Let’s do a little experiment. Get a six-sided die and roll it. Then write down the number on the top of the die. When I did that, I got 3. Now roll the die again and record its number. I got 2. Roll it 98 more times, recording all the results. I got 2, 6, 4, 6, 6, 2, 6, 4, 5, 1, 3, 3, 1, 5, 6, 6, 6, 5, 6, 1, 3, 1, 6, 5, 4, 1, 2, 4, 4, 2, 4, 1, 2, 6, 6, 5, 1, 1, 2, 4, 6, 3, 3, 1, 4, 6, 5, 3, 2, 4, 3, 3, 6, 2, 6, 4, 1, 3, 3, 3, 3, 1, 2, 5, 6, 1, 3, 2, 5, 6, 5, 4, 2, 6, 3, 3, 4, 3, 1, 5, 4, 3, 5, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 3, 2, 6, 5, and 2. Finally, add up all the numbers. My result was 339. I’ll bet your total was close to 350 too. If you do the experiment again and again, you will get a number close to 350 every time. This isn’t guaranteed, but it is very probable.
Now, let’s play a game. First, you give me $200. Then I’ll roll a six-sided die 100 times and add up the results. I’ll pay you that many dollars. Since you know that the sum will be close to 350, you are expecting that you will win about $350 with this gamble and make a profit of close to $150. So you give me $200.
I roll the die 100 times, and 7 of the rolls are ones, while the other 93 are twos. I add up all the numbers and pay you $193. Then I ask you if you want to play the game again.
You might think this was a fluke, and you want to win your money back, so you give me $200. This time, when I roll the die 100 times, 96 of them are ones, and the other 4 are twos. I smile and pay you $104.
By now, you are starting to think something’s up. With a hammer, you break the die and look inside it. Lo and behold, there are heavy weights glued to two of the sides so that it’s more likely to roll a one or a two than any other number. You turn to demand your money back, but I have already left the country.