"Secrete" Math in Australian Lottery

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Everyone wants to be a millionaire. One of the easiest ways to achieve this goal is through winning a lottery. In Australia, lots of people do have this dream. But have you ever considered about the probability (in mathematics) to win the first division?

Let me take the Saturday’s lotteries (Monday and Wednesday’s are same) as an example to illustrate this. In this lotto, you need to choose 6 numbers from 45 numbers. If all match, you will win the first division.

For each game you buy, the probability to win will be calculated as:

P = (6*5*4*3*2*1)/(45*44*43*42*41*40) 

After calculated, P =0.0000001227738 

In other words, you have a 1 in 8,145,060 chance of winning the lottery.

If you are rich enough, you can buy 8,145,060 games and you buy them in “Megapick” (each has 36 games). For each Megapick, you need pay $23.90 to a Newsagency.

So the total cost = 23.90 * 8145060 / 36 = AU$5,407,414.83 

That is about $5.4 million. The New Year eve’s (31 December 2011) lottery is 31 million. So if you were the only winner, it would be a very profitable game, because you would make a profit of 25.6 million dollars.

Unfortunately for  the fact is that for the New Year eve’s lottery there were 32 winners and each them can only get $968,750.00. If you bought 8,145,060 games as mentioned above, you would lose about 4.43 million dollars. So it’s not a good business for buyers.

Since each winner has a 1 in 8,145,060 chance of winning, we can roughly estimate how much the lottery company and Newsagencies can make from this time.

5.4 million * 32 = 172.8 million dollars.

Obviously it’s a very good business for them.