Quote from: justusranvier on March 06, 2015, 06:48:28 PM

Quote from: CIYAM on March 06, 2015, 06:42:37 PM

Sometimes the blocks can take more than one hour to solve (so we aren't just talking about those getting solved quicker).

The average is 10 minutes but there can be quite a bit of variance.

Variance should average out over time.

For every block that takes an hour, there should be one that takes a few seconds.

Encountering each case should be equally likely.

Hopefully someone who can explain the reasoning will show up here and explain why it works out the way it does.

If I walk into the room with the guy rolling the die, it's equally likely that he just rolled a 1 as it is that he just rolled something other than a 1, and yet, the average number of rolls until the next 1 is still 6 (regardless of whether he just rolled several 1's in a row or he hasn't rolled a 1 in the last 36 rolls).

I think there are probably a few effects in play here, but one that I notice right away, is that you are assuming that "average of 10 minutes" means "pretty close to 10 minutes most of the time". Then in your mental image, you are assuming that if you are 7 minutes after the most recent block, you are somehow "closer" to the next block than the previous block. Of course, if you are 7 minutes after the most recent block, then you can eliminate from your average all blocks that are less than 7 minutes apart (since if the next block was going to be 5 minutes, for example, after the previous one then it would already have happened and you'd really only be 2 minutes since the previous block)