The Powerball lottery drawing later this week has an estimated jackpot of $1.4 billion, the largest in US history, easily beating the $656 million Mega Millions prize in 2012. Although I don’t buy lottery tickets, the size of the prize made me wonder about the odds involved and whether it might be worthwhile to pick every single number to guarantee winning.
You have to apparently pick five separate numbers between 1 and 69 and then a sixth number called the Powerball that ranges from 1-26. The odds of picking the right set of numbers are one in 292 million. That implies that the number of combinations is 292 million and since each ticket costs $2, one could guarantee winning by buying one ticket for every possible number by spending close to $600 million, assuming that one has that amount of money lying around.
But one problem is that the $1.4 billion will be paid out over 30 years. If you choose to take the money immediately, which is a more accurate measure of the value of the prize, you will only get $868 million. Another problem is that if others buy that same set of numbers, you would have to share the prize equally and so you would make a profit only if you are the unique winner.
But the killer is that you have to pay taxes on the money. Since you will be paying the top marginal rate of 39.6%, that means that you will take home about $524 million, thus guaranteeing that you will take a loss even if you are the unique winner.
But even if the prize rises to such a level that you will clear a profit even after taxes as long as you are the unique winner, there is a major problem: time. Even at the rate of buying one ticket per second, it would take over nine years to buy every combination.
Since the drawing is tomorrow at 11:00
ampm, you can forget about it.