Synchronisation

[[vL]Kp]

The "H" and "F" means "Roy/I saw a hit recovery animation on the screen".
Because roy used a manshield, I wasn't able to check the life. But as far as I know, the current life is always the same for both players. (I don't remember a situation where someone had e.g. 500 life but I only saw 450 life or something)

Although not realy helpful for the topic you wrote some interesting things about synchronisation in general (Now I know why monsters sometimes "jump" all the time from one square to another).

Do you have any idea why both of us saw a "hit recovery animation" but no damage was done? (These situations are the most curious facts)
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Are you sure Roy did a hit recovery and not a block? You may want to repeat the tests without any Mana Shields involved.

Life is synchronized, along with some stat information. It's sent in every game update, even if nothing else is going on. Mana is not synchronized, which has some odd side effects (especially related to the collapse of Mana Shield due to attacks). As Jarulf said, synchronization is poor at best. Hit recovery calculations are done on the target's system, which is why you can have warriors who are block-locked by a rogue who insists she isn't even shooting near them.

Diablo's random number generation is quite a mess, so I'm not at all surprised it got out of sync for your tests. Much of that mess could be cleaned up by sending the seed for each attack along with the attack notification itself. Then the players could at least agree on the outcome, though you'd still have runs of behavior.