Why Does Antonius Run It Three Times?

You've seen the hand on High Stakes Poker: Jamie Gold hits his set of kings on the turn, but the king also fills up Patrik Antonius' straight. It's the biggest pot in the history of the show, $740,000.
"You wanna run it three times?" Gold asks Antonius, who agrees. We see it all the time on High Stakes Poker: players involved in big pots discuss how many times they should deal the remaining cards cheat poker.

Luck Evens Out But...

Twice, three times, four or even five times - anything is possible in a high-stakes cash game. But why are they doing it? Don't statistical fluctuations (aka luck) even out in the long run? We all know they do.
If you get the money in as a favorite, the positive expectation practically goes into your bankroll even if your opponent draws out on you in that particular hand. In the long run, the expected profits add up and bad beats are forgotten. Dealing it twice doesn't change your expectation.
So, what's going on here? "Are these big pros cowards or what...? I thought they were real gamblers." Why doesn't Antonius maximize his chances of winning the whole mega pot?
The thing is, the long run comes with a catch: it can be very long.

... How Long Is the Long Run?

How long is the long run, really? Well, the length depends on the size of the fluctuations, the variance. If variance is large (compared to the expectation) things will need more time to even out.
And in poker, variance is often very large.
In our example, Antonius has a 77% chance of earning $370,000 (half the pot). But he may also lose $370,000. His chance of that is 23%. His expectation in the pot (his EV) is $200,000.
If he played that same hand in the same way five times, he'd expect to earn one million dollars. Not bad, but even then there's still about an 8% chance he'd be an overall loser. Apparently, five repetitions is not the long run in this case.
But it's the biggest pot in the history of High Stakes Poker, so Antonius is not likely to play marked cards a similar hand very often, probably not five times during the whole season.
By splitting the pot in three parts and dealing a river card for each of them, Antonius' expectation is unchanged, but the standard deviation is about halved.
In a sense, by dealing it three times, the long run is made half as long.

When Risk of Ruin Is a Reality

Since dealing it twice or more doesn't influence the expected income, it involves no economic drawbacks in the long run. But it decreases the risk of losing the bankroll in a streak of negative variance (aka bad luck.)
If a pro loses his bankroll, he won't be around to enjoy the long run. The positive expectations from his great plays won't have time to add up. He may do everything right and still be put out of business.
That's probably why pros like to deal big pots several times. Even with their impressive bankrolls, losing $370,000 in one single hand is not without significance.
By the way, if you sit down at a poker table with $500,000, you're certainly a pretty big gambler by any reasonable definition.
And Patrik Antonius cannot be a coward. He's a Finn.