So weird question but say hero has AAxx Pot Limit Omaha vs villains KKJT 1-2 game $200 stacks Hero makes it $3 villain makes it $9 Hero makes it $27 villain calls


flop is JT2r pot $54 villains leads out and pots $54

total pot $108

Say just before Hero acts villains turns over his hand and shows Hero KKJT for Top two pair.

ProPokerTools Omaha Hi Simulation

600,000 trials (Randomized)

board: JT2

Hand	Pot equity	Wins	Ties
AA**	35.17%	209,947	2,093
KKJT	64.83%	387,960	2,093

So Hero needs 33% equity to call given pot $108 and is getting 35% with the AA**

do you call? or do you fold once you see your 65%-35% although slightly over with total equity but taking into account higher variance by calling vs folding.

assuming no rake id call, getting 2% enough odds and can play perfectly

Bad example because it isn't all in on the flop.

Say stacks are both $108 which leaves a all-in on the flop

This is correct, sorry.

fold flop




if it is all in on the flop and you have 33% pot odds and 35% equity and there is no rake, yes you can call

Or, you can fold. Yeah, you're passing up a small profit, and in return getting a reduction in variance. There are lots of reasons why this might be a good idea. There are some reasons you might call with a slightly -ev spot in the other direction, too.

Even if villain shows hand? can you explain one or two?

OK sure

1. "villian" is a reasonably solid player but has a good chance of going on monkey tilt if he loses this hand

2. you have 1 unit of money, you owe the mafia 3 units, they will kill you and your family if you don't pay. Let's say 1 unit is a LOT of money, more than anyone would loan you, or you can make yourself in the time allotted. Someone offers you a deal with is slightly -ev, you should probably consider it, if it'll let you pay off your debt.

3. You want to establish an image as a gambler, which you'll capitalize on later

Basically each of these is a scenario where you're paying a small vig now to set up a more profitable future situation. I'm sure you can think of more.

The flip is similar. For #1, what if it's YOU that'll go on monkey tilt if you lose too many buyins? Or what if losing this buyin will put you out of the game for the evening, and the game is still profitable (this one is a bit questionable, but hey) This and other situations are places where you can take a small loss of EV (by folding) in exchange for avoiding a larger future loss.

OK thanks. So just back to my original question again (folding due to small profit margin and variance), most will say variance will even out so calling with 2% equity profit is +EV, but also read some say variance doesn't even out. So my question is if villain shows cards and villain is 65-35 with a 2% profit in equity "adding variance", is there a correct play?

So there are good examples for both to call and to fold - but just wondering if there was a correct play because of variance.

If you have an infinite bankroll, calling is a must with an EV > 0. Even if you make 0,0000001 BB in a hand you must call.

Normally you want to play with a bankroll so that it is no longer of any significance in your decision.

Tom Dwan says "Don't mention the triads!"

Define what it means for a play to be "correct"

That's good question



This probably sums up thread as in the correct play, i think, unless you have a reason its not?

See my examples above. You can turn down a small edge now if you think it'll open up a larger edge later (that might not be there if you call now)

I think i understand what your saying, ok, so from a mental side of playing poker there are good reasons to not push the small equity edge even though ahead, but from a maths point of view, pushing even with 0.00000001 equity edge is always +EV, right?

Yes.

In isolation, yes.

I think his example was a more strategic reason, but there are also mental ones. I think RustyBrooks meant that it is sometimes more profitable to drop a small edge because there is some reason to believe a better spot will appear later and grabbing this small edge now may block this future juicy one. Perhaps you know a player will leave the table after hitting a small loss. In such a case it might get you more money if you wait for a bigger pot.

These strategic types of move are fine and it doesn't really have anything to do with lowering variance, it may not even do so.

From your initial question Variance is often cited in spots but I am not sure if the variance term is often used correctly. I think people usually mean that to drop some very close spots will give a smoother w-r. The variance aspect of these spots is a little difficult to calculate, for this one hand in isolation yes but the variance of your bb/100 hands is calculated from more than this one hand.

eg, if a great player decides to experiment and drop any nearly even ev spot, say refusing 51% return on a call. Will this reduce the variance seen in her bb/100, and by any large amount?
Well let's say the player is easily the table's largest stack and could call a river 50bb bet expecting a 51bb return by this. If the player doesn't take this hand she will have left on average 1+1bb more to the other stacks and actually probably a 50bb or so gain for someone from this pot. How would this affect the future variance seen?
If the next hand goes to allin with this same player it will be for 50+50bb bigger pot and this would have a much larger variance effect. The variance will be proportional to the pot size squared. Oddly through this scenario the player can have given up value and increased the variability in her w-r.
The alternative, if the call is taken, the Hero has to face either a 100bb rebuy or perhaps a 200b hand depending on the previous coin flip outcome. Yes, the chances are Hero's variance goes up but in the way a great player would actually want it too.

On average it is only giving a (1+1)bb gain to the other table stacks present but even this will slightly increase the future variance seen by the Hero.

That is just an example and I am trying to say it is difficult to assess what the exact amount variance will be modified by when giving up on close spots.

Warning, I don't play cash games and so don't know anything about the utility of not calling in close spots - maybe it is wise if you're pushing your BR to the edge. I also don't know if it is a done deal that doing so definitely lowers bb/100 variance, I suspect different styles of play eg, tight vs loose have a much greater effect on variance and the variance present should usually be accepted as a part of the game you are in. If you can modify it without losing out much at all then it is wise to do so but be careful and it is probably better to follow your poker intuition and take your best move.

Easy example of a situation where you might fold even though you would give up a significant amount of EV:

HU, first hand, 100bb deep against someone you beat for 50bb/100 on average. You know that villain will always insta quit the game if his stack reaches 0bb or 200bb.

Do you really want to get all-in in the first hand if calling is only 5bb better than folding? Knowing that calling means that the game is over after that hand no matter if you win or lose.