A handy school game (5)

I believe the answer is:

poker

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'game' is the definition.
(poker game is a kind of game)

I don't understand how the rest of the clue works.

(Other definitions for poker that I've seen before include "One of many irons in the fire" , "Fire-iron" , "Rod; betting game" , "Fire prod; game" , "Stiff rod; card game" .)

I've seen this clue in the Evening Standard.

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