60 Heads (*)

A simple pen-and-paper puzzle, no computers allowed and bonus points if you solve it in your head.

I'm going to toss a coin 100 times, and every time I toss more than 60 heads I'll pay you £1.

• Intuitively, how much are you willing to pay to play my game?
• After calculating, how much are you willing to pay to play my game?