Consider a gambling machine A. When you put in $X and pull the handle, it will spit out (equally likely) either $0.7*X, $0.8*X, $0.9*X, $1.1*X, $1.2*X, or $1.5*X.
Now consider the following two ways of playing this machine:
Put in $1, pull the handle, and keep whatever you get. Repeat.
Initially, put in $1. Pull the handle, then put in whatever you get. Repeat.
Can you win money with this machine? Which is the better way to play? How can this be?
The first two answers have been given (post 2) and verified (post 5) by a 100,000-pull simulation.
The discussion question elicited several thoughts (posts 5 7 8) that made the answers intuitive.
Finally, the answers can be changed (post 7) by changing the payoffs.