Nigel Richards - One-in-the-bag pre-endgame analysis (TWL06)

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 Brian Cappelletto is taken from here. The game was equal and it was Nigel's turn.
His rack: DGKLLTU
Unseen tiles from his point of view: AAAEINUU
Game in gcg format

Nigel played [KINGLET 13H 11 DLU], a move that won 75% of the time. Indeed, it lost the game by 11 points to an optimal endgame sequence if he picked a U. In that case, an optimal endgame sequence would have been: [GUINEA 11A 14 AA] [LOUD 11L 5 U] [AA 3K 11] [-] [end U +2].

There was a unique move that won all the time: [FLU 10M 8 DGKLT]. 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):

The moves that won at least 75% of the time were:

Example 2

This example between Nigel Richards and Will Anderson is taken from here. Nigel was 9 points behind.
His rack: ?EEIISS
Unseen tiles from his point of view: ADEEFKOR
Game in gcg format

Nigel played the best move: [SEISIN C9 14 ?E].

The seven best moves were:

Example 3

This example between Nigel Richards and Conrad Bassett-Bouchard is taken from here. Nigel was 24 points behind.
His rack: AEEHILR
Unseen tiles from his point of view: EEGLOPYZ
Game in gcg format

Nigel played [ELHI 1B 21 AER], by far the best move, with 62.5% winning chances assuming a completely random rack for his opponent.

The moves that did not lose all the time were the following:

It is to be noted that, since his opponent just played BI F2, it was safe to assume that his opponent had the remaining O to play OBI F1. Assuming his opponent had an O in his rack, Nigel's move [ELHI 1B 21 AER] actually won 71.4% of the time, well ahead of every other move.

Assuming his opponent had an O in his rack, the moves that did not lose all the time were the following:

Example 4

This example between Nigel Richards and Mark Milan is taken from here. Nigel was 62 points behind.
His rack: ?EGHSUV
Unseen tiles from his point of view: AACEENTU
Game in gcg format

Nigel played [NOG L10 8 ?EHSUV], picked an E and won the game.

The move Nigel played won 37.5% of the time, while all other moves lost all the time!

Example 5

This example between Nigel Richards and Mike Baron is taken from here. Nigel was 82 points behind.
His rack: ?CHIKSU
Unseen tiles from his point of view: AEIINNOR
Game in gcg format

Nigel played [NU 11L 2 ?CHIKS], one of only two moves that gave him winning chances. He hoped to pick the R; he would then threaten RICKSHa 15C 107 and sCHRIKS N5 84, both of which could not have been blocked simultaneously by his opponent.

The only two moves that offered winning chances were:

The move [NU 11L 2 ?CHIKS] that Nigel played is actually second best according to the mathematical expectation of the final spread of the game if we assume that the opponent had a totally random rack. 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):

Of course, Nigel might have inferred, based on his opponent's last plays for example, that he had more chances of picking the R than the E, hence choosing to play [NU 11L 2 ?CHIKS] instead of [PEC 14K 7 ?HIKSU].

Example 6

This example between Rafi Stern and Nigel Richards is taken from here. Rafi was 9 points behind.
His rack: ?DDGIIU
Unseen tiles from his point of view: BEFLORSW
Game in gcg format

Rafi played [ID 9L 19 DGIU?] which would have won if he picked the S, drawn if he picked the O and lost otherwise.

The exhaustive list of moves that didn't lose all the time is:

Example 7

This example between Nigel Richards and Brian Bowman is taken from here. The game was equal with Nigel to play.
His rack: AEKLQVY
Unseen tiles from his point of view: ?DELMNOU
Game in gcg format

Nigel played [KELLY 10B 30 AEQV], one of the only three moves that didn't lose all the time.

The three moves that didn't lose all the time were:

The move [KELLY 10B 30 AEQV] 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):

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