The most common and most likely answer to this crossword clue is the 9 letter word EIGHTBALL
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Buddy explains!

The straight part
We know that "Game involving sticks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case game involving sticks = eightball.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EIGHTBALL mean?
EIGHTBALL noun- A pocket billiards (pool) game played with sixteen balls (a cue ball and fifteen object balls) on a pool table with six pockets.
- The billards ball, almost always black, bearing the number eight.
- A portion of cocaine or methamphetamine weighing 1/8 of an ounce, or 3.5 grams.
- A black person.