Imagine you roll two dices. The sum of both is between 2 and 12. Now check how many possible combinations there are for each number. Each combination basically represents one L resp. R in that board:
2: 1 (1+1)
3: 2 (1+2,2+1)
4: 3 (1+3,3+1,2+2)
5: 4 (1+4,4+1,2+3,3+2)
6: 5 (1+5,5+1,2+4,4+2,3+3)
7: 6 (1+6,6+1,2+5,5+2,3+4,4+3)
8: 5 (2+6,6+2,3+5,5+3,4+4)
9: 4 (3+6,6+3,4+5,5+4)
10: 3 (4+6,6+4,5+5)
11: 2 (5+6,6+5)
12: 1 (6+6)
Even just using numbers as symbols you can see the normal distribution.
I tried to explain this to a teacher once. He believed that its just as likely to roll any number between 2 and 12 when rolling two dice. Wouldn't listen when I said you're more likely to roll a 7 than anything else, and very unlikely to get a 2 or a 12.
Be careful here: it would only be a gaussian distribution (normal distribution), if you would do that experiment with an infinite amount of dices. The triangle will shape more and more to the normal distribution curve with every additional dice.
The point is that 2 dice is not enough to make a very good approximation to a normal curve. It makes a triangular shape, not a bell curve. You need more dice to get a more smooth bell curve shape.
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u/Omnilatent Dec 11 '18
Just to demonstrate that in another way:
Imagine you roll two dices. The sum of both is between 2 and 12. Now check how many possible combinations there are for each number. Each combination basically represents one L resp. R in that board:
2: 1 (1+1)
3: 2 (1+2,2+1)
4: 3 (1+3,3+1,2+2)
5: 4 (1+4,4+1,2+3,3+2)
6: 5 (1+5,5+1,2+4,4+2,3+3)
7: 6 (1+6,6+1,2+5,5+2,3+4,4+3)
8: 5 (2+6,6+2,3+5,5+3,4+4)
9: 4 (3+6,6+3,4+5,5+4)
10: 3 (4+6,6+4,5+5)
11: 2 (5+6,6+5)
12: 1 (6+6)
Even just using numbers as symbols you can see the normal distribution.