Winning the lottery - what are the odds?

Computing the chances of winning the lottery is not that difficult. Anyone who regularly plays the lotto should think carefully about where he can make the most of his money. First of all, let us consider the mathematical probability of a first prize in the lottery (all main numbers) and the jackpot (all main numbers plus the jackpot number(s)). For the sake of simplicity, we will ignore all minor winnings in our calculation.

Mathematical formula to calculate the odds of winning the lotto

The probability of winning the lottery is the value of 1 divided by the number of possible combinations of numbers. The number of possible combinations of numbers will be calculated using the so-called factorial, also called n. The (simple) factorial of a number is obtained, when the number is multiplied by all integers that are smaller than the number itself

Example: Factorial of 5 - written as 5! = 1 x 2 x 3 x 4 x 5 = 120

In order to calculate the possible combinations of numbers a lotto where 6 out of a total of 49 are drawn, we would use the following formula:

49! / (6! · 43!) = 13.983.816

This means that the chance of having the 6 correct numbers out of 49 possibles is equal to approximately one divided by 14 million. If you assume that you need to hit one extra number between 1 and 9 to win the jackpot, then the odds to win the jackpot would be one in 125,854,344 (13,983,816 x = 9).

Here is a table with a calculation of winning chances for the major lotteries:

Which lottery has the best chances of winning?

Now that anyone can play all the big international lotteries online, you can compare and pick the best lotto jackpots from the list on the right side on our website. So far we have dealt only with pure probability - but there is an extremely important additional factor, namely the so-called winning expectation. Not all lotteries have the same level of prize money.

Some lotto events pay out a large part of the amount that they take in, some payout only much less. Most state lotteries finance from various things from the lottery proceeds. In a best-case scenario, the money is used for social and charitable programs, or the state simply considers this money as a kind of state revenue, but in some cases, the lottery companies also serve as a refuge for former politicians and party members who are given lucrative executive positions. Their salaries need to be paid from the lottery revenues of course ... This is, unfortunately, common practice in many countries.

So if you want to calculate your winning expectations, it is clear that this depends on three factors:

the number of possible combinations of numbers the cost of buying a ticket (in the table you will find the price of an online ticket) the potential gain (here, for simplicity, we are using the average jackpot only)

The mathematical expectation of winnings for the Lotto jackpot will be calculated as follows:

Amount of the lottery jackpot, divided by the possible combinations of numbers, divided by the cost of a ticket.

The expectancy shows in the above table as a percentage (see the last column on the right). The higher the percentage, the more "economic" the lottery. The best lottery winning chances from the player's perspective is the one with the highest percentage.

As you can see, the two major U.S. lotteries, Powerball and Mega Millions, offer much higher winning expectations than the others, even with a 50 Million jackpot. Despite the higher price for an online ticket, your chances are better here than your local lotto. If the jackpot were higher than in our table, your chances would be even better. For example, with a jackpot of 200 Million at Mega Millions, the winning expectation would be approximately 37% - compare that with what your local lotto offers!

It should, therefore, be quite easy to understand that it always makes more sense, for example, to spend 5 or 7 dollars to buy an online lotto ticket for an American lottery, when the jackpot is 15 times higher than your local lotto.