Take it from the voice of experience, Bill D's mystery case is the standard (probably fairly cheap(?)) carry-case sold for jointed pool/billiard cues.

The "slant" of the divider is so that the big end of the butt half can go on one end, while the mid-diameter small end of the butt and big end of the tip (both the same diameter) splits the middle at the other end, with the small tip back up by the big butt. With the cue unscrewed at the joint in the middle, the case leaves just enough room at one end for a chalk cube, or sometimes two.

I have used one as a make-shift case for a viola bow, but it's not a particularly good fit on much of anything musical.

If it's in good shape, last time I looked the going rate for a new case of the type was about $18 (US) - probably higher by now. If it's one of the "extra sturdy" one might get to around $35 for something similar, so it was a bargain at the price paid. Learning to play the game so as to have a personal use for it could be "expensive" if one goes to the wrong parlor...

John