Back on March 10, we wrote an article on how to increase your odds at winning the lottery.
In that article, we asked 2 questions.
- "How many draws will it take so each combination has been drawn at least once?"
- "How many lottery combinations would be chosen if we had 13,983,816 draws?"
In this article, we will be asking only the first question.
- "How many draws will it take so each combination has been drawn at least once?"
In the original article, we did a comparison for some of the "smaller lotteries".
The play format for these smaller lotteries was choosing 6 numbers from a pool of 49 numbers.
Smaller is a loose term, because the odds of winning the grand prize in these smaller lotteries is 1 in 13,983,816.
That is small compared to the "big" lotteries which are the national US lotteries.
Powerball and Megamillions
These mega lotteries have low odds of winning the grand prizes.
The Powerball odds of winning the jackpot are 1 in 292,201,338
Megamillion, the odds of winning are 1 in 302,575,350
First, Powerball.
We crunched the numbers multiple times programmatically to find the average using a simulation.
In order for each combination to be selected at least once, we would need on average 5,860,000,000 draws.
You may ask yourself, is this right?
How can a lottery with an odds of 1 in 292 million end up with the odds of 1 in 5.86 billion?
The answer is simple.
Duplicate sequences are drawn.
The rules we had....ie "How many draws would it take so each combination has been drawn at least once?", so our simulation stopped after each combination was hit.
There was one unlucky number combination who had to wait 5.86 billion draws for their number to be drawn once.
Some sequences were "lucky". One lottery sequence was hit 50 times waiting for the unlucky sequence to be hit once.
On average, each sequence was hit 18 times.
Now let's look at Megamillions.
We crunched the numbers in the simulator for Megamillions as well.
The odds of winning Megamillion is less than Powerball, with the chance being 1 in 302,575,350
In order for each combination to be hit at least once, we are looking at 1 in 6.08 billion.
That is 1 in 6,080,000,000
Crazy low odds.
But that is the true odds for 1 lottery sequence.
The reason the results are so high is because lottery draws are random.
Anytime there is random, there is the possibility of duplicates.
See our Why page for a demonstration.
Conclusion
Bottom line...random numbers produced duplicates and as you can see by the results, a lot of duplicates.
If there was only a way to eliminate duplicate entries.
Oh wait, there is.
And that way would be using chosen number sequences when you play the lottery.
We remove the duplicate factor.
If everyone chose our numbers when playing these mega lotteries, the odds of winning would be what the lotteries are stating.
Let's bring the odds down to the millions, not billions.
Chosen Numbers will do just that.