Find the best play on each board

Question

Each of these boards has a unique best play. What is it?

Answer 1

These non-regulation Scrabble words are all:

Surnames of Russian writers! Specifically, Aleksandr SOLZHENITSYN, Leo TOLSTOY, Mikhail LERMONTOV, Fyodor DOSTOEVSKY, and Vladimir NABOKOV.

They can be played as follows:

For scores of...

S₁O₁L₁Z₁₀H_4→12E₁N₁I₁T₁S₁Y_4→12N₁ = 93 (H and Y on triple-letter spaces, 43 for the word, plus the 50-point clear-rack bonus)

T₁O₁L₁S₁T₁O₁Y₄ = 97 (T and Y on triple-letter spaces, 7 for S₁T₁U₁N₁T_1→3, 20 for T_1→3O₁L₁S₁T₁O₁Y_4→12, 20 for Y_4→12E₁A₁R₁N₁I₁N₁G₂, plus the 50-point clear-rack bonus)

L₁E₁R₁M_3→6O₁N₁T₁O₁V₄ = 203 (M on double-letter space, L and O on triple-word scores - 17 multiplied by 9 is 153 for the word, plus the 50-point clear-rack bonus)

D₂O₁S₁T_1→2O₁E₁V₄S₁K₅Y₄ = 116 (T on double-letter space, D on triple-word score - 22 multiplied by 3 is 66 for the word, plus the 50-point clear-rack bonus)

N₁A₁B₃O₁K₅O₁V₄ = 94 (O and O on double-letter spaces, 18 for N₁A₁B₃O_1→2K₅O_1→2V₄, 15 for K₅N₁I₁G₂H₄T₁S₁, 11 for V₄A₁M₃P₃, plus the 50-point clear-rack bonus)

My solution path:

I first spotted that there was a tempting T_V opportunity across a triple-word score on the top-rightmost grid. Realising that two racks also had V's on them (an uncommon letter in English), I wonder whether we might be looking for Russian or Eastern European names, which commonly end in 'OV' or 'OVA'. Spotting that the second rack contained the letters of 'DOSTOEV' and that the bottom-left grid contained the ready-made sequence 'SKY', I realised that 'DOSTOEVSKY' was an option and there might be some mileage in this!

With DOSTOEVSKY placed, the next Russian author who came to my mind was Aleksandr SOLZHENITSYN, and the letters of the central rack looked very tempting... With the necessary substring 'NITS' placed in the first grid already, here was another solved!

I next spotted that two of the racks contained all of the required letters for TOLSTOY and NABOKOV. With no need of an existing word as a substring these would have far more options over where they could possibly be played, so I instead focussed on the last remaining rack, to see if I could solve that one and remove its board from contention. Consulting a list of Russian writers, I found that LERMONTOV would perfectly fit that suspicious gap that set me off on this whole train of thought.

Finally, noticing that NABOKOV could create the words KNIGHTS and VAMP on the last board, and that TOLSTOY could create the words STUNT and YEARNING on the middle-top one, I reasoned that these were likely their intended playing places.

(Disclaimer: I have not exhaustively sought to prove that these are indeed the unique best plays for each - which would be a very complicated process - but I reason that the sheer amount of additional points picked up by the bonus spaces, side-words, and clear-rack bonuses probably means these were highly likely the OP's intended plays.)