A single winner in Florida hit the "$1.58B" Mega Millions this week. The cash value (I saw on TV anyway) was about $783M. This begs the question: playing a regular $2 ticket, did a player have a positive return expectation (expected value of return > $2 bet)?
Answers:
1. Before income tax - yes, roughly $0.11 gain per $ bet (about +11% return)
2. After income tax - no, roughly $0.28 loss per $ bet if you assume a 35% tax rate on winnings. (about -28% return)
First, I looked up the number of tickets sold for this drawing, and it was about 171.7 million. Given that sales, we have to judge down the cash value jackpot expected value given the possibility of multiple winners. I did that and with 171.7M tickets, using the Binomial Distribution, we get about $597.5M Cash Jackpot Expected Value, given that you are a Jackpot winner.
OK, so now we calculate the overall EV of the return, assuming a tax rate. Let's start with no income tax:
Yea! We are ahead with about 11.1% positive expectation!
Now, here comes Uncle Sam (and state tax collectors, as applicable)...
Aw shucks! Now we have about -27.8% return.
No doubt some will argue that most people won't actually report and pay the taxes on the small returns (which, arguably, they don't owe given offsetting losses). Maybe, but most of the overall expected value of the game comes from the jackpot. You most definitely will get a W2G on the high tier prizes. Pay up my friend!