In poker cash games it is customary to run the board twice when two or more players are all-in and plenty of money is on the line.
Under which circumstances is running it twice advantageous? Does it benefit the player who is ahead or should the player with a draw insist on running it twice? Does it increase or decrease the probability of winning? How does running it twice impact profits in the long run?
We want to address these questions in detail in this article.
TL/DR: For the impatient readers, those are the answers to the questions:
- Running the board multiple times reduces variance.
- The expected value does not change at all when running it twice or more often.
- In general, weaker players should insist on running it only once, while stronger players benefit from reduced variance and multiple runs.
How Does Running it Twice work?
Let’s take a look at a simple example: Two players are all-in on the turn with the board showing Q♦8♦6♠5♣. They are holding the following hands:
- Player A: Q♥Q♠
- Player B: J♦T♦
Player A has a set and Player B has a straight flush draw and exactly 10 outs (any diamond except the Six and Five and any Nine).
If the players agree to run it twice, the river is dealt twice. If Player A wins both times, he gets the entire pot. Likewise, if Player B wins twice, he gets the entire pot. If Player A wins once and Player B wins once, the pot is split.
Occasionally, players may also agree to deal the river three or four times, and the pot is divided according to the number of their respective wins.
It is also possible to deal the turn and river on earlier betting rounds or even the entire board two or more times when going all-in before the flop.
What Exactly Happens When Running it Twice?
The reason for dealing the board multiple times when going all-in is simple: It reduces the chance of losing the all-in and increases the chance of winning a portion of the pot.
Let’s take the above example. Player A has the lead, but Player B has 10 outs. This means that Player B has a chance of winning the pot of 22.7% if the board is only dealt once.
If the river is dealt once, there are two possible outcomes:
- Outcome 1: Player A wins (77.3%)
- Outcome 2: Player B wins (22.7%)
However, if the river is dealt twice, there are three possible outcomes:
- Outcome 1: Player A wins both times (59.3%)
- Outcome 2: Player B wins both times (4.8%)
- Outcome 3: Each player wins half the pot (35.9%)
For Player A, it is now much less likely that he will lose the entire pot, and for Player B, it is much more likely that he will at least win half of the pot.
For both players, a running it twice is a form of insurance: both accept the trade-off of winning the entire pot less often, for a reduced risk of losing the entire pot.
Does the Expected Value Change When Running it Twice?
The expected value always remains the same for both players, regardless of whether they run it once, twice or many more times.
Let’s take the above example again. Assuming there is $10,000 in the pot. If the river is dealt only once, Player A wins $10,000 in 77.3% of cases, resulting in an expected value of:
If the river is dealt twice, Player A wins $10,000 in 59.3% of cases and wins $5,000 (half the pot) in 35.9% of cases. This has an expected value of:
The calculations work the same for the expected value of Player B. If the EV of Player A remains the same, that of Player B must also remain the same.
Even if the river is dealt three, four, or ten times, the expected value does not change. Let’s simply assume the river is dealt ten times in the example. These are the probabilities for the different outcomes:
|# of wins for Play A||Probability|
Adding up the expected values again leads to the aforementioned $7,727.
Is Running it Twice Worthwhile?
Should the underdog seek a run-it-twice or does it benefit the player who is ahead?
In fact, dealing the board multiple times neither helps nor harms any player – at least not from the perspective of EV and long-term winnings.
However, the underdog significantly reduces his chances to land suckout. Take a look at the above example: Without running it twice, the player with the draw had almost a 23% chance of winning the entire pot. When running it twice, the probability of him winning the entire pot is less than 5%.
On the other hand, his probability of a complete loss has decreased from over 77% to under 60%.
The purpose of running it twice is solely to reduce the variance of the players. If you want to learn more about variance, check our variance calculator and read about the impacts of variance in cash games.
Simply put, run-it-twice halves the variance and makes it easier to win consistently in the long run.
From this, a simple conclusion follows: If you consider yourself the better of the two players, you should try to run it twice, but if you consider your opponent to be better, you should prefer to have the board dealt only once.
This pattern applies to almost all variance questions in poker: weaker players should welcome variance because a lucky punch is the best they can achieve in the long run. Stronger players, on the other hand, should seek ways to reduce variance to play closer to their (positive) expected value.
Dont use run it twice online
A side note: Some casinos or online providers charge a small extra fee for running it twice. In this case, it is definitely not worthwhile to use it. Because ultimately, you still reduce your expected value (even if only minimally) with the fee.
Running it Twice: Showing the EV does not change
It may not be entirely intuitive that running it twice does not change the expected value at all.
A possible objection is, for example: What if I’m all-in with a flush draw on the flop and both, turn and river complete my draw in the first run. Won’t I be missing that one unnecessary out in the second run?
While it is true that the probability of hitting the flush in the second run is lower when two outs are dead, at the same time the probability of hitting the flush is higher when no outs were drawn in the first run and all outs are still in play.
Let’s take a simple example of running it twice on the turn and river and calculate the probabilities in detail to see that the expected value remains identical:
- Flop: J♦9♠2♥
- Player 1: A♥A♦
- Player 2: K♠K♣
In this example, Player B has exactly two outs (the two kings) and Player A has two outs to re-draws (the two aces) if Player B hits his set.
The players are all-in and agreed to deal the turn and river twice.
There are still 45 cards left in the deck, so there are
different possibilities for the first run of turn and river.
There are six distinguishable cases that can occur in the first run:
- Case 1 (XX): Neither ace nor king hit. There are 820 combinations for this case.
- Case 2 (KX): Exactly one king hits and no ace. There are 82 combinations for this case.
- Case 3 (KK): Both kings hit. There is one combination for this case.
- Case 4 (AX): Exactly one ace hits and no king. There are 82 combinations for this case.
- Case 5 (AA): Both aces hit. There is one combination for this case.
- Case 6 (AK): One king and one ace hit. There are four combinations for this case.
No matter which of these six cases occurs, there are now
different ways for the second run to be dealt.
The same six cases can occur in the second run. The number of combinations for each case in the second run depends on how the first run turned out.
We have summarized the number of combinations for the second run depending on the first run in a table here:
|Run 2 / Run 1||XX|
This allows us to calculate the probability of every occurrence for each distribution for Run 1 and Run 2. The following table lists the probabilities. Below each is noted who wins the pot in the each case:
|Run 2 / Run 1||XX||KX||KK||AX||AA||AK|
Now we can add up all the probabilities:
- Player A wins both runs: 83.6%
- Player B wins both runs: 0.04%
- Players A and B split the pot: 16.0%
Therefore, in the long run, player A has the following equity in the pot:
This is exactly the same as the probability of winning the hand when the turn and river are only dealt once. The same is true for Player B’s equity. Meaning: running it twice does not change the probability or equity of any player in the hand.
The same applies to all other all-in situations, whether only the river, turn and river, or the entire board is dealt multiple times: the expected value always remains the same.
Video: Getting Lucky Running it Four Times Against Hellmuth
One of the most glorious hands involving multiple runs is certainly Ernest Wiggins’ all-in against Phil Hellmuth. With just a two-outer the amateur somehow managed to win three out of four runs against the Poker Brat:
What is running it twice in poker?
Running it twice in poker is when two or more players are all-in and the board is dealt multiple times, reducing the variance of the game.
When is running it twice advantageous?
Running it twice reduces variance and benefits stronger players who seek to reduce their risk of losing the entire pot.
Does running it twice increase or decrease the probability of winning?
Running it twice doesn’t change the expected value or probability of winning for either player.
How does running it twice impact profits in the long run?
Running it twice doesn’t change the expected value or long-term profits for either player. It only reduces variance.
Should weaker players insist on running it only once?
In general, weaker players benefit from variance and should prefer to run it once, while stronger players should seek to reduce variance and run it multiple times.
Is it worthwhile to use run-it-twice online?
Most casinos or online providers charge an extra fee for running it twice. The extra cost makes running it twice not worthwhile.
Does the expected value change when running it twice?
The expected value always remains the same for both players, regardless of how many times the board is dealt.