he Player On the Other Side (1963)

The essence of the game of chess lies in the ability of the player to foresee which move the player on the other side will make. That in itself is difficult enough. Not knowing the identity of your advisory only adds to the problem put before you. The four inhabitants of the 'castles' around York Square are made part of an unpleasant and dangerous chess game. One question almost immediately springs to mind if in fact one of the pawns isn't a player also? Are Robert, Emily, Myra and Percival York: " players or being played? (cover)

The murders began with a note:

Dear Walt:
You know who I am. You do not know that you know.
You shall.
I write this to let you know that I know who you really are. 
I know the skill of your hands. I know the quality of your obedience. I know where you come from and what you are doing.
I know what you think. 1 know what you want.
I know your great destiny.
I like you.
Y

This was the overture to the murders. The note came to Walt, for many years handyman for the four miniature castles that made up York Square.
Robert York was in the flesh what York Square was in stone-punctilious, outmoded, predictable. Not all the Yorks were like that, of course. Myra, younger than Robert, had a secret unmentioned by the other Yorks, as anyone who got close enough to see the gentle unfocused eyes became uneasily aware.
Emily York was younger than Myra and looked older. Compelled like her cousins, by their uncle's eccentric will, to live in a castle, Emily recorded a permanent protest against such trumpery by taking as her own the smallest of the maids' rooms and decorating it with all the elaboration of a Trappist cell.
And then there was Percival York, playboy, gambler, drunkard, gentleman, man of many personalities-a totally unpredictable character.
These were the people whose lives were threatened by "Y"-until "Y" was finally checkmated by Ellery Queen, called into the York case when it baffled the police. 

Several references to other writers. E.g. to Borges' "Death and the Compass", Bernard Shaw and Huxley. That would be Thomas Henry Huxley (1825-1895) a British biologist and defender of the theories of Darwin. In the essay "A Liberal Education and Where to Find It" (1868) the actual (slightly larger) quote is even more intriguing:

"Yet it is a very plain and elementary truth, that the life, the fortune, and the happiness of every one of us, and, more or less, of those who are connected with us, do depend upon our knowing something of the rules of a game infinitely more difficult and complicated than chess. It is a game which has been played for untold ages, every man and woman of us being one of the two players in a game of his or her own.  The chessboard is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of Nature.  The player on the other side is hidden from us.  We know that his play is always fair, just, and patient.  But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.  To the man who plays well, the highest stakes are paid, with that sort of overflowing generosity with which the strong shows delight in strength.  And one who plays ill is checkmated--without haste, but without remorse."

The book received an Edgar nomination for the best novel in 1964.