> investigating dice rolling patterns
A friend showed me a dice rolling game where you roll a bunch of dice and add up the values. I mentioned that if you roll enough dice and add up all the values, at some point it gets a lot less “random”.
And result turned out "true"? Rolled a die for 2500 times and the sum is all around 8500! I wonder what would be the results for 25/250 times? So, this is sum(expectations).. and for rolling a die, it is 3.5 [(1+2+3+4+5+6)/6 => 21/6], so the answer was 3.5 x 2500 = 8750. Should hold good for all numbers relatively large.
This is a classic illustration of the Central Limit Theorem--in fact, the example is even on the Wikipedia page [0]. The distribution tends towards a normal distribution as n increases (though to actually take the limit you need to rescale).
> investigating dice rolling patterns A friend showed me a dice rolling game where you roll a bunch of dice and add up the values. I mentioned that if you roll enough dice and add up all the values, at some point it gets a lot less “random”.
And result turned out "true"? Rolled a die for 2500 times and the sum is all around 8500! I wonder what would be the results for 25/250 times? So, this is sum(expectations).. and for rolling a die, it is 3.5 [(1+2+3+4+5+6)/6 => 21/6], so the answer was 3.5 x 2500 = 8750. Should hold good for all numbers relatively large.