Chew vs. Kaufman
On Sunday, June 15th, 1997, in Toronto (Canada), John Chew [JC] and Zev Kaufman [ZK] played the following game as part of an NSA-sanctioned tournament directed by Mike Wise, setting a world record.
Note: 8D designates a horizontal play along row 8, beginning at the intersection of row 8 and column D. The notation D8 would indicate a vertical play along column D, starting at the same square.
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."
Position after 1 ... NAH
2. JC: [AEIJOSX] JO 9I +38 = 64
Position after 2 ... OVER(D)ONE
3. JC: [AEEILSX] PAX F8 +55 = 119
Position after 3 ... WAP
4. JC: [EEEIILS] LEI 11I +16 = 135
Position after 4 ... SQUEALER
5. JC: [EEINOST] ESSONITE B4 +62 = 197
Position after 5 ... TINY
6. JC: [BDHNTUV] HUB A7 +39 = 236
Position after 6 ... ALEWIFE
7. JC: [DEINRTV] INVERTED O1 +158 = 394
Position after 7 ... UTMOST(S)
8. JC: [DEFGIRY] DIRGY A11 +0 [the play was challenged and found unacceptable] = 394
Position after 8 ... OCTAN
9. JC: [DEFGIRY] AERIFY 14A +40 = 434
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) hot spot for Kaufman at C13, while eliminating small hot spots in Chew's favor 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.
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 hot spot 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.
Position after 9 ... AGO
10. JC: [DDGIRRZ] RID D10 +18 = 452
Much better would have been ZIG 3G 31, 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 18 is even better, though it requires Chew to spend a few more seconds scanning the rest of the board to find it.
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.
Position after 10 ... BIKIE
11: JC: [ADGMRSZ] GROSZ 3C +50 = 502
Final position
Final record (bingos
in red)
John Chew |
Zev Kaufman |
1. COPULA 26 | NAH 25 |
2. JO 38 | OVER(D)ONE 70 |
3. PAX 55 | WAP 29 |
4. LEI 16 | SQUEALER 67 |
5. ESSONITE 62 | TINY 42 |
6. HUB 39 | ALEWIFE 80 |
7. INVERTED 158 | UTMOST(S) 84 |
8. DIRGY# 0 | OCTAN 32 |
9. AERIFY 40 | AGO 17 |
10. RID 18 | BIKIE 25 |
11. GROSZ 50 | DOGE 29 |
++ADM 12 | |
1:00 overtime -10 | |
Total: 502 | Total: 502 |
Power tile distribution
John Chew |
Zev Kaufman |
J, S, S, X, Z | ?, ?, Q, S, S |