You understand that the number of times you run the board (the river card, in this case) doesn't change th EV of the situation, right? Whether they run it once, twice, or 15 times, the long term EV os the situation remains exactly the same. All running it more than once does is lower the short term variance by basically forcing the monetary results of the hand to be slightly closer to the actual equity each player has in the pot.
I would think the results of the running it three times alone would answer your question as to why Antonius would say OK.
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