What is the expected time until the next block is found? https://bitcoin.stackexchange.com/a/3908/659 says:


  Luckily, you'll only have to wait five minutes on average for a block to be found (blocks are one every ten minutes, so the expected delay until the next block is five minutes).


Upon reading it, I instantly felt that this was incorrect, and that the expected time until the next block is always 10 minutes (assuming the network hash rate matches the current difficulty).

If the blocks were generated exactly every 10 minutes, than it would be true that the expected time would be 5 minutes, but they're not.

So what's the real expected time?  Please make a plausible argument for why it is so.
10 minutes. Assuming, as you say, that the current network hashrate matches the difficulty - otherwise it is proportionally higher or lower.

Block finding is a Poisson process. The rate parameter λ is chosen so that 2016 blocks on average are found every 2 weeks, and since in such a process the expected number of events is proportional to the time span, it means λ is 1/(10 minutes).

The time until the next event (the next block found in our case) follows the exponential distribution with mean 1/λ, which is 10 minutes. This distribution is memoryless - the amount of time spent waiting for a block has no effect on the amount of time left to wait. When a block is found the expected time until the next block is 10 minutes (which is intuitive), and it is also 10 minutes at any other time.

If blocks arrived once every 10 minutes like clockwork, the expected time until the next block at a random point would be indeed 5 minutes - but then we wouldn't have to worry about expectations, we'd know exactly when the next block will be found.

In the future, the decreased generation reward might cause the total hashrate to fluctuate as transaction fees accumulate, causing reduced variability in block finding times, and reduced expected waiting time.