from Metalogue: Why Do Things Have Outlines by Gregory Bateson 1953.

...

Father

Yes, we were talking about flamingos. The point is that the man who wrote Alice was thinking about the same things that we are. And he amused himself with little Alice by imagining a game of croquet that would be all muddle, just absolute muddle. So he said they should use flamingos as mallets because the flamingos would bend their necks so the player wouldn't know even whether his mallet would hit the ball or how it would hit the ball

Daughter

Anyhow the ball might walk away of its own accord because it was a hedgehog.

F

That's right. So that it's all so muddled that nobody can tell at all what's going to happen.

D

And the hoops walked around, too, because they were soldiers.

F

That's right---everything could move and nobody could tell how it would move.

D

Did everything have to be alive so as to make a complete muddle?

F

No---he could have made it a muddle by . . . no, I suppose you are right. Because if he'd muddled things any other way, the players could have learned how to deal with the muddling details. I mean, suppose the croquet lawn was bumpy, or the balls were a funny shape, or the heads of the mallets just wobbly instead of being alive, then the people could still learn and the game would only be more difficult---it wouldn't be impossible. But once you bring live things into it, it becomes impossible. I wouldn't have expected that.

It would also remain a game if pure noise is injected (eg rolling dice or shuffling cards).