A: I'd love to watch the final, but I haven't got a ticket.
B: Well, I've got two free tickets to the match. I ____ give you one.
Should I use "will give" or "am going to give"?
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Choosing between 'will give' and 'am going to give', 'will give' is more logical. Personally, I feel like it is more reasonable to say 'I can give you one.' This way it presents the extra ticket as an offer. The two options that you have provided, while both being correct as suggested by anotherdave, feel like you are forcefully giving 'A' your ticket. This may be different for different cultures, but I feel like 'can' is a better fit than 'will' and 'am going to' for this situation.
Use Will for decisions made at the time of speaking
Use Going to for decisions made in the past