Name the Director

Darren Aronofsky?

@DarthPazuzu

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I’m here only on Mondays, Wednesdays & Fridays. That’s why I’m here now.

Most definitely Aronofsky. The Fountain, Requiem for a Dream, and Black Swan.

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"Film is a disease. When it infects your bloodstream it takes over as the number one hormone. It bosses the enzymes, directs the pineal gland, plays Iago to your psyche. As with heroin, the antidote to Film is more Film." - Frank Capra

Then @Claireofthemoon must be up.

Elia Kazan?

Assuming SuperMetro is correct, I'll go next:

Kiss Me Deadly

Director
Robert Aldrich
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The Legend of Lylah Clare (1968)

Director
Robert Aldrich
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What Ever Happened to Baby Jane? (1962)

Director
Robert Aldrich

Correct!

Open floor...

Gotta be Liliana Cavani?

@DarthPazuzu

Yes, it is!

Open forum...

I guess I'm going next!

Martin Scorsese

Correct!

You're not necessarily obliged to follow up with one of your own, but I can't think of everything all at once, you know...

Name the director through the abbreviations of the movies.

TSS
WS
TAGD
P
HOTW
SFAM
C&W
AS
F&A

Hint: What is something that you can not beat, especially at a game of chess.

If these are all by one director I will say, Ingmar Bergman

Definitely.