How many dice rolls until things even out?

How many times would you have to roll 2 dice (2d6) until they started to match their probability averages? In other words, I could roll snake eyes (total 2) five times in a row, but how long until the rolls begin to get closer to the probability averages?

2d6 total	probability occurring
2	2.78
3	5.56
4	8.33
5	11.11
6	13.89
7	16.67
8	13.89
9	11.11
10	8.33
11	5.56
12	2.78

Based on the Wizard's response to previous "dice influence test" questions, I suspect 3,600 rolls should produce a relatively uniform distribution most of the time.

Read the article on the WoO site here (scroll down to the question with the large graph.)

Quote: Ayecarumba

Based on the Wizard's response to previous "dice influence test" questions, I suspect 3,600 rolls should produce a relatively uniform distribution most of the time.

Read the article on the WoO site here (scroll down to the question with the large graph.)

Just ran a quick simulation, and 3600 didn't always get very close. The Chi-square test frequently produced percentages well over 50%.

Quote: Joseph

How many times would you have to roll 2 dice (2d6) until they started to match their probability averages? In other words, I could roll snake eyes (total 2) five times in a row, but how long until the rolls begin to get closer to the probability averages?]

Bold emphasis added.

I haven't thought this through, but is the key issue the wording "started to match" and "begin to get closer"? Doesn't this tendency start right away? No, it doesn't get closer with every roll from roll #1. Some rolls take the data farther from the theoretical. Even after a million rolls, each roll makes the observed percentage of each number either increase or decrease, taking it either closer or farther from the theoretical, not always closer, but that's the tendency from the very beginning, isn't it?

Did I misunderstand the question?