I noticed patterns in actual dice rolls as well. It seems that often after a 6 is rolled, a 1 will come next, or vice versa. Also, 3 and 4 seem to be more popular than any other number for some reason. When I roll the dice, I drop the dice into a tin (dice can land in any position at the bottom of the tin). Then I place a lid on the tin and shake the tin (more randomization). I remove the lid and drop the dice onto the floor so that it bounces before coming to rest. Yet despite all that, I still see the patterns mentioned above.
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