How To Solve TRICKY Problem Only 18% Of Mathematicians Could Solve

This puzzle went viral in the discrete mathematics community because so many people got it wrong! You roll a fair dice until you get a 6. What is the expected number of rolls, including the roll of 6, conditioned on the event that all previous rolls (if any) were even numbers? Gil Kalai did a survey on his blog that covers graduate level mathematics, and only about 18 percent guessed correctly. Over 50 percent chose the same wrong answer. Can you figure it this counter-intuitive puzzle?

My blog post for this video
https://wp.me/p6aMk-5jL

Oxford Dictionary of English definition and usage for dice
https://en.oxforddictionaries.com/def...
(*In the video I incorrectly said "Oxford English Dictionary" which turns out to be a whole other thing. The definition quoted is correct as it comes from the dictionary that explains current language and practical usage---http://public.oed.com/about/the-oed-a...)

Gil Kalai blog test your intuition (puzzle and poll)
https://gilkalai.wordpress.com/2017/0...

This puzzle is credited to credit to Elchanan Mossel. via Gil Kalai blog solution
https://gilkalai.wordpress.com/2017/0...

Puzzling StackExchange
https://puzzling.stackexchange.com/qu...

Math With Bad Drawings - A Probability Puzzle That You’ll Get Wrong
https://mathwithbaddrawings.com/2017/...

*The Puzzling StackExchange post was removed (I am not sure why). Here is another discussion:
https://math.stackexchange.com/questi...

And another explanation:
http://www.yichijin.com/files/elchana...

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