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?

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