The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one.
It's a big number and it's a hard number to put into perspective. If you play $1 each draw, it is expected that you will have to put up your $1 for 170 million drawings before it is statistically likely for your numbers to hit.
But that's based on buying only one ticket at a time. Most people buy many tickets and a lot of people participate in lotto pools to increase their chances of winning.
While buying more tickets does increase your chances for hitting the jackpot, it's a difference that really doesn't have an impact.
No one person can buy enough tickets to swing the odds in their favor.
It would be profitable for someone to buy every possible combination of numbers if the jackpot is over $200 million. However, there are two things to consider. First, if someone else hits the numbers, you will split the pot with them and that would result in a net loss of $70 million on your investment. Secondly, it is logistically impossible for any one person or even a coordinated group of 20,000 to purchase all possible combinations.
Lotto pools are also at the mercy of statistical anomalies in order to turn a profit.
I did research on this and developed a program that simulates lotto pools. The program generates random quick pick tickets, and compares them against previous winning numbers.
The size of the simulated pools ranged from 25 members up to 65,000 members. Each member put up $1 for five draws. Each member invested $5 in an effort to turn a profit.
The results were very consistent. The average rate of return (for Mega Millions) was between $.06 and $.08 for every dollar invested, regardless of the size of the pool.
One thing was notable in my research; the average rate of return increased slightly as the number of members increased. However, in no case did the members turn a profit at the end of five draws. On a rare occasion, they did turn a profit on a single draw, but the profit was not enough to offset the losses of the other four draws.
For this example I will use a 65,000-member lotto pool for five drawings. Each person has put up $5 and the object is to turn a profit by having more than $5 at the end of the fifth draw.
Our total investment is $65,000 per drawing or $325,000 total.
The way you can visualize this is by imagining me walking up to the guy at the counter and saying, "Yes, I would like 65,000 quick picks for five draws". I hand the guy $325,000 and cross my fingers.
Images below show how many winning tickets we have. Below the images is the total $$$ won for that draw.
DRAW #1
Rate of Return: $.10 (this draw)
Rate of Return: $.02 (overall)
DRAW #2
Rate of Return: $1.94 (this draw)
Rate of Return: $.40 (overall)
DRAW #3
Rate of Return: $.25 (this draw)
Rate of Return: $.46 (overall)
DRAW #4
Rate of Return: $.11 (this draw)
Rate of Return: $.48 (overall)
DRAW #5
Rate of Return: $.11 (this draw)
Rate of Return: $.50 (overall)
At the end of this lotto pool we won a total of $164,431. We divide that equally between our members and each person gets back fifty cents on their $5 investment. This amount is above the observed average for Mega Millions.
There is something that I need to comment on. Some people will say that the winnings are spread too thin when too many people are in a pool. It's true that it will be impossible to win millions or very large sums of money with a pool of this size. But, the rate of return is in-line with lotto pools of any size.
Some will then argue that if the pool were small the winnings would be much larger because of the big winning ticket in draw #2. The thing to keep in mind is that getting that winning ticket relied solely on the large pool size. That winning ticket was the 21,935th ticket purchased for that draw. This means that any pool with less than 21,935 members would not have gotten that ticket. The value of that ticket was $120,450. If we divide that by the minimum number of members (21,935), each person would get $5.49. Not exactly a life changing win.
If the ticket were the 8th ticket purchased for a ten-person pool, each person would have gotten $12,045. But what are the odds of getting that ticket when buying only ten tickets?
Here’s the kicker; we will need more than 2,600 draws before it becomes statistically likely that our 65,000 person lotto pool will hit the jackpot.
The moral of the story is.... It doesn't matter what you do, to strike it rich in the lottery, you must rely on luck to achieve the allusive "Statistical Anomaly."