Plan to cycle around, meeting one on foot for game (3-3-3)

I believe the answer is:
tic-tac-toe
'game' is the definition.
(I have seen 'American game' mean 'tic tac toe' so perhaps 'game' could also mean 'tic tac toe')
'plan to cycle around meeting one on foot' is the wordplay.
I cannot quite see how this works, but
'to' is found in the answer.
'around' could be 'c' (abbreviation for 'circa') and 'c' is located in the answer.
'one' could be 'ace' (ace has a value of one in some card games) and 'ace' is found in the remaining letters.
The remaining letters 'tit' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'for' acts as a link.
Can you help me to learn more?
