Nigel Richards - One-in-the-bag pre-endgame analysis (CSW19)

Moves with equal percentages of wins, losses and draws are sorted descendingly according to the following heuristic:

H := (points scored with the move) + (mathematical expectation of the player's highest score next turn) - (mathematical expectation of the opponent's highest score next turn)

While this heuristic is generally good, the ordering according to it should be taken with a grain of salt; for selected examples, we give a better sub-ranking of the moves according to the mathematical expectation of the final spread of the game.

Example 1

This example between Nigel Richards and Jesse Day is taken from here. Nigel had a 13 points deficit.
His rack: AAHIRTY
Unseen tiles from his point of view: AEELLNSU
Game in gcg format

Nigel played [ARIGHT L2 20 AY] and won the game.

Here are the winning moves:

Move	H	W-L-D	Wins
[AY A14 32 AHIRT]	37.000	8-0-0	+A +E +L +N +S +U
[ARIGHT L2 20 AY]	31.125	8-0-0	+A +E +L +N +S +U
[AIGHT L3 18 ARY]	29.125	8-0-0	+A +E +L +N +S +U

The move [ARIGHT L2 20 AY] that Nigel played is actually best according to the mathematical expectation of the final spread of the game. Here are the final spreads of the game from Nigel's point of view after each pick (hover over a spread to see an optimal endgame sequence):

Move	A	E (2)	L (2)	N	S	U	Min	Max	𝔼[final spread]
[ARIGHT L2 20 AY]	+9	+13	+11	+5	+16	+10	+5	+16	+11.000
[AIGHT L3 18 ARY]	+15	+15	+8	+9	+14	+2	+2	+15	+10.750
[AY A14 32 AHIRT]	+10	+6	+1	+9	+20	+8	+1	+20	+7.625

Example 2

This example between Nigel Richards and Rik Kennedy is taken from here. Nigel had a 17 points deficit.
His rack: ACDOPTU
Unseen tiles from his point of view: AAEIIMST
Game in gcg format

Nigel played [PART 4F 25 CDOU], a move that won if he drew the M or the S and that lost otherwise.

The five best moves were:

Move	H	W-L-D	Wins	Losses
[CURD 4F 27 AOPT]	26.000	3-5-0	+M +S +T	+A +E +I
[CARD 4F 27 OPTU]	23.500	3-5-0	+M +S +T	+A +E +I
[CURT 4F 25 ADOP]	22.625	3-5-0	+M +S +T	+A +E +I
[CART 4F 25 DOPU]	21.375	3-5-0	+M +S +T	+A +E +I
[TURD 4F 23 ACOP]	20.500	3-5-0	+M +S +T	+A +E +I

Example 3

This example between Nigel Richards and David Eldar is taken from here. Nigel was trailing by 29 points.
His rack: ?AIJLRV
Unseen tiles from his point of view: EGNNOPTT
Game in gcg format

Nigel played [JARVIe 1E 49 L], by far the best move even though commentators did not think much of it when it was broadcasted live.

Here were the five best moves:

Move	H	W-L-D	Wins	Losses	Draws
[JARVIe 1E 49 L]	25.750	6-2-0	+E +G +O +P +T	+N
[LAV G11 10 ?AIJLR]	51.250	4-4-0	+E +O +T	+G +N +P
[VeIL 13G 35 AJR]	41.500	3-5-0	+E +O +P	+G +N +T
[VELAR K11 16 ?IJ]	32.750	3-5-0	+E +G +O	+N +P +T
[AXIAL H11 36 ?JRV]	36.500	2-5-1	+E +O	+G +N +T	+P

Example 4

This example between Nigel Richards and Rik Kennedy is taken from here. Nigel was trailing by 21 points.
His rack: CEELNPU
Unseen tiles from his point of view: ?EILOQRR
Game in gcg format

Nigel played [NEE 11J 14 CLPU] which was second best in terms of winning percentage.

The eight best moves were:

Move	H	W-L-D	Wins	Losses
[CLEPE G2 30 NU]	18.500	4-4-0	+? +E +I +O	+L +Q +R
[CEPE G3 31 LNU]	21.875	3-5-0	+? +E +O	+I +L +Q +R
[NEE 11J 14 CLPU]	17.250	3-5-0	+? +E +I	+L +O +Q +R
[EN O1 17 CELPU]	15.500	3-5-0	+? +E +O	+I +L +Q +R
[AXEL 6E 15 CENPU]	11.500	3-5-0	+? +E +I	+L +O +Q +R
[CLUE G1 12 ENP]	10.875	3-5-0	+? +E +O	+I +L +Q +R
[LEEP 11J 20 CNU]	8.750	3-5-0	+? +E +I	+L +O +Q +R
[CLEEP G1 20 NU]	6.875	3-5-0	+? +E +O	+I +L +Q +R

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