Question: What is 'with' mean in this situation?(in 'FRIENDS')
Thease are sitcom 'FRIENDS's lines.(Seasion1, episode18)
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Phoebe: You guys, you know what I just realized? 'Joker' is 'poker' with a 'J.' Coincidence?

Chandler: Hey, that's... that's 'joincidence' with a 'C'!
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(All script are http://www.friendscafe.org/scripts/s1/118.php)

Question1:
What is 'with' mean in this situation? 'with' exchange the first letter of the 'poker'?

Question2:
What is the 'joincidence'? What deference between 'coincidence' and 'joincidence'?

Thank you.

Question

Question: What is 'with' mean in this situation?(in 'FRIENDS')
Thease are sitcom 'FRIENDS's lines.(Seasion1, episode18)
--------------------------------------------------------------------------------------------------------
Phoebe: You guys, you know what I just realized? 'Joker' is 'poker' with a 'J.' Coincidence?

Chandler: Hey, that's... that's 'joincidence' with a 'C'!
--------------------------------------------------------------------------------------------------------
(All script are http://www.friendscafe.org/scripts/s1/118.php)

Question1:
What is 'with' mean in this situation? 'with' exchange the first letter of the 'poker'?

Question2:
What is the 'joincidence'? What deference between 'coincidence' and 'joincidence'?

Thank you.

Answer

"Joincidence " doesn't exist. It's a joke that Chandler made just to say that Phoebe's realization was stupid and useless ... =D and he took the word "coincidence" because she said "coincidence, huh... I don't think so... "

At least, from my point of view ^^

Answer

/with/ in this case means /substitution/.
Phoebe is often joking with words, and this is no exception;
the result of a word transformation in a word game does not need to exist,
just to be fun enough.
I humbly confirm your initial  hypothesis .
Thank you for reminding me something funny and interesting as Phoebe's 
character!

Answer

"with" refers to the spelling of the word
Joker spelt with a P is Poker

Joincidence is Coincidence spelt with a J 
Joincidence is not a real word, but a word constructed for the purpose of the joke.