Situation while "running it twice" during home cash game

[FireStorm]

75-25. This should be obvious.

EV is neutral. Long-term, the results are the same, 12 outers will win their expected % against sets, or whatever situation. Running it X number of times simply reduces variance. There are a number of reasons for this - keep fish in the game, keep pots fair/small against people you're friends with, or for people who only come to the game with one or two buy ins. None of these are necessarily great reasons, but they are what they are.

As far as not "being stupid and running it twice", this is silly commentary. Please keep in mind that this is not online. Live players don't get to play 18000 hands a month, and can't click a button in a matter of four seconds to put another buy in on the table. Also, they don't (or shouldn't) have access to every last cent of their bankroll at every minute. Therefore, the human element comes in and people run it twice simply to avoid losing huge amounts of money in one shot. Does this conform with the 2p2 mantra of accepting variance and obsessing over winrates and all things +EV? No. It's simply a live play angle for the above reasons.

FWIW, some clubs run it 3x in order to guarantee a "winner" in situations like sets vs OESFD's when you are essentially racing and most twice-runs will result in splits.

[PokerintheI]

[ QUOTE ]
Running it twice is never +EV. It is never -EV.
(These are assuming it is done properly, not the messed up way the OP's game did it).
The point is not changing your EV, it is lowering variance, which it does for both players, regardless of their equity.

[/ QUOTE ]

I'm not saying that the actual running of the board twice affects EV. You are right in that it is primarily going to affect variance.

Where you get a positive expectation is when allowing a river to run twice gets you a call that you wouldn't otherwise get. If running the river twice gets your opponent to call your bet with pot odds of 1 : 3.25 when his actual odds to win are 1 : 5, then running it twice is a +EV action.
__________________________________________________ ______________

Scenario 1
Pot in each case is $250 and Player A has AA on the turn and bets $200;

Without running it twice, Player B folds;

Total EV for Player A in scenario 1 is $450.
__________________________________________________ _______________

Scenario 2

Player B says he will call if you will run the river twice. Player B has only the nut flush draw.

In this case it works out as:

River 1: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is: $261.3

River 2: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is $261.3

Total EV for Player A in scenario 2: $522.6

[ QUOTE ]
Getting your opponent with a set to run it twice when you are behind with a draw and already have the money in is definitely +EV.

[/ QUOTE ]

Yeah, this was definitely an incorrect statement. Several people have correctly pointed out that the only impact is on variance and not EV. Although, as FireStorm pointed out, reducing variance can sometimes be worth it enough to warrant the decision.

[ QUOTE ]
Offering it or accepting it when you are ahead and your opponent has already called is stupid.

[/ QUOTE ]

This was clearly a personal judgement on my part. I do however stand by it so long as you won't negatively impact the texture of a game by say, making the fish unhappy so he chooses not to rebuy again or shifting the table from happy w/action to somber w/o action.

[Lottery Larry]

[ QUOTE ]
In this case it works out as:

River 1: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is: $261.3

River 2: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is $261.3

Total EV for Player A in scenario 2: $522.6

[/ QUOTE ]

Minor quibble- it won't be 80.4% the second time, it will be less. You've already run 3-5 cards out that didn't hurt your hand.

[yjbrewer]

running it twice is gay. never do it. Someone will end up sucking 1 outer on you

[Lottery Larry]

At least you're happy while being dumb

[PokerintheI]

[ QUOTE ]
[ QUOTE ]
In this case it works out as:

River 1: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is: $261.3

River 2: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is $261.3

Total EV for Player A in scenario 2: $522.6

[/ QUOTE ]

Minor quibble- it won't be 80.4% the second time, it will be less. You've already run 3-5 cards out that didn't hurt your hand.

[/ QUOTE ]

I wasn't certain on this math, but here was my reasoning:

For the second river there are 2 possibilities:

There is a 19.6% chance you have 8 outs out of 45 because you hit your flush on the first river. This gives you a 17.77% chance to hit another flush card.

There is a 80.4% chance you have 9 outs out of 45 because you didn't hit the flush on the first river. This gives you a 20% chance to hit a flush.

17.77% x .196 + 20% x .804 =
3.469% + 16.08% =
weighted average chance of flush on second river = 19.55% = 19.6%

I felt like I might be missing something, but I'm not a math guru by any means.

[chillrob]

You are correct that the "meta EV" of keeping people in the game or hand could be good. I had never heard of people discussing running it twice before the money even went in.

[JimmyGunz]

75-25

[Zetack]

[ QUOTE ]
[ QUOTE ]
Running it twice is never +EV. It is never -EV.
(These are assuming it is done properly, not the messed up way the OP's game did it).
The point is not changing your EV, it is lowering variance, which it does for both players, regardless of their equity.

[/ QUOTE ]

I'm not saying that the actual running of the board twice affects EV. You are right in that it is primarily going to affect variance.

Where you get a positive expectation is when allowing a river to run twice gets you a call that you wouldn't otherwise get. If running the river twice gets your opponent to call your bet with pot odds of 1 : 3.25 when his actual odds to win are 1 : 5, then running it twice is a +EV action.
__________________________________________________ ______________

Scenario 1
Pot in each case is $250 and Player A has AA on the turn and bets $200;

Without running it twice, Player B folds;

Total EV for Player A in scenario 1 is $450.
__________________________________________________ _______________

Scenario 2

Player B says he will call if you will run the river twice. Player B has only the nut flush draw.

In this case it works out as:

River 1: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is: $261.3

River 2: (pot $325) Player A expects his hand to hold up 80.4% of the time. Expected value for Player A is $261.3

Total EV for Player A in scenario 2: $522.6



[/ QUOTE ]

Although you are correct in your conclusion that getting the other player to call with incorrect pot odds to do so is plus EV over having him fold, you might want to look at how one calculates EV, because you aren't doing it right.

For instance, in scenario 1, you appear to be assuming that your opponent will fold to a 200 dollar bet (if you don't run it twice) 100 % of the time. If this is the case, your ev in that situation is $250 dollars, not $450.

To demonstrate that this is so on an intuitive level, suppose that instead of 200 dollars, you bet a thousand (and again your opponent will fold 100% of the time. ) Your EV has not jumpted to $1250 in the hand, it is still $250. Suppose you bet a million dollars. Your EV is not $1,000,250, it is still $250. Suppose that your opponent was all-in, but for whatever brain dead reason would muck his hand to a $200 bet 100% of the time, your EV if you make the bet is still $250, not $450 (since there is nor functional difference between an inability and an unwillingness to make a call.)


Anyway, and rounding more than you are, I put the EV of not running it twice (for the 100% fold) at $250 and the EV of running it twice (for the 100% call) at $320. So, yes, a plus ev move.

However, since it is obvious that anytime you can induce a call from a player with improper pot odds to call you have a postive EV situation, the only relevant point here would be to show that your EV is unchanged whether you run it once or twice (and thus running it twice is EV if running it once would be, and vice versa). So a more relevant post would have been to demonstrate mathematically, that, in the event of a call, your EV is the same whether you run it once or twice.

Also a much more interesting calculation would assume, that like so much in life, your opponents decision is not 100% either way. If you assume, for example, that if you don't offer to run it twice, that your opponent will still call say twenty percent of the time, and even if you do offer to run it twice your opponent will still decide to fold 10% of the time, your EV caculations get much closer. While still plus EV, (if I've done the math right, which is always a question since I suck at math) and again with a bit more rounding than you were doing, I show the EV of only offering to run it once increasing to $264 (since 20% of the time he incorrectly calls) and the EV of offering to run it twice falls to $313 (since 10% of the time he folds anyway).

As you change those numbers, the plus EV of inducing the call may may make it a more marginal, though still plus EV, play.

--Zetack

[PokerintheI]

[ QUOTE ]


Although you are correct in your conclusion that getting the other player to call with incorrect pot odds to do so is plus EV over having him fold, you might want to look at how one calculates EV, because you aren't doing it right.

For instance, in scenario 1, you appear to be assuming that your opponent will fold to a 200 dollar bet (if you don't run it twice) 100 % of the time. If this is the case, your ev in that situation is $250 dollars, not $450.

To demonstrate that this is so on an intuitive level, suppose that instead of 200 dollars, you bet a thousand (and again your opponent will fold 100% of the time. ) Your EV has not jumpted to $1250 in the hand, it is still $250. Suppose you bet a million dollars. Your EV is not $1,000,250, it is still $250. Suppose that your opponent was all-in, but for whatever brain dead reason would muck his hand to a $200 bet 100% of the time, your EV if you make the bet is still $250, not $450 (since there is nor functional difference between an inability and an unwillingness to make a call.)


Anyway, and rounding more than you are, I put the EV of not running it twice (for the 100% fold) at $250 and the EV of running it twice (for the 100% call) at $320. So, yes, a plus ev move.

However, since it is obvious that anytime you can induce a call from a player with improper pot odds to call you have a postive EV situation, the only relevant point here would be to show that your EV is unchanged whether you run it once or twice (and thus running it twice is EV if running it once would be, and vice versa). So a more relevant post would have been to demonstrate mathematically, that, in the event of a call, your EV is the same whether you run it once or twice.

Also a much more interesting calculation would assume, that like so much in life, your opponents decision is not 100% either way. If you assume, for example, that if you don't offer to run it twice, that your opponent will still call say twenty percent of the time, and even if you do offer to run it twice your opponent will still decide to fold 10% of the time, your EV caculations get much closer. While still plus EV, (if I've done the math right, which is always a question since I suck at math) and again with a bit more rounding than you were doing, I show the EV of only offering to run it once increasing to $264 (since 20% of the time he incorrectly calls) and the EV of offering to run it twice falls to $313 (since 10% of the time he folds anyway).

As you change those numbers, the plus EV of inducing the call may may make it a more marginal, though still plus EV, play.

--Zetack

[/ QUOTE ]

Yeah, I had a feeling I was calculating something incorrectly there.

In my experience with running it twice, it is generally the person calling that asks about running 2 rivers. And it generally involves a relatively large pot with some deepish stacks and regular players. So the determinations with regard to what they might be drawing to or if they might call or fold can be made with the insight gained from playing with the same person for 3 years.

I would agree that in a game with people you don't know as well you would need to factor in the "fold anyway" or "call anyway" percentages to a greater degree.