This question mentions "running it twice" - I can infer the basics, but can someone define exactly what this means, and how (and why) it happens?
The two players may:
Player may do this to try to reduce the variance impact of very large pots on their win rate.
Basically, if a player is all-in at some point during the betting, the other player can offer to run it a number of times e.g. twice.
If they decide to run it twice, then the pot is divided in half and awarded to the winner of each "run". A run, is the rest of the cards still to come - so if you've already seen the flop then this is the turn and river. If the play went all in on the turn, then it's just the river. If the player went all in pre-flop then you'd seen an entire board twice.
Similiarly, if you run it 3 times then the winner of each run gets a third of the pot.
Running it multiple times helps with combatting variance. Whilst you should win a particular situation say 9 out of 10 times (because of the outs), by running it twice, it is far less likely that you'll lose the whole pot on some freak outcome. In a situation where things are very close e.g. a coin flip after the flop, then by running it twice, there is a reasonable chance that both players will win half the pot each - which reflects the odds. It means that your winnings more closely match the probabilties of the situations you end up in, and not just on the particular outcome of that particular hand.
Hope that helps.
Running it twice usually happens when one player is all in and there are still some cards that have not been dealt yet. The two players discuss the terms of their agreement and then the rest of the cards are dealt multiple times.
The pot is split up according to how many times the cards were run, IE half if running it twice, thirds if running it three times, etc. Whichever player wins the particular set of cards wins that portion of the pot.
It is a way of smoothing out the volatility. A player with a huge hand is not going to lose quite as much on average on those rare occasions when he gets beat. A player with a long shot has a slightly better chance of taking away some of the pot.
The reason it happens when one player is all in is because in that case the cards have been shown. Part of the agreement is knowing in advance who is ahead/behind and what the odds are.