I just had a game of Random Draft and wanted to repick Phantom Lancer after Earthshaker and Bloodseeker were picked against us. I know that in some game modes such as All Random you can repick.
I am not sure whether I just didn't find the repick option quick enough, or if it is disabled in Random Draft.
Now, I just checked the Liquipedia and Gamepedia, neither has an article on repicking, nor lists whether repicking is possible for each mode in the Game Mode.
Which game modes in DotA2 allow repicking?
Best Answer
So, after creating a few lobbies against bots for science:
The repick button is located in the bottom left, above the map.
The following game modes allow repicking:
These game modes do not allow repicking:
Couldn't test the captain modes, as bots don't pick captains. ;)
Edit: I would assume though that all Captain Modes don't allow repicking, as that would make no sense.