The current Powerball jackpot is at roughly 675 million USD and the chances of winning with one random ticket is 1 in 292.2 million. Each ticket costs 2 USD.
From a general perspective, it appears that the Powerball lottery tickets have a positive expected value but we didn't include all the other factors yet.
If we decide to take the entire winnings at once instead of getting paid over 30 years, we should be expecting to receive 428 million before taxes. Then we have to include both state and (25%) federal tax which shaves off at least another 100 million for the United States.
Then we would also have to include the possible of the Powerball having multiple winners. We could estimate how many people will purchase tickets for the next drawing based on how many purchased for the last one.
Lastly, we would also have to factor in the cost of maintenance for this large amount of money.
How can we go about calculating our expected value when purchasing a ticket in hopes of hitting the jackpot? Do these tickets truly give us a positive return at its current price?