can i send an email with BGE ?
http://www.tutorialspoint.com/python/python_sending_email.htm
Im not sure if it works in BGE but it should.
yes you can as long as you know python. I just been checking the tutorial. doesn’t look that complex
it’s not working , can you help us with a blend retro 
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sure, what do you want help with?
EDIT: One more thing, you will need a server on the computer your sending from to send it and a listener too. check this out http://www.tutorialspoint.com/python/python_sending_email.htm
can i send an email with my Gmail account ? in the game
it will be a test Gmail account .
I have just did a test and I managed to send an email from my Gmail acount to my hotmail account.
check out my thread.
It has the source code for sending emails using a google account from python.
It wouldn’t be that hard to put that code into blender either check it.