Correct, half the time you win $2, but what happens the other half of the time?<p>With the other half... half of the time you win at least $4.
With the other half of that... half of the time you win at least $8.
With the other half of that... half of the time you win at least $16.<p>So, if you simulate the average winnings in a single round, you get data like this:<p>[8, 2, 8, 2, 8, 32, 8, 8, 4, 4, 2, 4, 4, 16, 2, 2, 16, 4, 8, 2]<p>Which even with losses of $3 and $1 for most games still works out to a $44 profit at $5 game.<p>However, and this is the point of the paradox, if you run the numbers for 100 rounds, you start to see average winnings per round like:<p>[6.48, 6.6, 15.68, 10.02, 10.26, 17.04, 5.86, 11.96, 8.92, 7.34, 6.56, 17.14, 9.92, 9.64, 11.48, 12.44, 19.64, 171.42, 12.82, 5.9]<p>So if you had played those 20 times, at $5&#x2F;game * 100 rounds you would have a $27,000 profit on $10000.