Expected Value: When Does Buying a Ticket Become Rationally Profitable?

Beyond the Face Value

A $500 million jackpot isn't actually $500 million. Between the cash option discount (usually ~40%) and federal taxes (37%), the net value is much lower. But when does it become 'positive EV'?

The EV Formula

Expected Value = (Probability of Winning * Net Prize) - (Probability of Losing * Cost of Ticket). Most of the time, this number is negative. However, during record-breaking jackpots, the math shifts.