Here’s the story. Suppose I wish to pre-roll a large number of results from the roll of 3 six-sided dice (perhaps I do not wish to bring the dice with me, for example). Say I roll one result, write it down on a blank card, and then generate another result.

If I have, said, recorded down 30 results, and stop for the day. The next day I roll the dice another 10 times and hence obtained 10 more numbers. Is it valid to add those 10 news results together to the set of yesterday’s results?

A variation: say I am using a computer to generate the numbers, using a pseudo-number algorithm. I am using a very good one, say from http://www.random.org. I generate one set of 30 results, and another set of 10 results … can I combine them together and derive the probability of each number from them?