Odds of Winning the Lottery

Your odds of winning the lottery are absolutely zero if you don't play, and nearly zero if you do. States advertise much higher odds than what is mathematically possible, and this serves as encouragement for you to play and donate your hard earned money to them.

Giving away my money isn't my idea of frugal living, and it shouldn't be yours either, but you have to decide for yourself.



My advice is don't waste your money on the lottery, and don't believe what you're being told by the lottery commissions. It is in their best interest to make the lottery as appealing as possible. I've e-mailed the lotteries in California and Delaware to ask them how they calculate the odds of winning the lottery.

When they reply, I'll post it here. I'm not holding my breath. It's been months and they haven't replied.

In the meantime, find out how you can calculate your odds of winning the lottery, so you're prepared to defend yourself against the false advertising coming from our government.

The lottery is just a numbers game. Figuring out the odds of winning a "numbers game" is a little number game in itself. The math involved is relatively simple. I learned it as Combinations in high school.

A simple example

The odds of selecting a number that was previously selected (random or otherwise) out of a number set of 0 to 99 is one out of 100. We know this intuitively.

Here is the "strong arm" approach to figuring this out: If you count starting with the number 0 until you reach 99, that gives you 100 possible numbers (99 positive numbers, plus the number 0).

If you need to "pick" a certain number in a lottery, then your odds of winning the lottery are 1 chance out of 100. But how is that expressed mathematically? Simply like this:

There are two positions for numbers to be in this number set of 0 to 99. We learned these as the 1's column and the 10's column. Let's look at the first ten numbers and the last ten numbers that occupy these "columns" so we know how they are expressed. They are:

First ten: 00, 01, 02, 03, 04, 05, 06, 07, 08, 09

Last ten: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

You can see that not all of the numbers have a positive integer in one of the two positions where a number can be. Sometimes the integer is zero.

Therefore, in a lottery where you have to match an unknown number from 0 to 99, you are really guessing from 00 to 99. Remember there are two positions to consider; one place for the first digit, (the 1's column), where we can put any number from 0 through 9, And, and one place for the second digit, (the 10's column), where we can put any number from 0 through 9.

To solve the simple example above, we ask ourselves: How many possibilities are there for the first position? The answer is 10 (0 through 9). Now we ask: How many possibilities are there for the second position? The answer is also 10 (0 through 9).

So, we multiply the possibilities together (10 times 10), and that gives us 100, the same odds we figured out by the "strong arm" method. Again to figure your odds of winning the lottery, you simply multiply the number of possibilities for each position by each other.

Note: since numbers are not duplicated in a lottery draw, we need to make certain to reduce each successive number in the equation by 1 to eliminate exaggerating the odds by including duplicate numbers.

Real examples

California has a game they call Fantasy 5. You pick five numbers out of a data set that starts with 1 and ends with 39. They call it the "Better Odds Lottery Game", so we should have better odds of winning the lottery. Yeah, right!

They say the odds of winning are 1 in 575,757. I'm a bit skeptical, so I'll do the math.

Winning the lottery requires that my five numbers match exactly to the randomly drawn numbers, so that's a possibility of 39 different numbers in the first of five positions. Since we can't duplicate numbers, that leaves only 38 different possibilities for the second position, 37 in the third position, 36 in the fourth position, and 35 in the fifth position.

So, the possibility of winning by matching all five numbers is "1 in" 39 times 38 times 37 times 36 times 35. And, that equals 1 in 6,909,840. That's a lot less likely than what they said it would be, isn't it?

They claim that your odds of winning the lottery are roughly a 1 in 600,000, but the true odds of winning are roughly 1 in 7,000,000. How can they be off by a factor of 10? It doesn't matter to me, it only tells me that I'll not be one to be induced to play their game; not with the kind of math they're using.

The odds of winning the lottery they call the Mega Millions game is even more of an imagination stretcher. This game requires you to match 5 numbers from 1 to 56, and they say your odds are 1 in 3,904,701.

I'll bet you it's just another fib to get you to play. I did the math and the chances are 1 in 458,377,920. Again, they're not consistent with my calculations, but this time they're off by a factor of 100. Could that just be a mistake or are they playing a "numbers game" behind the scenes?

Please understand from this example that your chance of getting the exact 5 number combination is less than the chance of you randomnly picking the same name (that someone else also randomly picked) out of a comprehensive stack of phone directories that include the names of all residents of all ages of both the United States and Canada.

One last example of your odds of winning the lottery. The Mega Millions game has nine ways to win. One of the ways is getting the Mega number only. For this, the winner must "hit" the same 5 numbers that are randomly selected from a field of 46 possibilities (numbers 1 through 46).

In other words, you select 5 numbers from the number set 1 to 46, with no repeats. They say the odds of winning are 1 in 75. Do you believe it? Multiply 46 times 45 times 44 times 43 times 42, and that will be your "1 in" so many chances number.

Just the number 46 multiplied by 45 is 2070, so do you think factoring in the other 3 two digit numbers is going to get us closer to or farther away from 75? Does the number you come up with look anything like 75? I didn't think so.

Now, what do you think about your odds of winning the lottery? How about your odds of getting a straight answer from those who run the lottery? I probably have a better chance of winning the lottery.

If you're focused on frugal living, you'll stay away from scams like these.

Done with Odds of Winning the Lottery, take me back to Powerball