At a certain prize level it makes statistical sense to buy a Mega Millions lottery ticket.
What is grand prize amount that makes it make sense?
I asked this question previously, but didn’t get any math answers. I did the stats myself and came up with the number of $303M.
The small amounts contribute about 22 cents of expected value.
The chance of 1 or more winners is 1 in 176 M, = (5/56*4/55*3/54*2/53*1/51&1/46)
The chance of exactly 1 winner is 1 in 212M
The chance of exactly 2 winners is 1 in 1.2B
The chance of exactly 3 winners in 1 in 7B
The jackpot contributes 78 cents of after tax lump sum payment expected value when the jackpot is 303M.
PrizeOddsPercentEV
$250,000 3,819,816 0.00003%$0.07
$10,000 650,783 0.00015%$0.02
$150 14,147 0.01%$0.01
$150 12,515 0.01%$0.01
$10 708 0.14%$0.01
$7 272 0.37%$0.03
$3 98 1.0%$0.03
$2 46 2.2%$0.04
Total $0.22
Albert
Comments
The jackpot will never be high enough, as I said in my previous answer to the same question.
Even if the prize was advertised at $303m, you still would not be getting fair odds for the prize. Remember that after tax and the penalty for taking a lump sum you are probably looking at something like $100m tops, which is less than the odds of hitting.
The biggest ever jackpot was $390m, which actually equals $223m before tax, and probably $160m max after tax. Two people shared that prize.
So again I reiterate at no point in history has the jackpot ever become so big that you are getting fair odds on winning. And they are talking about making it even harder to win by next year, just as Powerball are going to do in January.
you can check more about mega millions here
as you can see from the odds there, you have like 1 in 175,711,538 chances to hit the correct numbers for the big jackpot – therefore, for a $1 ticket to make sense from a mathematical point of view, the 1st prize should be of at least $175,711,538. However remember that even though chances are not on your side at any lottery games, we still have winners on a regular basis – it’s all about luck and playing smart if possible (choose more numbers on a ticket in order to increase your chances – this comes with a more expensive ticket)
Buy a ticket, I am.
