If the game had a four sided die instead of a two sided coin and three sides were winners, one a loser, then at a $2 game
a $2 fee has a 75% chance of breaking even
a $4 fee has a 56% chance of breaking even
an $8 fee has a 42% chance of breaking even
a $16 fee has a 32% chance of breaking even.
A reasonable person would pay $4,
If I had one drink I would pay $8
If I had two drinks I would pay $16
If I had three drinks I would pay $32
If I had four drinks I would pass out and not play.
The lesson: don’t drink or have 4 drinks.