Run it Twice?A variance-reduction techniqueby Lee H. Jones | Published: Oct 11, 2006 |
|
"You go back, Jack, do it again"
I can still remember the first time I watched a poker game in a casino. It was seven-card stud at Circus Circus in Las Vegas, and undoubtedly was some extremely low-limit game, progressing at a snail's pace. But back then, they might as well have been playing a combination of chess and rugby, for all I could understand what was going on.
I'm sure that many readers will chuckle at the above paragraph, recalling their own first experiences in (or watching) a live casino poker game. The players are speaking a dialect all their own, people throw money and/or cards toward the center of the table at seemingly random times. And then, occasionally, the dealer shoves the money in the middle toward one player. If you're like me, it was hypnotic, even though unfathomable.
If you're reading this column, you're probably well past that point, and the action around a poker table is as comfortable to you as your favorite pair of jeans. Side pots, out-of-turn action, change being made, and even the occasional prop bet changing hands doesn't faze you. But poker is a tricky beast, and occasionally something happens that makes even some of the "veterans" (by that I mean people more than 22 years old) scratch their heads.
This happened recently in a live game I was in at a brick-and-mortar poker room in a large casino. It was pot-limit hold'em, and a monster pot got built between two players – multiple thousands of dollars. One of the players was all in on the flop. Before the dealer could burn and turn the next cards, the all-in player said to his opponent, "Wanna run it twice?"
"Sure," his opponent replied.
I was tickled to see a couple of the iPod-and-headset kids take off their sunglasses and look closely. They had no idea what was going on, probably because it never happens online.
Before going into the mechanics of what happened at the table, let me give you a little background. In the old days, if a couple of players built a $4,000 pot with one of the players all in, they might have agreed to turn up their cards and let bystanders "insure" one of the hands. For instance, suppose the board is K 10 2. One player has K-10 and the other player has Q-J. The top two pair is almost a 3-1 favorite over the straight draw. But if the money in the middle represents all the money that the current leader has, he might not be eager to have a 25 percent chance of "going broke."
Enter the insurance man.
The insurance man, an uninvolved third party, might step in and say to the player with the top two, "I'll give you $2,500 for your hand." In short, he's providing insurance by buying the player's interest in the hand. If the dreaded straight card comes up, the player still has $2,500. Of course, since he's a 3-1 favorite in a $4,000 pot, he has $3,000 equity. But he might (1) not know what his true equity is, and/or (2) be willing to part with some equity to ensure having money in front of him when the river card comes out.
As you might imagine, this whole procedure was disruptive to the game. There might be haggling over a fair price, and multiple insurance men might bid for the hands. And there was nothing to prevent an insurance man from bidding on the hand that was behind at the moment, either. One could envision a clever insurance broker insuring both sides of the pot, paying $2,800 to one player and $900 to the other, and being assured of a $300 profit, no matter what happened.
Eventually, these antics were replaced with a much easier protocol: simply run out the hand multiple times.
Consider the same situation, but instead of all the haggling, they let the cards work it out. They might agree to run it three times. In that case, the pot is divided into three equal stacks. The dealer puts out a turn and river card. The winner takes one-third of the pot. The dealer pushes aside the last two cards, and burns and turns another turn-river pair. That winner takes the next one-third of the pot. The process is repeated a third and final time. Of course, it's possible that one player will win all three times, rendering the exercise pointless (it's the same outcome you would have gotten had you simply dealt the hand out). But oftentimes one player will get one-third and the other player will get two-thirds.
Just like insurance, this is a variance-reduction technique. It effectively brings the statistical "long run" closer. To take this to an extreme, you could run it 10 times for one-tenth of the pot each time. The more times you run it, the closer the net result will be to the actual equity that each player has in the pot.
Now, should you offer to run the hand out multiple times, or agree to do so if asked? That is totally up to you – as it doesn't change the mathematics of the situation a bit.
If you are playing a bit over your head in terms of the game's size, you might choose to do it so that you reduce the chances of losing your entire stack to one or two bad cards.
You might choose to do it simply to keep the game friendly and reduce the amplitude of the monetary swings.
Conversely, you might choose to say, "No thanks," if asked. Some players in big cash games count on being able to run the hands two or three times if they get all in. It makes them more willing to take a close gamble because they figure they aren't really risking their entire stack. If you have a reputation for being unwilling to run the hand multiple times, they might not want to gamble with you as much – because if all the chips go in, you force them to accept the results as they fall the first time.
Note that no player is under any obligation to run a hand multiple times. It doesn't change your expected win (or loss) a single bit; it simply changes the variance (the up and down swings). Say yes or no as you see fit, but at least now you'll know what you're discussing.
Oh – that huge pot-limit hand? They ran it twice. Each player won once. They split the pot in half and settled in for the next deal.
"All that excitement, no charge," said the dealer.
"Wheel turning 'round and 'round"
Lee Jones is the poker room manager for PokerStars.com, and is the author of the best-selling book Winning Low Limit Hold'em.
Features
From the Publisher
The Inside Straight
Commentaries & Personalities
Tournament Circuit
Strategies & Analysis
Humor