Why does ‘you’re on’ mean ‘I agree’?

Question

One dictionary says ‘you’re on’ is used tell someone that you accept a bet or an invitation to compete against them. Then why does it use ‘you’ instead of ‘I’? What’s the ‘on’? In terms of the meaning, ‘I’m on’ is more understandable and easier to memorize, at least for me.

Just for your information, I found the phrase in the following scene.

”Yeah,” said Harry. “Yeah … we’ve helped each other out, haven’t we? We both got here. Let’s just take it together.”

For a moment, Cedric looked as though he couldn’t believe his ears; then his face split in a grin.

”You’re on,” he said. “Come here.” (Harry Potter 4 [US Version]: p.634) [Bold font is mine]

N.B.: Harry and Cedric are competing for the cup a few feet away from them, but they are friends now because they were helping each other during the tournament.

I have two questions on this phrase.

1. Why does the phrase use ‘you’, not ‘I’?

2. What’s the meaning of ‘on’?

Answer 1

"On" is one of those words that have quite a lot of meanings, plus it is used in lots of phrases with various meanings. The meaning of on, in the term used is this (from yourdictionary):

adjective
arranged or planned for: tomorrow's game is still on

also read through all of the meanings here to try to get the feeling for the patterns.

Now, as to why "You" instead of "I" - well, usually the phrase is used to answer a challenge, and in this case it is more natural to say "You are on" because it is the challenge that has conditions that needs to be activated, accepted or started (there is some semantical overlap between the word "on" and these verbs). Also, you could have several challenges at the same time from several people - saying "I am on" would be ambiguous in that scenario, where "You are on" is not.

Answer 2

The New Oxford American Dictionary has:

you're on: (informal) said by way of accepting a challenge or bet.