Lotterycodex Mathematics Meets The Lottery

How to Win the U.S. Mega Millions 5/70 According To Math


The U.S. Mega Millions has recently changed its format. Now, players will choose five numbers from 1 to 70 and a single number from 1 to 25.  Perhaps, the most exciting change introduced is the increased in jackpot prize from $15 million to $40 million.

However, as always, the government will not introduce these changes as giveaway goodies.   So, let’s talk about how this new development in the U.S. Mega Millions affects your odds of winning the jackpot prize from a mathematical standpoint.

How To Win The U.S. Mega Millions 5/70 According to Math

The Odds Of The US Mega Millions 5/70

The Mega Millions’ 5/70 game format can have a total of 12,103,014 playable combinations.  Therefore, your odds of matching five correct numbers is 1 in 12 million chances.  But to win the jackpot prize, you have to match the mega ball by choosing a number between 1 to 25.

The new changes can mean both good news and bad news.

First of all, the bad news:

Now, winning the main jackpot prize is harder than ever.  The odds before was 1 to 259 million. But now, it’s 1 to 302.6 million.

Then, the good news:

It is much easier now to win five number match without the mega ball.  In the old format, the odds for the second tier prize was 1 to 18 million.  Now, with the new format, it’s 1 to 12.6 million.

The objective of every player:

The promise of a minimum $40 million jackpot sounds fair enough with the new rules.  But whether that is good news or bad news is up to you depending on your objective.

Either way, I always recommend that you play the U.S. Mega Millions with the right number patterns.  The complete list of the best and the worst number patterns for Mega Millions are available for free in the lottery analysis section.

Let’s talk about some of these number patterns for the new U.S. Mega Millions 5/70 game below:

Odd-Even Number Patterns in Mega Millions 5/70

Pattern Possible Combinations Probability
5-odd-and-0-even 324632 0.026822409690677
4-odd-and-1-even 1832600 0.15141682889898
3-odd-and-2-even 3894275 0.32176076141034
2-odd-and-3-even 3894275 0.32176076141034
1-odd-and-4-even 1832600 0.15141682889898
0-odd-and-5-even 324632 0.026822409690677
12103014 1

Further, we can classify these odd-even patterns into three groups:

Best Group Fair Group Bad Group
3-odd-2-even 4-odd-1-even 5-even-0-odd (All even numbers)
2-odd-3-even 1-odd-4-even 5-odd-0-even (All odd numbers)

Clearly, the table above shows that the 3-odd-2-even and the 2-odd-3-even number patterns put you in a better position to win.

As you can see, the “all-even-number” pattern appears three times in every 100 draws.  Whereas, the 3-odd-2-even pattern appears approximately 32 times.  Obviously, the difference in probability is so wide and self-explanatory.

Therefore, the statement that each number combination has equal chances of getting drawn in the lottery is a mistake.  The table above can attest to that.  See my post: Top 10 Lottery Strategy Myths Debunked.

So, if you play the U.S. Mega Millions, you don’t want to waste your money on some patterns.  More about that later.

Testing Probability Against the Actual U.S. Mega Millions 5/70 Results

The new format has just started October 2017.  At the time of writing, there were only six draws to analyze and it’s not enough to come up with any conclusive comparison between the actual graph and theoretical graph.

However, the probability analysis we have done with other lotteries show substantial evidence of accuracy.  And that is the power of logical reasoning.  Math remains a powerful guide on how to win the lottery.

Here’s a little challenge:

Together, let’s watch the outcome of the U.S. Mega Millions for the next 1000 draws.  You tally the odd-even patterns from the actual results.  After you reach the 1000 draws, go back to this article and compare the table with your own statistics.  I’ll bet, you will believe with your own eyes that math never fails.

Especially relevant, my analysis of the old U.S. Mega Millions 5/75 format is a solid proof that math works.

How to compute the expected frequency of each pattern?

The expected frequency is computed by multiplying the Probability by 1000 draws.

Expected Frequency = Probability x 1000 draws

In the case of 3-odd-and-2-even patterns with the probability of 0.32176076141034, the expected frequency will be 322.

Expected Frequency (3-odd-and-2-even) 
= 0.32176076141034 x 1000 = 321.76076141034
or 322

Following the same computation for the rest of the patterns, we will arrive at the complete prediction table below:

Likely Results Of the U.S. Mega Millions for Odd/Even Number Patterns in the Next 1000 Draws

Pattern Probability Expected frequency
in every 1000 draws
5-odd-and-0-even 0.026822409690677 27
4-odd-and-1-even 0.15141682889898 151
3-odd-and-2-even 0.32176076141034 322
2-odd-and-3-even 0.32176076141034 322
1-odd-and-4-even 0.15141682889898 151
0-odd-and-5-even 0.026822409690677 27

Can you see the difference?

The Six Winning Patterns In Mega Millions

80% to 90% of the players are not aware of the patterns they are playing. For example, I can imagine that many players will waste their money on the following number combinations:

Pattern Probability Expected Occurrence
#568 0.0001735105 Once in every 10,000 draws
#598 0.0001673137 Once in every 10,000 draws
#646 0.0000991489 9x in every 100,000 draws
#658 0.0000694042 6x in every 100,000 draws
#671 0.0000104106 Once in every 100,000 draws

So, your objective as a lottery player is to win.  Certainly, to win the game, you should not play a number combination that will not likely occur in any draw.  Therefore, knowing the exact number pattern with a high probability of occurring in a lottery draw is worth your time and effort.

I invite you to see the complete list of these number patterns inside the lottery analysis section.

There are 672 patterns in the Mega Millions 5/70.  My probability analysis shows that 6 of them come out the best, 15 are fair, and the rest are just lousy number patterns you shouldn’t bother to use at all.

How To Win Mega Millions 5/70 Game

Imagine. You play one of the bad 651 number patterns.  How much money are you putting in to go down the drain?

So, just because lottery should be played for fun doesn’t mean it’s a fair reason to waste money.

Remember that the lottery is your entrance to a world free of money worries.  It’s not the only way.  But, if you play with solid strategy, this could be one of the ways to have the best life you can ever have.

So play the lottery for fun.  But do it with a strategy and playing will be much more fun that way.

Here are my recommendations:

  1. Avoid the all-odd, and all-even combinations
  2. Focus on patterns #1, #2, #3, #4, #5, and #6 and avoid the rest of the patterns.

Along with the solid strategy, there are other things you should consider when you play.  One of them is to make sure you play the lottery responsibly.  It’s vital that you implement a lottery game plan to keep your spending going beyond your means.

Moreover, anyone could be at risk of lottery addiction problem.  Like I said earlier, the lottery is just a fun game.  Your gambling losses are merely the price of a good time, in much the same way as cinema tickets are the cost of the entertainment.

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Edvin Hiltner

I get a good grasp of mathematical theory through persistent learning. I get my inspirations from the works of Gerolamo Cardano and Renato Gianella in the fields of Combinatorics and Probability theory.

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