Originally Posted by shrtstakatak
Where is the advantage and when is it allowed?
Most of the other questions have been answered above, so I'll just address this part.
I don't know that you'd call it an 'advantage' as such.
For the player that's behind, it gives them additional chances to catch the cards they need to finish with at least some of the pot. For the player that's ahead, it reduces the chances of one suckout taking all their money: they may have slightly reduced their chances of winning the entire pot, but they've greatly increased their chances of taking at least some of it.
So it's mostly intended to reduce variance. The more times you run the same situation, the closer in theory you get to the statistical norm for that situation. If a hand was 80% to win when the money went in, it still has 80% equity in the total pot (it can be affected slightly depending on the number of times it's run and whether it's done preflop, on the flop or on the turn, but it'll still be in the same ballpark) and in the long run can expect to take the money 80% of the time.
You can only really do it in cash games, as the only parties affected by it are those in the pot and it's (relatively) easy to get consensus on whether it's going to be allowed for this hand and how many times to run it. In a tournament, in theory everyone
at the table (or indeed in the field) can be affected by the outcome and getting agreement would be nigh impossible, so it's just not done.
If you're in a casino, it's usually only the higher stakes games that allow running boards multiple times.