Lottery Probability

Step 1: Identify The Basics

To work out the exact odds of any lottery requires two things: the total amount of balls that appear in each draw, and the range of numbers that players have to choose from.

With these two bits of information you have everything you need to calculate the odds, except a calculator of course.

Step 2: Crunch The Numbers

The process is simpler than you may have expected, but it does take some big calculations.

To better explain the process, we'll be using a number of examples. If you have a lottery with 6 balls ranging between 1 and 50, you would proceed as follows:

Equation 1: 6/50 = 0.12 (this is the likelihood that one of the first 6 picks will match with your first number)

Equation 2: 5/49 = ~0.10 (this is the likelihood that one of the 5 remaining balls will match with your second number.

Equation 3: 4/48 = 0.08 (the probability of ball 4 matching your third number)

Equation 4: 3/47 = ~0.06 (probability that the 3rd remaining ball will match your fourth number)

Equation 5: 2/46 = ~0.04 (probability of one of the last two picks matching your fifth number)

Equation 6: 1/45 = 0.02 (the likelihood of the final pick matching your last number).

Note: ~ means an approximation 

If you had a 7 ball lottery with numbers ranging between 1 and 60, you would do the following equations:

7/60
6/59
5/58
4/57
3/56
2/55
1/54

Essentially, your first equation is the highest available number in the lottery's range divided by the total amount of balls that are drawn, then proceed down in a descending order until you reach number 1.

Step 3: Probability

To find your overall chance of winning, simply multiply the results of all the equations made in Step 2 together, and this will give the probability of claiming the jackpot.

For our example, the answer would be ~0.0000000629.

Step 4: Tell Me The Odds

The final step is to simply divide the number generated in Step 3 by 1.

1 / 0.0000000629 = 15,890,700

Therefore the odds on you winning a 6 ball lottery with a number range of 1 to 50 is 1 : 15,890,700

What About Bonus Balls?

So, most lotteries have one or two bonus balls to factor in when working out your odds. While it's a little more time consuming, it's not difficult once you know how.

Returning to our 6 ball lottery with a number range of 1-50, you would repeat Step 2 again, just as before.

Then you would need to work out the bonus ball equation based on how many there are per draw, and what numbers are available to players.

For this example, we'll base it off the Eurojackpot draw, meaning players make 2 picks between 1 and 10.

Bonus Ball Equation 1: 2/10 = 0.2

Bonus Ball Equation 2: 1/10 = 0.1

Then simply repeat Step 3 and 4 to give the final odds.

For a great breakdown of the various lottery bets available on Lottoland, including the ones with the best jackpot odds, check out our lottery alternatives review.