Tie in tic-tac-toe / MON 5-31-21 / German industrial valley / Quaint shoppe descriptor / Bicolor cookies also called half-moons

Constructor: Michael Lieberman

Relative difficulty: Medium (i.e. Easy + 4D and to a lesser extent 38D = Medium) (3:00)

THEME: COCO CHANEL (57A: Fashion designer associated with the item spelled out by the starts of 17-, 26- and 42-Across) —she's associated with the LITTLE, BLACK, DRESS:

Theme answers:

• LITTLE ROCK (17A: Arkansas's capital)
• BLACK-AND-WHITES (26A: Bicolor cookies also called half-moons)
• DRESS REHEARSAL (42A: Final practice before the big show)

Word of the Day: CAT'S GAME (4D: Tie in tic-tac-toe) —

[Can anyone explain why a tie game of Tic-Tac-Toe called "Cat's game"?]

There seems to be no one theory so take your pick from the ones listed below.
Since I need to get back to work now I have not cleaned up the spelling and usage mistakes--good luck.

Why is a tie in Tic-Tac-Toe called a Cat's Game?:

I think a tie in Tic Tac Toe is a Cat's Game because Tac spelled backwards is Cat.

Olive, Alfie, cat games

I believe this comes from a tie being considered a "scratch game". Call
it a "Cat's Game" if you will.
Cats scratch.

Tic Tac Toe ties are called cats game because no matter how hard a cat tries
to win against its tale it never wins and yet has fun

I believe that it is a cat-mouse game.if not one of the two players gets
the point making it a tie game. Therefore, cat gets mouse(point).

It's a game of skills the cat goes one way and the mouse goes another. So
when it's a tie that's what it means cat's game. A cat and mouse
chase. When mouse gets away the cat looses. And the mouse gets away. A game
that goes in any direction just like a cat and mouse.

There was a tic on a tac on a cats toe.

Because cats scratch (https://www.phrases.org.uk/bulletin_board/44/messages/373.html)

The theme is a bit of a zero. I'd like LITTLE BLACK DRESS as fill (even if it would require an oversized grid), but just having themers that start with each of those words?? That is no kind of accomplishment. At all. Plain White T, Big Yellow Taxi, Other 3-word Thing, where does it end? Just no zing to the execution here. And the fill is deeply ordinary, i.e. kind of boring ... *except* for CAT'S GAME, what in the world is that? I want to say it's old-fashioned, but I'm old-fashioned, so ... it's OLDE-fashioned, I guess. Why would you give a name to a tie tic-tac-toe game? Also, why are you playing tic-tac-toe, what are you, in a 19th-century prison or something? I played tic-tac-toe with my daughter when she was little, mostly on the backs of paper menus while we waited for food to arrive. Tie games were abundant. Neither of us ever thought to call them CAT'S GAMEs. As you can see from the "definition" posted above ... it's not even clear why CAT'S GAMEs are called that (if, in fact, they are called that, which ... again, never in real life heard the term used). It's a tie. Baffled by the idea that a term needed to be invented to describe a tie in This Particular Game. Anyway, that is off-the-charts the most obscure thing in the grid, and single-handedly took this puzzle from very easy to a little easy. The inscrutable-to-me clue on ABSTRACT took it the rest of the way to straight-up Medium ordinary Monday (38D: Existing in the mind only). I just don't think of ABSTRACT as the opposite of "actual." I mean, imaginary friends exist "in the mind only," but you wouldn't call them ABSTRACT. I had A-, and then AB-, and I kept trying to think of Latin phrases that fit, like, uh, A PRIORI or AB OVO or something actually makes sense in this context. So those two (symmetrical) answers alone were responsible for literally all of the difficulty in the puzzle. Unless you hadn't heard of JORTS (36A: Portmanteau for denim cutoffs), which ... honestly, you were better off, weren't you? Go back to not knowing, it's nicer.