thanks all for your answers!
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Paraxis / [MENTION=6775031]Saelorn[/MENTION], it's the page 272 DMG stuff I was looking for... Since I'm not mastering, I did not read that (but our DM did not either...) anyway, that opens the route to a DEX based escape route as well.
this i don't understand, however: both the Tumble and Overrun rules say "as an action or a bonus action" - if you can use this as a bonus action, why would you ever use it as an action??
one important point here is that the rules make this a contest against your opponent, as opposed to 3.5/PF where tumble through enemy square was a DC15 acrobatics check, which at higher levels, at least for high dex characters, became trivial. Now the difficulty scales with the opponent, which is good, and the system is much flatter...
nonetheless, some answerers did suggest to just improvise an ability check - for those ppl: at what DC would you position this? 15? 20? higher, in the middle?
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sithramir: while I agree that you should never have an immovable guard blocking a door, i'm glad there IS the tumble option, as otherwise you would completely loose the monk's key feature of being able to weave between opponents using his DEX (if the only way out would be the STR based contest in the PHB).
V