Game of Chance

Inspired by a book about statistics I'm currently reading, I did a few calculations about the lottery as it is played in Germany.

First the basics, so you can understand what I'm going on about. In the German lottery, 6 numbers out of 49 (numbers 1 to 49, obviously) are drawn each week. Having all six of those numbers is something a lot of people - including my parents - dream of. Inspired, as I already said, by that book, I started doing some simple calculations of my own about the chance of really having all the right numbers. Statistically, the chance for six right numbers is 1 to 13,983,816. Makes the so-called 'impossible' chance of "one in a million" look rather possible, doesn't it? Still, statistically, if every person in Germany played lotto, six of them should win (the population of Germany consists of about 88,000,000 people). But not all people are playing (I, for instance, don't) and life is not a statistic. There have been times when 12 or more people won and times when nobody has had the right numbers. That's real life for you.

Now I have been wondering - and calculating - what chance in percent you have for each of the six numbers drawn to be yours. This is what I found out (provided every time one of 'my' numbers was drawn):

• when the first number is drawn, all 49 balls are still in the machine; each number has a chance of 2.04 % and the chance of one of the numbers I bet on to be drawn is 12.24 % (as all six numbers are still in the machine)
• when the second number is drawn, 48 balls are left in the machine; each number has a chance of 2,08 % and the chance of one of the numbers I bet on to be drawn is 10.42 % (as five numbers are still in the machine)
• when the third number is drawn, 47 balls are left in the machine; each number has a chance of 2.13 % and the chance of one of the numbers I bet on to be drawn is 8.51 % (as four numbers are still in the machine)
• when the fourth number is drawn, 46 balls are left in the machine; each number has a chance of 2.17 % and the chance of one of the numbers I bet on to be drawn is 6.52 % (as three numbers are still in the machine)
• when the fifth number is drawn, 45 balls are left in the machine; each number has a chance of 2.22 % and the chance of one of the numbers I bet on to be drawn is 4.44 % (as two numbers are still in the machine)
• when finally the sixth number is drawn, 44 balls are left in the machine; the chance of each number and of one of the numbers I bet on to be drawn is 2.27 % (as only one of my numbers is still in the machine)

As you can see (if you survived that list of numbers I just wrote down), the chance of each number to be drawn is rising slowly and slightly, while the chance of one of my numbers to be drawn is descending really rapidly. In other words: the more of 'my' numbers are actually drawn, the smaller the chance to actually get one more of them.

If I were playing lotto, my little experiment with those numbers would put me off it really quickly, to be honest. But I doubt it would put my parents off. Hope springs eternal, as they say - and it's the last thing to die.

And the combination of human intelligence - as opposing to logic -, a hope and a little greed makes sure people still play lotto every week.