So the multi-state Mega Millions jackpot will be up to $252 million or so on Wednesday. The odds of winning the jackpot are 1 in 175,711,536. But actually doing the analysis to figure out if it makes sense to buy a ticket needs to also take into account the chance of others winning based on the number of tickets sold for the drawing… here are further details. As they point out, they don’t typically give out the number of tickets sold as a statistic, but given that there were 1.9 million winners in the last drawing of lesser prizes, and it is said there is a 1 in 40 chance of winning, 80-90 million tickets seems fair. Also, if the jackpot went up from $207 million to $252 million expected this time, assuming 50% goes into prizes that’s about 45 x 2 = 90 million tickets ($1 each). So let’s say 90 million, so chances of someone winning are 90,000,000 / 175,711,536 = 51.22%.

Thus calculating the Poisson distribution, and using the cash payout instead of the overall jackpot we get:

W = $159.2 million x ( 1 – e ^(- 0.522)) / (0.522)

W= $124,582,387

So then we look at your expected prize winnings in relation to your chance of winning, which gives you (when you include the chance of winning one of the smaller prizes, which by the other estimate are around $0.20 for every $1 of tickets purchased, we get this:

$124,582,387 / 175,711,536 + 0.20 = 0.70901 + 0.20 = 0.90901 or …

For every $1 ticket you buy at this level, you can expect to make about $0.91 (today).