3 ms·
You have to pay for every game. Half of the time you win $2 which means half of the time you lose $3 if a game costs $5.
by danbruc 11y ago
You have to pay for every game. Half of the time you win $2 which means half of the time you lose $3 if a game costs $5.
- logicallee 11y ago(you've misunderstood the description.)
- justinsaccount 11y agoCorrect, half the time you win $2, but what happens the other half of the time? 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. So, if you simulate the average winnings in a single round, you get data like this: [8, 2, 8, 2, 8, 32, 8, 8, 4, 4, 2, 4, 4, 16, 2, 2, 16, 4, 8, 2] Which even with losses of $3 and $1 for most games still works out to a $44 profit at $5 game. 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: [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] So if you had played those 20 times, at $5/game * 100 rounds you would have a $27,000 profit on $10000.