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.

From a statistical standpoint, this game gives you the greatest odds of winning.  Think of it as the blackjack of the Michigan Lottery.  A straight ticket (match the three numbers that are drawn, in order) gives you a 1 in 720 chance of winning.  Let’s look at a few ways to increase your odds and spend your money wisely.

Eliminate One Number

The payout for a straight ticket is $250.  You won’t be quitting your day job, but it’s nothing to scoff at.  If we take the approach of ensuring that we have at least on number right, we’ll need to buy 10 tickets that have each number, 0-9, in one spot once. To put it another way, we buy our first ticket with a 0 in the first position, our second ticket with a 1 in the first position, and so on.  At $0.50 each, we’ve spent $5.00 on our plan so far.

Let’s look at the numbers now.  Since we know we have one number right, we only have to match the other two (in order).  That puts our odds at 1 in 100, or in other words we’ve increased the probability that we’re going to win $250 by 7.2 times by spending an additional $4.50.  If we look at it from the standpoint of marginal gain, each additional $0.50 is buying us just shy of a 1x greater probability of winning.

Box 3-Way

Another ticket you can play in the Michigan Lottery is the box 3-way.  That means to win you still need to match all three winning numbers, but order no longer matters. So buying a 1-2-3 ticket, you’ll win with 1-2-3, 2-1-3, 3-1-2, 1-3-2, 3-2-1, and 2-3-1.  Just taking order out of the equation gives you an immediate boost to your odds of winning, which are 1 in 120.  The ticket is still $0.50, but the payout is significantly less at $83.  If you use the same method outlined above and eliminate one number, your odds rise to an impressive 1 in 45.

Eliminate Matched Numbers

If you look at the Michigan Lottery results, almost 70% of the Daily 3 winning numbers are unmatched. This means that picking 0-0-0 or 1-1-1 will significantly reduce your odds of winning.  Or, if we take it a step further, picking unmatched numbers will increase your odds of winning. Combine this little nugget of information with your box betting and number elimination and you’ll be well on your way to winning the Michigan Lottery