A bit of a long title. The past few days I've been having this discussion with a couple of other pokerplayers. We're not math wizards by any means so we need other people to provide some proof for either statement.

I think (probably read feel) like when avoiding these spots it will give you a lower winrate in the longrun and would also end up with the variance being higher than when always going into every marginal +EV spot getting a higher winrate and it will give u lower variance in the long-run.

I'm unsure about my previous statement however "feel" that avoiding these spots should at least give u longer break even stretches but maybe not bigger swings in terms of buy-ins.

So in short: avoiding high variance +ev spots:

1. increase or decrease long term stbb/100?
2. gives u longer break even stretches?

Ps. This got started because someone played a hand differently so that he would get more folds and avoid a troublesome even more +EV spot with higher variance. And I told him it was stupid because it would increase his long-term variance because of the lower winrate.

I would really appreciate some answers/proof.

answer to question 1. decreases, GREATLY.
2. not true, unless you were a winning player. If you're a losing player, you'll just lose more.

you MUST take/make any bet with EV>0, PERIOD.

If you can't grasp that, quit poker.

example: 20BB stack, 6-max cash game.

Hero: (QsJh) SB

UTG raises 4x, HJ calls, CO calls, BTN folds, hero shoves.

That's a +EV, but high risk play. Folding is terrible there.

I don't wanna get into the math but do rocky players increase their variance by avoiding high variance nope they keep their wins and loses small. So you would decreasing your winrate but your variance wouldn't increase as long as the rest of your game was inline with avoiding these spots.

regarding pushing every edge.

especially low volume students i've seen who are on a dowswing, passing up on those high variance plays, and getting your money in as a bigger favorite isn't the worse thing in the world. variance in someones game tends to make them lose confidence, and I think the benefit from getting confidence back, especially in times of a dowswing, is more +ev than making plays that will in all actuality only earn them a few bb's in the long run.

Mostly I think this type of advice comes from losing players. As a poker player you are naturally accepting a decent amount of variance. There is no zero variance way to just take the money. The smaller your variance the closer and closer you get to simply losing to the rake and/or blinds. Often times we are trading variance for EV. Playing our strong draws fast gives us multiple ways to win, they can fold, or they can call and we can still outrun them. Playing them mega-passively and just calling until we hit usually gives up our ability to turn a profit. We frequently put in chip after chip and then fold, and when we do make our hand they often refuse to put in more money.

There is broad confusion on the term varaince. There is actual statistical measure, and then there is the swingy feel to the game. We might trade a large portion of our winrate to reduce the statistical mesure of variance (in terms of std/dev), but the game will feel more swingy. There are some exceptions, like if we have a tiny bankroll that cannot be replenished, we may consider taking a smaller variance rather than risk too large a percentage of our roll in a +EV but high variance spot. An example, you might make a very consistent 5 to 10$ an hour in a 1/2 limit game and play with a roll of 500$. You might see a tournament with players far worse than what you beat at 1/2 with a buyin of 250$, where your hourly might be 20$ an hour in it, but you wuold not choose to play because it is far too much of your roll. Theres a real example of choosing a lower variance option with a lower winrate, and a good idea.

Most of the time tho, people are discussing how they play a hand. Flat calling preflop instead of re-raising when they are only thinly ahead. Skipping a value bet on the river because its only marginally ev+. Calling with a draw instead of jamming up to wait until they make it or miss. Most of these are fairly bad strategies, as a general rule. Now the above post is another example of clear thinking. In a tournament where we have a big edge, we might choose to eliminate some of the very high variance plays from our playbook early, or even later in the tournament we might choose to pass up a very thin EV play in order to have a higher density of cashes.

4Card

Whilst it sounds good, this is not true, either in theory or in practice.

I will make up a few deliberately extreme examples in order to show the point.

1. You are sitting in a live game next to a truly terrible player who, despite your repeated gentle reminders, exposes his cards to you every single hand. You are both super deep and you have position on him. You have put all of the money you brought out with you on the table in order to cover him, and will not be able to reload if you get stacked. You raise QQ utg, and it is folded round to him in the BB. When he looks at his cards you see them as usual. He has AK. He shoves all-in for a HUGE overbet. Are you calling?

2. You are a big long-term winner at high stakes poker and enjoy a really comfortable standard of living as a result. You have a very sufficient bankroll, plus savings etc to ensure that you can continue to play with an edge in these games, and thus continue to enjoy a really good life, for years and years to come. Someone offers to gamble your entire bankroll and savings on the toss of a single coin, giving you 11 to 10 odds in your favour. You somehow know that this offer is genuine, and there is no chance at all of you being ripped off etc. Are you taking the bet?

Get familiar with the Kelly Criterion and think about what it means for small edges. You may be "rolled" for say, 25NL with 20 buyins. You double up after getting it in with aces against kings for another 100BB.

Now you're sitting with $50, your total bankroll being $1025, and you find yourself facing an EV+ choice: You can get it in preflop with some hand, knowing for certain that you are a 52% favorite against your opponent's range, for 200BB ($50).

You should pass on this edge. Getting 1:1 on your money, you should bet no more than 4% of your bankroll as a 52% favorite. Your bankroll being $1025, 4% is $41. You have 200BB, which is more than the maximum you should bet according to the Kelly Criterion, and so wagering it would be a mistake.

I mean, I doubt this is a situation that ever really comes up, but it's theoretically possible.

Would you bet your entire net worth, getting 1:1, as a 60% favorite? It would be EV+, but still disastrous.

Ok this is obv. getting way of track because we should be talking about spots with a sufficient bankroll without a risk of ruin.

But ac on do you maybe have some numbers or a way to simulate a large sample with +ev high variance spots and taking these spots and not taking these spots and the effect on this sample. Or is it just logical that even when it increase winrate it will still affect variance to increase? It should actually be logical with the numbers but it feels like avoiding these spots would still increase my variance in the long-run.

sigh gonna pay attention next statistics class...

I don't know man, that is a great play against consistent TAGS but to say it is +EV everytime is incorrect in my mind. QJo is a weak hand and there are players out there who will pick up on your tendencies and call you with Ax everytime, even worse if you get it multiway. So in a way it is +EV in situations where your opponents are likely to fold and it gives you more value on hands like AA/KK/AK but doing that every single time isn't +EV if you have done it often enough that your opponents notice.

Look at it from the other point of view. I've played against enough people who use that trick to pick up on the times when I am most probably ahead. And I am usually right, when a player raises all in or raises big in a certain spot consistently, eventually I am calling with AJo and your QJo is looking pretty dead. The line of EV is thin here, but if you shove often enough I am widening my range to a range that is slightly tighter than your shove range so that I am +EV in the long run against you.

Phil Galfond disagrees with you, he mentioned in one bluefire vid how he thinks it's fine and sometimes optimal to pass up extremely small edges to decrease variance.

As to the OP interesting question. Let's put some numbers to it. Say a normal edge is 55% coin flip. Now we get offered a bunch of 50.5%'s. How is our variance impacted. What do long-term graphs of each respective player look like. Obviously in the long run we would want to take those edges but how are the swings comparatively.

Also I'm a huge BR nit so I generally have no problem winning/losing one buy-in so push every edge I can and don't mind playing a high-variance style. So I'm with you on philosophy but don't just dismiss the other side as they should quit poker.

lol if you're ever raise/folding AJ with 20bb in a 6max game you're doing something wrong unless you have a super-nitty opening range or the guy shoving doesn't know your range is wide. I'm not sure if QJ should be part of that range but he should be shoving pretty much all pairs, tons of broadway hands, etc. He's not trying to make you fold AJ lol.

You see what he did there was made two cold callers in a cash game. So its hard to imagine any ranges where we dont have at least some fold equity, especially because they can push each other out. Even if your calling with the AJo thats fine cause theres 10 dead in the pot so hes getting 20 to win 50+ The cold callers also pretty much never have a dominating high pair.

Its a cash game too so chips is money.

Phils point is sound from a perspective of tilt, but if we are truly tiltless as well, then we shouldnt pass up +EV spots in a cash game assuming we are rolled for the game and action, and assuming we have no tilt.

There are many opponents whose shove range does not include QJo in that spot. To assume that you do one thing and that it is +EV for you does not mean everyone else includes that play in their game, I'm not saying you are doing it wrong, but I think it is a mistake for you to say that shoving in that spot is +EV everytime because some people will adjust to what you are doing and some will call with the wrong hands.

In fact, this exact situation happened to me and I trapped a guy with AJo and called his JTo shove from that exact spot. It wasn't +EV for him there because I knew what he was going to do before he did it.

Conversely there are plenty of guys I am folding to with AJo that just don't ever come over the top of me with a non premium hand. This is an extreme difference in play styles, but this difference does exist in players out there and to say a play is +EV every time is simply a mistake.

edit: and you completely discount any form of trapping with a premium hand from any of the players.

I'm saying I'm not 100% sure but I'm pretty sure if UTG's opening range is wide enough shoving QJo is unexploitable (ie if they call too much you win because you have the best hand a ton and if they fold too much you win because of the FE).

I see exactly what you are saying. But If I see this happen more than once I am focusing on tightening my range enough so that your play is exploitable. And I am also trying to setup situations where you trap yourself. You have two forms of equity in that you can beat me in a showdown and there is fold equity. But think about if I eliminate your showdown equity by knowing your range and exploiting it. Then all you have is fold equity. However you gain a third form of equity in that your good hands get paid off more often so the EV range becomes very thin over a long period of time between two thinking players. Every once in a while I end up on a very nitty table against one other aggressive player and I get to hone my play against them, usually I end up calling their shove with +EV so I have confidence in what I am saying, even if it is incorrect due to variance siding with me, thus I am always willing to listen to reason.

would also depend on if your shoving these high variance spots or calling off? Is this spot rare/unique or a regular see it all the time spot ie final table of some event? Future edge also plays a factor.

You could run scenarios either way.

I would think pure maths won't give you the answer unless you look at the broader picture and factor in the none maths variables.

That was a great explanation, I think it is really the core of what poker is to a good player. Someone who thinks about complex situations where you take factors into your head and run the scenario multiple ways to see what the most profitable situation is. The very best players in the world focus on giving their opponent as few factors as necessary so they have less information to make decisions on. I find most players don't even think about multiple situations or play the situation based on probability, they just play their cards and the pot size. I like these kind of players. They give me money.

iam very interested on your kelly criterion do you have some article on this?
thanks

That still doesn't mean its not a +EV play for him.

So what you're saying is, if we are considering long term ev, there has to be "long term" already in place(ie a big bankroll) for us to consider it?

Regarding flipping, or taking a 101:100 shot for your life savings or entire BR, I'm not advocating that.

What I'm saying is that there are certain situations in poker that are +EV, such as C/R shoving certain draws after sufficient action behind you, or squeezing when there are are one or more cold callers.

The differing points in seizing marginally +EV situations brings us back to the old argument of playing <6 tables with huge reads and waiting for huge spots, vs playing 24 and taking every known +EV play possible. Unless you're playing high stakes, I'd say the latter is far more profitable.

-C/R shoving draws
-Squeezing with cold callers

got any more?

ok I'm gonna say I have no idea if QJ is a good shove in that spot but that it sounds right. I avoid shortstackers as much as I can but talk to mtt players they know this stuff really well. Basically the concept is that if you fold too much (to "trap" them) they're making money when they don't have QJ and you let them win the pot so while you're right sometimes in a vacuum shoving QJ is not +ev an overall strategy including shoving QJ is likely 100% profitable and unexploitable. That is you can make the QJ shove unprofitable but in doing so are opening yourself up so that when he wins without having to shove it makes up for the slight ev hit he takes from shoving QJ unprofitably.

Let's use a simpler example though that's already been solved. HU sng with <10bb. If both players are good players and adjusting there is a nash equilibrium shoving and calling range. Both players should play this strategy. No matter what the other one does, if one is using that strategy they simply cannot be exploited. Sometimes it's better to open yourself up to exploitation (generally with the idea that your opponent simply won't adjust and exploit you) and further exploit your opponent by shoving a bit wider or a bit tighter but generally if you play with the nash shoving ranges you can not be exploited and if your opponent folds too much that's a mistake and if he shoves too much that's a mistake too both of which you profit from.

Well bankrolls are always finite. It matters how big. If I'm taking 90-10's I'm comfortable with only 4-5 buy-ins. If I'm taking a bunch of 50.1%'s 50 buy-ins could be super short. Personally I like to have 100+ buy-ins to seriously grind a level I don't know the math or Kelly Criteria stuff but I've had multiple 30 buy-in downswings in the past so just like to be extra safe. But the higher the variance the higher the BR needed generally right?