Lotterycodex Mathematics Meets The Lottery

How to Win the US Mega Millions 5/75 (Ended October 2017)


NOTE: This article is about the probability analysis of the U.S. Mega Millions based on its previous 5/75 game format which officially ended in October 2017.  For the analysis that applies to the new 5/70 game rules, see the New U.S. Mega Millions 5/70 analysis page.

I’ve heard a lot of people, playing the Mega Millions with hot numbers, birthdates, lucky numbers, important dates of their lives, numbers given to them by their favorite fortune teller, etc., etc. I respect everyone’s style but I, for one, believe that Math is the best strategy to play the Mega Millions.

Today, I will explain to you how the Math works in the lottery, and I promised that you don’t need to have a math degree to understand everything.

how to win the us mega millions according to mathematics

The Odds Of Winning The US Mega Millions

There are 17 million playable combinations in the US Mega Millions. If we add the extra ball from 1 to 15, the odds of winning will become 1 to 258 million.

If you think about your odds in Mega Millions, your odds of winning the mayoralty position in Washington D.C. is way much better. So in short, it’s difficult to win a jackpot in the US Mega Millions. In fact, the U.S. Mega Millions is one of the lotteries with the worst odds in the world along with its sister the U.S. Powerball.

But you can improve your chances of winning if you stop using lotto playing techniques that don’t work and start using Mathematics instead. To increase your chances at the Mega Millions, you have to look at combinations differently. The key strategy is the number pattern.

To illustrate, let’s talk about simple odd-even patterns below.

Odd-Even Patterns In The U.S. Mega Millions

The odd-even number patterns play a vital role in your chances of winning the U.S. Mega Millions. The table below shows the complete odd-even patterns with their corresponding probability:

Patterns Combinations Probability
3-odd-2-even 5618376 0.325525757283427
2-odd-3-even 5462310 0.316483375136665
4-odd-1-even 2731155 0.158241687568332
1-odd-4-even 2509710 0.145411280468197
5-odd-0-even 501942 0.0290822560936395
0-odd-5-even 435897 0.0252556434497395
17259390 1

These odd-even patterns can be divided further into three groups:

Best Group Fair Group Bad Group
3-odd-2-even 4-odd-1-even All-even-numbers
2-odd-3-even 1-odd-4-even All-odd-numbers

My analysis shows that the best way to play the Mega Millions is either the 3-odd-2-even or the 3-even-2-odd patterns.

Let’s prove this mathematically.

Odd-Even Patterns According To The Actual Results of the U.S. Mega Millions

The table below shows the comparison between the expected frequency and the actual frequency. The data are based on the 353 draws of the actual U.S. Mega Millions draw from October 22, 2013, to March 07, 2017.

The expected frequency is computed by multiplying the Probability by 353 draws.

Expected Frequency = Probability x 353 draws

In the case of 3-odd-and-2-even patterns with the probability of 0.325525757283427, the expected frequency will be 115.

Expected Frequency (3-odd-and-2-even) 
= 0.325525757283427 x 353 = 114.910592321
or 115

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

Patterns Expected frequency in 353 draws Actual frequency in 353 draws
3-odd-2-even 115 128
2-odd-3-even 112 98
4-odd-1-even 56 58
1-odd-4-even 51 53
5-odd-0-even 10 8
0-odd-5-even 9 8
353 353

Probability estimation compared to actual U.S. Megamillions 5-75 results

The close match between expected frequency and actual frequency proves that the Mega Millions behaves in a predictable pattern. Hence, I say the lottery can be predicted to an extent. Fortunately, we can use Mathematics to determine the trending pattern. Thanks to Probability.

The 3-odd-2-even pattern is expected to appear 115 times, and it occurred 128 times in the actual draw. The 4-odd-1-even pattern is estimated to occur 56 times, and it’s just two counts away from the real draws. The 5-odd-0-even pattern demonstrates similar closeness in estimation.

If we use Probability to predict future performance, here is how I predict the U.S. Mega Millions in 1000 draws:

Patterns Probability Expected Frequency in 1000 draws
3-odd-2-even 0.325525757283427 326
2-odd-3-even 0.316483375136665 316
4-odd-1-even 0.158241687568332 158
1-odd-4-even 0.145411280468197 145
5-odd-0-even 0.0290822560936395 29
0-odd-5-even 0.0252556434497395 25

You can see the huge difference between the first and the last patterns.

As a U.S. Mega Millions player, you should put your money on those patterns that will give you the best chances of winning. In U.S. Mega Millions your best patterns are 3-odd-2-even or 2-odd-3-even patterns.

Remember, you play to win not the other way around. That is the basic idea of Probability Analysis in Lottery. But there’s more to the lottery than just odd and even. If you just look more deeply, you will find more intricate patterns that could be the key on how to win the US Mega Millions.

The Six Winning Patterns In Mega Millions

The U.S. Mega Millions are divided into three groups.

Group Patterns Number of Patterns
Best patterns Patterns #1 to #6 6
Fair patterns Patterns #7 to #196 190
Bad patterns Patterns #197 to #792 596
792 total patterns

From the table above, the best patterns in Mega Millions are patterns #1, #2, #3, #4, #5, and #6.

Pattern #1 has a probability of 0.0057939475 which means this pattern occurs approximately five times in every 1000 draws or approximately once in every 200 draws. Patterns #2, #3, #4, #5, #6 exhibit the same value of probability.

Based on the table above, there are 596 bad patterns in U.S. Mega Millions. Playing with these bad patterns are just waste of time and money.

The problem, almost 80 to 90% of the US Mega Millions of players, are not aware of the patterns they are playing. For example, players waste money on the following patterns:

Pattern Probability Expected Occurrence
#788 0.0000086909 8x in every 1,000,000 draws
#789 0.0000086909 8x in every 1,000,000 draws
#790 0.0000078218 7x in every 1,000,000 draws
#791 0.0000073004 7x in every 1,000,000 draws
#792 0.0000003476 3x in every 10,000,000 draws

The complete list of the U.S. Mega Millions number patterns is available for free here.

If you are playing the US Mega Millions without knowing the probability of your patterns, there is no guarantee you are not incidentally playing with pattern #788 or #790 or #792.

So with Mathematical strategy, you get two advantages:

1. You save money
2. You increase your probability of winning

How To Play US Mega Millions To Win

Some patterns will never appear, and they are so numerous to list here. The best thing you can do is to avoid them simply. Access to the lottery analysis is free so just check the complete list of patterns and play smart.

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.

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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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