How long does a modern computer need to simulate a random chess game?

By a random chess game, I mean a chess game simulation where each player picks a move uniformly at random in their turn until the game ends. In order to simulate such a game, the computer needs to find all possible moves at any given state of the game and chose one randomly in each turn.

Such a simulation is needed in many Monte Carlo Tree Search algorithms (in default policy) and since these algorithms are very successful lately, I think it must be fast. But how fast exactly?

Note: I have programmed one that lasts 0.065 seconds on average using a single thread.