Nigel Richards - One-in-the-bag pre-endgame analysis (CSW07)

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 John O’Laughlin is taken from here. Nigel had a 22 points deficit.
His rack: ?AENNTU
Unseen tiles from his point of view: AAEEIILQ
Game in gcg format

Nigel played [ENAUNTEr B4 61] which would have lost him the game had he drawn the Q. Indeed, in that case, John could have won the game by 34 points by playing the following sequence of moves with no possible reply from Nigel: [ER H13 2 AAEIIL], [LA 15G 17 AEII], [IF 7G 10 AEI], [YA 6F 9 EI], [DE O13 3 I] and [DEI O13 12].

Our analysis shows that there were four non-losing moves, three of them winning:

Example 2

This example between Pakorn Nemitrmansuk and Nigel Richards is taken from here. Pakorn had a 22 points deficit.
His rack: ?DLRSTU
Unseen tiles from his point of view: ABDEEOOO
Game in gcg format

Pakorn played [SOD I1 6 ?LRSTU] and won the game.

Our analysis shows that exactly three moves were winning no matter what letter Pakorn would have picked:

Example 3

This example between Pakorn Nemitrmansuk and Nigel Richards is taken from here. Pakorn had a 44 points deficit.
His rack: ?GINNWX
Unseen tiles from his point of view: AEIILOTT
Game in gcg format

Pakorn played [DRENCHING 15G 48 ?NWX] which would have lost him the game had he drawn the O for example. Indeed, in that case, the optimal endgame sequence would have given Nigel a 3 points win: [ILEA N5 16 ITT] followed by [Xi L3 36 NOW] and [TITE F5 15].

Our analysis shows that one move, and only one, was winning no matter what letter Pakorn would have picked: [WING L3 46 ?NX].

Here are the moves that didn't lose all the time:

Example 4

This example between Nigel Richards and Chollapat Itthi-aree is taken from here. Chollapat had a 35 points deficit.
His rack: ?DNOOWX
Unseen tiles from his point of view: AACEFFTU
Game in gcg format

Chollapat played [WOX 3C 44 ?DNO] that drew if he picked the U and lost otherwise.

Here are the moves that didn't lose all the time:

Example 5

This example between Nigel Richards and Jakkrit Klaphajone is taken from here. Scores were even and it was Jakkrit's turn.
His rack: BEERTUU
Unseen tiles from his point of view: ADILLOVW
Game in gcg format

Jakkrit won the game by playing the only winning move: [TUQUE 3I 30 BER]. The five best moves were:

Example 6

This example between Hubert Wee and Nigel Richards is taken from here. Nigel had a 15 points deficit.
His rack: ?ARRSTU
Unseen tiles from his point of view: AAEFIIJX
Game in gcg format

Nigel played [ROT 9M 9 ?ARSU], picked the X and lost the endgame. He was unlucky, as the move he played was one of the only two that lost only one eighth of the time:

The move [ROT 9M 9 ?ARSU] 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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