"Running it Twice" in NLHold'em

I have a question perhaps only a Wizard can answer. This is my first post, and having this question answered is the reason i joined. I play a lot of No Limit Texas Hold'em and in high stakes time raked games, am often given the choice, by the casino and by my opponents, whether I would like to "run the board twice" or some other number of times. This option has been added to the game by players who, as Phil Helmuth puts it, "...want to stay rich.", or reduce variance, in all-in situations. The way it works is that when two and only two players become all in and there are still more community cards left to fall, the players can, if they agree, run the remaining cards some number of times other than (the normal) once. This means the community cards left to fall run out face up as usual the first time, but then what remains of the deck is used to run that same number of cards out again, layed below their counterparts on the table, with the same pattern of burns, and perhaps again until there are as many rows of the new community cards as the players agreed to run. Then the pot is divided into that many equal parts, and each part is awarded to the winner of each runout, which consists of the concatenation of the community cards that fell before the all in with the cards in each new row. Players may run multiple rivers, turns and rivers, or even the entire board flop turn and river if the all in occurred preflop.

My question is the one begging to be asked. What does running it more than once do to my equity in the pot. Clearly, if the cards, once run, are replaced back into the remaining deck and reshuffled before running the following time(s), each player's expected stake in the pot is unchanged, and the variance is reduced by the square of the number of times run. So any effect on equity would be due to card removal, which, if existent, should be miniscule. But still I would like to know whether certain situations exist in which there is some effect on equity, and which player tends to gain equity by running it multiple times. Or an argument or proof that card removal has no effect. I have done the math on the simplest of situations in which the equity is somehow exactly unchanged. Also, assume that the pot in dollars is equally divisible by the number of times run. If not, the added equity of receiving the extra odd chip for being out of position may even outweigh any effects of multiple runs. Thank you. I hope this question hasn't already been asked.

Running it twice will, more often than not, benefit the player who is mathematically behind pre-flop. Let's take an example where player A has AK suited and player B has pocket 8's. With the pocket pair, player B is ahead approximately 52% to 47%. Player B has an advantage albeit a slim one assuming they are are run only once.

If the players choose to run it twice, now player A has 2 shots at 50% of the pot each run. The cards are typically NOT replaced and shuffled after each run so EOR is important. Let's say that on the first run, the board shows A,Q,9,6,3 with 2 hearts. Player A has now locked up half of the pot and beaten the odds. The second run however will now have one fewer ace left in the deck and 2 fewer hearts, giving a greater advantage to player B this time around.

That's how it works at a near 50/50 scenario and the main difference between running it once in this situation and running it twice is that there is a very good likelihood that the players will end up chopping the pot if it is run twice where there will be only one winner of the whole pot if it is only run once. Call it a hedge if you will.

When the odds are strongly in favour of one hand over another pre-flop, like pocket KK versus 8,9 suited (approximately 4-1 advantage), it is definitely in the best interest of the underdog to run it more than once as it gives a greater chance of retrieving at least a portion of the pot as opposed to going in as a 4-1 dog. Any board that doesn't give the underdog a win on the first run will mean there is a slightly greater chance of hitting those winning cards the second (or third) run.

I'm not a fan of running it twice but if I'm a big dog pre-flop and my opponent wants to give me 2 or more shots at recouping some of the pot, I'll usually take it. I would never offer the same opportunity to my opponent if the situation was reversed.

If you are the favorite and run it more than once, you deserve to lose each time it is run. You play the game to get an edge, have all your money in with an edge , and now you want to give your advantage away.

Either you are stupid or playing with money you can not afford to lose. Really stupid

Quote: Buzzard

If you are the favorite and run it more than once, you deserve to lose each time it is run. You play the game to get an edge, have all your money in with an edge , and now you want to give your advantage away.

Either you are stupid or playing with money you can not afford to lose. Really stupid

I will have to disagree with giving up SOME value is Really stupid. unless you are giveing your self an overall disadvantage causing you to have -EV overall. I would gladly play a 3% AP over a 4% AP if I could cut down on the fluctuation drastically. For instance id rather play a VP promotion worth 3% cash back then a 4% progressive.

I have noticed that players on shows like poker after dark will never run it twice. If they are going to run it more than 1 time it should be 3 that way there is still a winner on the hand.

Quote: AxelWolf

I will have to disagree with giving up SOME value is Really stupid. unless you are giveing your self an overall disadvantage causing you to have -EV overall. I would gladly play a 3% AP over a 4% AP if I could cut down on the fluctuation drastically. For instance id rather play a VP promotion worth 3% cash back then a 4% progressive.

Then in a no-limit game you are playing beyond your bankroll ! Talking about poker here.

Quote: Buzzard

If you are the favorite and run it more than once, you deserve to lose each time it is run. You play the game to get an edge, have all your money in with an edge , and now you want to give your advantage away.

Absolutely in agreement with this. Why a favourite would accept, or worse yet offer to run it more than once is beyond me. I've seen buddies do this to mitigate risk for the underdog but in a serious game it almost never happens. Too many people watching Poker After Dark and figure it's just cool to say "Run it twice bro?".

If you're 100% against ever running it twice then you shoyld be against paying for home owner insurance, car insurance, heath insurance and others.

I don't play against 9 other home insurance policy holders for their policy.

Everything I've ever read says that running it more than once doesn't change the EV, just reduces the variance. It balances out because if you win the first time, your chance to win the next run decreases and vice versa. If you went all the way to limit, i.e. with only the river left you ran it 44 times, you would always end up with your exact % equity in the pot -- same EV but zero variance.

So conventional wisdom says you should seek to limit variance if you have the edge. So if you think you're better than the guy you're up against you should want to run it multiple times, not so if you think they're better. All of this assumes that the pot size isn't large in comparison to your bankroll. FWIW, I don't ever run it more than once myself. Maybe it's because I'm not the best poker player, which I freely admit, but mainly because I think it kind of violates the spirit of the game.

If you are known to run it twice people's shoving ranges will be super wide, therefore you're giving a freeroll to pretty much anyone who wants a free shot at you.

If you aren't known to run it twice, then you can get the best of it by offering it when the edge is super small (51% vs 49%).

Either way it seems to be in your favor to not pick one side or the other 100% of the time.

Quote: smileyfish

Everything I've ever read says that running it more than once doesn't change the EV, just reduces the variance. It balances out because if you win the first time, your chance to win the next run decreases and vice versa. If you went all the way to limit, i.e. with only the river left you ran it 44 times, you would always end up with your exact % equity in the pot -- same EV but zero variance.

Yes this is correct, and that last sentence in your post clearly shows why your EV doesn't change.

So smileyfish and tringlomane disagree with earlier posters... maybe I should have made this a poll. Smileyfish's argument convinces me that when there is one card left to fall, the EV does not change. But how do you know that this will be true in general? What convinces you that 7h8h vs Ah2h on 4h5h8c has the same EV for all number of times run?! Others claim Ah2h, being behind, increases her equity by running it twice rather than once, but I do not follow the reasoning.

Being a professional poker player, I would also like to point out that it is most definitely not stupid to reduce one's variance with minimal or potential no effects on EV, no matter the situation. A desire to reduce variance, on the contrary, is simply a desire to stay rich and is most decidedly a beneficial tendency for an AP.

It mostly turned into more of a general discussion on whether to run it twice. Most didn't consider (except Axel) the big benefit of running it twice. And that is, as you mentioned, to lower variance. Lowering variance in turn will lower your bankroll needs. I would generally run it twice UNLESS they charge extra rake for the option.

As for EV, I'm not going to try to prove it generically for all cases because I am not a mathematician by trade, but here is an example showing that the equity doesn't change.

AK vs 77 on a 625Q board: AK needs to hit an Ace or King obviously, 6 outs.

Running once and AK wins: 6/44 = 3/22 = 0.136363636

Running Twice:

AK wins both:
(6/44)*(5/43) = 30/1892 = 15/946 = 0.015856236

77 wins both (38 outs to begin with):
(38/44)*(37/43) = 1406/1892 = 703/946 = 0.743128964

Hands split the pot:
AK wins first:
(6/44)*(38/43) = 228/1892 = 114/946 = 0.1205074

77 wins first:
(38/44)*(6/43) = 228/1892 = 114/946 = 0.1205074

Total probability of a split: 228/946 = 0.2410148

Equity of AK running it twice:
(15/946)*(1) + (228/946)*(1/2) + (703/946)*(0) = 129/946 = 6/44 = 3/22 = 0.136363636


What about running it 3 times:

AK wins all three:
(6/44)*(5/43)*(4/42) = 120/79464

AK wins two and loses one:
(6/44)*(5/43)*(38/42) = 1140/79464
plus
(6/44)*(38/43)*(5/42) = 1140/79464
plus
(38/44)*(6/43)*(5/42) = 1140/79464
Total: 3420/79464

AK wins one and loses two:
(6/44)*(38/43)*(37/42) = 8436/79464
plus
(38/44)*(6/43)*(37/42) = 8436/79464
plus
(38/44)*(37/43)*(6/42) = 8436/79464
Total: 25308/79464

AK loses all three:
(38/44)*(37/43)*(36/42) = 50616/79464

Equity for AK:
(120/79464)*(1) + (3420/79464)*(2/3) + (25308/79464)*(1/3) + (50616/79464)*(0) = 10836/79464 = 6/44 = 3/22 = 0.136363636

We can keep going on and on with this example, but I don't want to bang my head against a wall...haha

Here is a thread on 2+2 also discussing this topic and is part of the FAQ in "Poker Theory". There's more flaming for those who don't agree with it being the same EV...haha Also it's a site much more devoted to poker than this one.

http://forumserver.twoplustwo.com/15/poker-theory/run-twice-ev-question-633089/

Quote: philosophizor

So smileyfish and tringlomane disagree with earlier posters... maybe I should have made this a poll. Smileyfish's argument convinces me that when there is one card left to fall, the EV does not change. But how do you know that this will be true in general? What convinces you that 7h8h vs Ah2h on 4h5h8c has the same EV for all number of times run?! Others claim Ah2h, being behind, increases her equity by running it twice rather than once, but I do not follow the reasoning.

Tringlomane and Axelwolf have very good points about the benefits of running it more than once in order to reduce variance. But returning to the OP's original question about EV:

The EV will stay the same regardless of how many times you run it. Here is the best explanation I can come up with.

Instead of cards, think of things in terms of outcomes. With only 1 card to go, each card is an outcome. But with say 2 cards to go, each pair of cards represents an outcome (e.g. for 2 players heads up there would be 990 possible outcomes). The EV for player A of running it once, EV_A,1, is determined by adding up their return for each outcome and dividing by the number of outcomes. Let's call the sum of each of these returns for player A: R_A.

If you run it more than once with more than 1 card to go, the first outcome (i.e. set of cards) makes some outcomes impossible for future runs, since one or more of the cards they need already came out. For example, in the 2 players, 2 card to go example, the second run only has 903 possible outcomes, down from 990 for the first run. But to calculate the EV for running it multiple times, you would go through every possible combination of collections of n outcomes, total up the returns for the outcomes and divide by the total number of possibilities times n.

If you recognize two facts, it becomes clear that the EV has to stay the same. One, all outcomes are equally likely. So when you total up all the possibilities, there is no way any particular outcome can come any more or less often than any of the others. That means when you total up for returns for a player A it we be some multiple of R_A. Thus EV_A,n will have to some multiple of EV_A,1. Call this multiple m, i.e. EV_A,n = m*EV_A,1

This multiple is purely a function of counting up the possibilities. So the multiple has to be same for every player involved in the pot, e.g. EV_B,n = m*EV_B,1

Fact two is that the total EV over all players has to be the same regardless of how many times you run it, since the size of the pot stays the same. This means that the multiple m has to be 1 and thus EV_A,n = EV_A,1

But what if you have a big edge against a HUMAN player ? Math is math, but putting a big beat on an opponent may cause him to go on tilt. What if he is more skilled and this is a chance to put him out of commission for the time being ? How will running it several times affect your table image ? Will more players lower their calling limits if they think you will run it several times ? Or will the fact that you never run it more than once allow you to bluff more successfully ?

Poker is all about making the right decisions. That prism is different for each player.

Running it more than once does NOT change equity, at all.

I always prefer to run it as many times as possible, but most home game players don't like it. In my favorite home game, there are a couple super loose preflop players who'll get it all in super, super, super light - then we'll run it like 4 times. I almost never end that game behind...

Quote: Boney526

Running it more than once does NOT change equity, at all.

I always prefer to run it as many times as possible, but most home game players don't like it. In my favorite home game, there are a couple super loose preflop players who'll get it all in super, super, super light - then we'll run it like 4 times. I almost never end that game behind...

" Will more players lower their calling limits if they think you will run it several times ? " thanks for answering that question.

Running it more than once makes it more likely that you'll end up with an outcome near the expected result. With that in mind:

Quote: Buzzard

What if he is more skilled and this is a chance to put him out of commission for the time being ?

Your best chance to inflict a big beat is to run it as many times as you can if you have a sizable edge. You won't necessarily get 100% of the pot, but you increase your chances of getting a significant portion of it. By the same logic, you'd only want to run it once if you were behind. You have the highest change of getting a big chuck of the pot (i.e. all of it) this way, but you also have the highest chance of getting nothing.

Quote: Buzzard

Will more players lower their calling limits if they think you will run it several times ?

I'm guessing if the players you're up against react this way, then you're extremely happy. You exploit the fact that they'll call you light and get paid off on your value bets. Over the long run, since your EV in each pot doesn't change due to running it multiple times, you'll end up ahead.

Quote: Buzzard

Or will the fact that you never run it more than once allow you to bluff more successfully ?

I'm less sure about this one, but again if it were true of the players you're up against, you could exploit this also.

For the one particular pot, running it multiple times has no effect on EV, and reduces variance. As to what effect running or not running it more than once might have on the future hands, I guess my short answer is that if you can gain any insight or predictions of your opponents' behaviour, you can come up with some way to use that to your advantage.

" Your best chance to inflict a big beat is to run it as many times as you can if you have the edge."

This I do not agree with.

Quote: Buzzard

" Will more players lower their calling limits if they think you will run it several times ? " thanks for answering that question.

I wasn't replying to you (as I hadn't even read the whole thread,) I was replying to the OP, but I suppose given my example - it can. But it still depends on the type of player. Better players won't lower their calling ranges based on the number of times it's likely to be run. However, I've had history with that one opponent that leads him to know I'll always run it up to 4 times - and he ends up 3 bet calling me really light pre-flop if there's dead money in the pot. Knowing his range was ridiculously wide I was able to keep this up for a while when that game ran... But that's a very specific situation. Honestly I feel like most players are playing the game without thinking about the possibility of the number of times it could get run out, but some will take the option of running more than once.

EDIT: By 3-bet call, I mean would call to my 4 bet, and with basically any suited connnectors+

Quote: Buzzard

" Your best chance to inflict a big beat is to run it as many times as you can if you have the edge."

This I do not agree with.

Fast reply, got in before I could finish editing my earlier post. =)

It should be "sizable edge". If you are a 51-49 favourite, you'll get closer to 51-49 if you run it a bunch of times. In that case, your best bet to get a big piece is probably to just go once. But if you were say 80-20, then I'd suggest you run it multiple times.

[edit] Bah. I should read everything.

Quote: smileyfish

Fast reply, got in before I could finish editing my earlier post. =)

It should be "sizable edge". If you are a 51-49 favourite, you'll get closer to 51-49 if you run it a bunch of times. In that case, your best bet to get a big piece is probably to just go once. But if you were say 80-20, then I'd suggest you run it multiple times.

I don't understand why it'd be your goal to win a big piece as often as possible. It should be your goal to maximize EV, and IMO, minimizing Variance is also a good thing.

However, as Buzz pointed out, there are times when refusing to run it out more than once - and then winning will put the other player on tilt. Or that if you always run it multiple times certain players will call your bluffs more often. I suppose that could be helpful or hurtful, but really that scenario and the one I posted earlier are very specific examples of times when running it more than once affects EV ONLY because it affects how others play against you.

So running it more than once has no affect on the EV of any specific hand, but could have an affect on future EV in specific scenarios. I wouldn't suggest anybody start thinking about these more player specific scenarios until they can understand the reasoning behind EV. What I mean by that is that if you don't understand WHY running it twice has no effect an a hand's EV then you should really be studying more about poker/gaming math... Because if you don't understand the core concepts applying slightly more advanced ones will go wrong.

Running it through multiple times does not change the equity of that hand. If you want to reduce variance, you should favor it. If you want variance, you should oppose it. There are a host of reasons to want or avoid variance in a tournament, which I won't get into.

I'd compare this question to multi-play video poker. For example, on any given draw and pay table, the expected return is the same for one play at a $500 bet as 100-play at $5 per hand. However, variance is much less on the 100-play game, unless you're holding all five cards.

Can you guys tell me of casinos you know of that allow this practice?

Thanks

I've never seen it done in a casino, but I'd have to assume most casinos would allow it. If anything, it's beneficial for the casino to keep more players on the table...

Obviously it's never allowed in a tournament, though.

Quote: Boney526

I've never seen it done in a casino, but I'd have to assume most casinos would allow it. If anything, it's beneficial for the casino to keep more players on the table...

Obviously it's never allowed in a tournament, though.

Thanks bud,

I have never heard of the expression nor seen in in practice so I was quite keen to see if casinos allow it or not. It seems it may work in small rooms with not much action. As you rightly mention the more players on the game the more times the minimum amount of rake per hand will be reached. It is however different when you have busy rooms with a long waiting list?

deleted

Quote: Boney526

I've never seen it done in a casino, but I'd have to assume most casinos would allow it. If anything, it's beneficial for the casino to keep more players on the table...

Obviously it's never allowed in a tournament, though.

I haven't seen it done in person either. It's usually restricted to higher stakes that I can't afford.

And Buzz brings up some good points on opponents. If they call you lighter because you'll run it twice, that's a good thing as long as their "extra calls" are worse EV for them than their folds if you would have ran it once.

Quote: Tomspur

Can you guys tell me of casinos you know of that allow this practice?

Thanks

The Venetian allows it in their Pot Limit Omaha games.

Quote: Boney526

I don't understand why it'd be your goal to win a big piece as often as possible. It should be your goal to maximize EV, and IMO, minimizing Variance is also a good thing.

However, as Buzz pointed out, there are times when refusing to run it out more than once - and then winning will put the other player on tilt.

It was in response to something Buzz asked in his post -- about trying to win a big piece to put the other guy on tilt. Sorry, the confusion is because my lousy writing/editing skills caused my thought to get fractured into multiple posts.

Actually, reading his post again, I probably misinterpreted what he meant. He likely was referring to winning the entire pot as you say.

Quote: Tomspur

Thanks bud,

I have never heard of the expression nor seen in in practice so I was quite keen to see if casinos allow it or not. It seems it may work in small rooms with not much action. As you rightly mention the more players on the game the more times the minimum amount of rake per hand will be reached. It is however different when you have busy rooms with a long waiting list?

I would guess it doesn't matter on business - just that very few people even ask to run it twice. I can't imagine much reason why a casino wouldn't want it's dealers to do so... It's gonna take slightly more time to chop up the pot if necessary, but as I said it's more likely to leave more players on the table.

I guess you could ask next time you play. There is a chance I'm wrong and most poker rooms will not allow it at normal stakes.

Quote: Boney526

I guess you could ask next time you play. There is a chance I'm wrong and most poker rooms will not allow it at normal stakes.

At 1/2 NLHE, I am not sure if any room would allow it. Definitely never have seen it done before at that level (the only level I can afford), but I don't play much NL.

I have never seen it run more than once in any poker room legit or otherwise in Colorado. Remember it's head up at that time. Other players want to play a new hand, not watching somebody else win.

Quote: Wizard

Running it through multiple times does not change the equity of that hand. If you want to reduce variance, you should favor it. If you want variance, you should oppose it. There are a host of reasons to want or avoid variance in a tournament, which I won't get into.

I'd compare this question to multi-play video poker. For example, on any given draw and pay table, the expected return is the same for one play at a $500 bet as 100-play at $5 per hand. However, variance is much less on the 100-play game, unless you're holding all five cards.

Thanks for skipping tournament reply. People always call a Poker Tournament the wrong way. It is a Tournament first and Poker
second.