Michigan Lottery

There’s a lot of confusion out there when it comes to calculating the odds for winning in different lottery systems and games.  The problem is, there’s no on-shot way to figure out all the small variations in the games, but people still want to use the only system they know how, which is usually the “multiply the chance of guessing one number by the next, and the next”.  This works for basic systems, but not all.  Let’s take a look at a basic system.

Our baseline from the Michigan Lottery games will be the Michigan Lottery Daily 3.  A “straight” ticket means you have to pick three numbers, in order, and the pool of numbers continually replenishes itself.  By that, I mean that you could draw a “1″ three times in a row.  When you get into some of the bigger games that’s not always the case.

It’s pretty simple to figure out that our chance of drawing any one of the ten numbers on the first try is 1 in 10, or 10%.  Now, since order maters, to get two correct numbers we need to factor in our chances of drawing the first one correctly, which we already know to be 10%.  Since the chance of drawing the second number correctly is also 10%, all we need to do is multiply the two probabilities by each other to come up with our overall odds, 1 in 100 or 1%.

To continue down the line we simply continue to multiply.  We find our chance of picking the winning number is 1 in 1000.  Pretty good odds in the lottery world.

Let’s look at this another way, though.  If we play the Daily 3 with a ticket called a box 6-way, that essentially means we’ve picked three different numbers and can win if they are picked in any order.  So, a ticket with 1-2-3 will win if 1, 2, and 3 are drawn in any order.  The 6-way comes from the fact that there’s 6 different ways 3 numbers can combine to form a unique group.  If we had four unique numbers, they could combine in 24 different ways.

So the way we calculate order-irrelevant tickets is to find the number of different possible combinations for that set and divide the ordered probability.  For a Daily 3 where order doesn’t matter, that means we start with our probability of 1 in 1000, and divide it by 6, giving us a 1 in 133 chance.

We’ll delve into some more complicated systems in the next post.