I couldn’t find the information, so maybe someone here can. I’m looking for a fact, not speculation. Thanks.
I won’t get back until tonight to look at this.
I think the news last night said something like 1.5B. Not sure if that was just between Tue and Fri, or the time since the last winner.
Lottery officials try and hide hard statistics, but here’s what I’ve been able to calculate about Mega Millions.
There are 175.7m combinations. Let’s call this a standard_pool
1.491 billion tickets were sold since the last big jackpot in January. That’s 8.49 pools.
650m (million) tickets were sold on Friday, 30-MAR-12. That’s 3.70 pools.
What I don’t know is how many tickets were sold on Wednesday/Thursday. For ease of computation, let’s assume all three big winners bought their tickets on Friday.
The small payouts ($250k and smaller) amount to $32.0 million per pool, or 18.2% of the sales.
The lump-sum payout of $158m per winner means that the mega-lump-sum payout is $474m (158*3). The mega payouts amount to $55.8m per pool, or 31.8% of the sales.
Total return to players is 50% (18.2+31.8), before taxes. After taxes, I estimate the total return is about 32% of each dollar played. This assumes those prizes under $1000 pay no tax, and the $10k prize pays a lower tax than $250k and up. I also assumed a state tax rate of 5% as it is here in Massachusetts.
For those of you who wait until the jackpot is large because the expected return is more than 100%, you’re wrong. If 100% of the big payouts occurred in the final 650m tickets, then the mega-payout of $474m would amount to 72.9% (474/650). Add in the small payout return of 18.2% for a total return of 91.1% before taxes, or about 58% after taxes.
There were three big winners on Friday. I wonder how many children did not get a good meal Friday night because daddy blew it all on Mega Millions.
Thanks for the work. I figured they wouldn’t publish the number of tickets sold, and my efforts weren’t just bad at finding something available. It’s a shame information like this is required to be published by states that allow lotteries.
About 1.5 billion tickets . . . see 8th paragraph in this article:
Wow. With that many tickets sold, I’m surprised only three hit the jackpot. I’m not in a position to do any calcs right now, but what are the chances that many tickets would produce three or fewer winners, assuming (and this is a big assumption, I know) the numbers were picked randomly?
It sounds like the 1.5 billion number is not correct, since that includes all ticket sales since the prior jackpot (many of which were from prior draws and therefore not eligible).
If you assume that only 650mm tickets were sold in total for the drawing - and that the numbers were random - you’d expect an average of 3-4 tickets for each possible combination. However, since 650mm tickets were sold on Friday alone, it might be reasonable to assume something like 900mm tickets were sold for the drawing, which (assuming they were random) would mean there were an average of ~5 tickets for each possible combination. Therefore, doesn’t seem that surprising that we only had 3 winners.
Separately, I recall seeing a pretty thorough analysis before the drawing where someone had estimated there was only a 5-6% chance that no one would win the drawing (don’t have the link handy though).
I can’t reconcile the idea that there is simultaneously:
A) likely to be 3 or more tickets per possible combination
B) 5% chance that no one wins.
I don’t have time to run the numbers myself, but this comes down to the old head and tails problem with flipping a coin. On average, each flip is 50% chance, but there is a probability that at some point in a sequence there will be 10 heads in a row. That is to say that the average probability does not cover all possibilities.
So in this circumstance all 175M combinations are covered on average 3 times, but there are still 5% of number combinations that have not been taken/purchased.
I’m looking for the actual number of tickets sold, not a rounded number.
There’s a binomial probability calculator here.
With n = 900000000, k=0, p=0.00000000569114597006, I get either 2% (via normal approximation) or 0.6% (via Poisson approximation) for nobody winning with 900 million tickets sold. Somebody would have to explain to me the differences between these approximations. Also, the chances of three or fewer people winning would be about 25%, so not too crazy, assuming 900 million tickets sold, not 1.5 billion. With the 1.5 billion number, you’re looking at around a 3-4%.