sims more than 3.5 points better against random racks, reflecting the small threat posed by RIDGY A11 or D10. On the other hand, Kaufman's clock is ticking down from three minutes to one on this move, including a long 'hold' on DIRGY. 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. GENOA kills the top of the board, blocking in particular the K spot at H4, and keeps two consonants that might end up being hard to play.
9. JC: [DEFGIRY] AERIFY 14A +40 = 434
Sims four points better than DEIFY D10 35 and five points better than RIDGY D10 30 over 4700 infinite-depth iterations, winning 21% of the time compared respectively to 16% and 17%. 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.

With so many scoring opportunities on the board, opening the bottom row isn't a significant additional risk: opponent will reply with an average 38 points after AERIFY or 37 after DEIFY or RIDGY. The problem with DEIFY is that it sets up a new little (4-point) hotspot for Kaufman at C13, while eliminating small hotspots in Chew's favour at B2, K5 and M5. In other words, DEIFY scores only eight points for the F while giving Kaufman a chance at just as many for it, instead of saving the tile for a play in which it can earn 12 or 16 points. The problem with RIDGY is of course that even though it plays off the troublesome, potentially doubled DG, it scores too few points in doing so and wastes the Y.

... ZK: [ABDEEGO] AGO 15F +17 = 447
Kaufman makes a mistake under time pressure, with less than a minute on his clock. Immediately after the game, he regretted not having played ADOBE 15F 29 for fear that it might set up a big play in row 14, choosing instead just to get rid of the G and O that he thought might hinder his endgame.

In unlimited-depth simulations with DG known to be on opponent's rack, Maven favours ABODE 15F 29 (wins 76% of the time) over ADOBE (75%) and CADGE D8 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; and 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 DOGE 3G 18 or EGAD 3h 19. This would be a good idea if external (tournament) conditions required only that we not lose by a large margin; otherwise, since there's only a 10% chance of Chew making a 70-point play at H1, the ten-point sacrifice isn't worth the seven-point risk.

Joel also suggests OBE 15F 20, given that we know Chew holds DG, 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 pt, compared to only 32 pt after OBE.

10. JC: [DDGIRRZ] RID D10 +18 = 452
Chew still has about 15 minutes on his clock and Kaufman is 20 seconds overtime. Chew decides this isn't the key play and slaps down a poor play right away, to score a few points, split duplicate tiles for endgame flexibility, and put Kaufman back under time pressure.

Much better would have been ZIG 3G 32, which scores best while blocking H1 plays and forcing Kaufman to keep any Is he has if he wants to play the K at H4. ZIG wins 83% of the time compared to 50% for RID. 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 RIGID M3 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. Joel points out that RIGID D11 is even better, though it requires Chew to spend a few more seconds scanning the rest of the board to find it.

... ZK: [BDEEIIK] BIKIE 14H +25 = 472
Kaufman takes 39 seconds to play, leaving his clock at 59 seconds overtime when he draws the last two tiles out of the bag. If Kaufman can make the rest of his plays in one second, BIKIE wins 22 times in 36, while KIBE 3G 28 (keeping the other I to play at K3) wins 25/36. If his clock ticks over another minute, BIKIE wins 18/36 to KIBE's 15.5/36. Assuming Kaufman can make one play but not two in his remaining second, BIKIE and KIBE both win 21/36. (For example, if he plays BIKIE and draws AO, he can win only by taking two turns to set up and play at 1H, and the margin doesn't offset the extra ten-point penalty.) Given that it's significantly easier to play four tiles in one second than five tiles, he's better off taking his chances with BIKIE.

Note that BIKE H2 38 or DIKE H2 37 score better this turn but lead to longer endgames and win only 16.5/36 and 15.5/36 respectively.

11: JC: [ADGMRSZ] GROSZ 3C +50 = 502
Chew has plenty of time, and tells Kaufman (who looks a little tense) to sit back and relax. Having thrown away an endgame with no time pressure the previous day, he's going to spend as long as it takes to analyse this position. A few minutes into it, Kaufman knocks a pencil off the table. Seconds tick by before he announces correctly that he won't be needing the pencil before game end, and will therefore not pick it up. After twelve minutes, Chew finally persuades himself that GROSZ is indeed optimal, even though it gives him a one-point loss unless Kaufman takes more than a second to play out.
... ZK: [DEGO] DOGE 15L +29 (ADM) +12 (-1:00) -10 = 503
After a harrowing recount, Kaufman is found to have overscored SQUEALER by one point, and the game is a 502-point tie, the highest ever recorded in a sanctioned tournament game.