This makes me think of the classic Monty Hall problem, where Monty opens a door and asks if you would like to switch or stay.. which is actually giving you info

This makes me think of the classic Monty Hall problem, where Monty opens a door and asks if you would like to switch or stay.. which is actually giving you information that the door opened was a goat (which he had to do if you picked the door with the other goat). So when try to understand "how long until the block is mined?" at t=10, you're given information that the block has not been mined yet and have to update your predictions, thus making the average time from t=10 another 10 minutes away. The hard part I have internalizing is if I were to make a progress bar for block mining, it would be totally useless because it'd always show 10 minutes away, until BOOM it hits 100% when a block is found (or someone else does). Then I had a realization that it's the wrong question to ask because the time is truly unknown, but instead we could show a "progress" bar of the percentile! So starts at 0.1%, then 5%, then 50% (median time whatever that is). Thinking this way becomes very intuitive, because now you're no longer wondering when it will finish, but instead are given a benchmark of survival time and can think things like "crazy, only 1% of blocks have taken more than 40 minutes to mine." and at the same time get the piece of mind of seeing something "progress" while at the same time being comfortable that it will never finish, until it does.