If you are asking whether the expected value of a ticket exceeds its purchase price, it’s hard to say. To value the ticket, start with the value of the cash prize, not the annuity, so you know the real present value of the prize. It’s easy to say the odds are roughly 1 in 300 million and the ticket price is $2 so if the present value of the prize is $600 million, the expected value is $2. But that estimated expected value is wrong because it fails to account for the additional possibility of winning a lesser prize. I think those lower prizes add about 20 cents to the expected value. More important though, it fails to account for the possibility that you will buy a ticket whose numbers match somebody else’s numbers and you have to share the prize. The likelihood that your ticket matches someone else’s is a hard-to-estimate function of the number of tickets sold and the randomness of the distribution of the picks (others and yours).

The tv news said 80% of jackpot winning tickets were numbers randomly selected by computer. I will infer that means that the inverse, 20%, of ticket buyers select their own numbers in drawings (there is a logical weakness in this estimate I’m ignoring but I won’t dwell on it because I decided don’t want to research the actual number of manual vs. automatic number selections).

Those 20% of tickets have a lot of commonality. People don’t pick numbers randomly. They usually pick specific numbers for some reason. One lottery result I remember reading from Massachusetts involved picking six numbers on a six-by-six grid (1-36). The ticket from had six grids you could choose numbers on. One week, the numbers drawn were, I believe, 6, 11, 16, 21, 26, 31. There were like 20 winners and the grand prize was worth very little when shared. Why so many winners? Those winners selected numbers by picking six tickets off the grid- the top row, the bottom row, the left column, the right column and the two diagonal lines. One of the diagonals won. Many more people play numbers based on significant dates. If the next Powerball numbers are a variation of the dates that the Red Sox won the world series, I’ll bet the winners would be clustered around Boston. Even personally significant dates are likely to cluster. Lots of numbers 1-12, more clustering of 1-30, etc.

So to reduce the chance of sharing your prize and maximize the value of your ticket, you’d have to consciously avoid numbers that others might have picked manually. How much that adds to the value of a ticket is hard to guess. There might be additional value if you design a better random number generator than the lottery’s picking system so you can avoid any clustering their algorithm introduces, but i don’t know anything about potential weakness in their randomizer.

Ironically, taxes don’t really reduce the expected value of your prize. You can deduct your gambling losses from your winnings. If you guaranteed your win by buying every number combination, you would pay taxes only on the amount of the prize in excess of your cost to purchase the tickets. But systematically buying 300 million tickets and then sorting through them to find all the lower valued winners too would be a logistical nightmare. Furthermore you’d still face the risk of sharing the prize which could wipe you out.