Q: My question is about calling UTG open raise (say 3.5X) on the button with small pairs (say 22 – 55). Unless UTG will stack off with one pair it doesn’t seem profitable to set mine. Say UTG has AA but will only lose 40 in a single raised pot, but will obviously get it in with a set of AA. I can’t call and then pot control when I hit a set. With set mining I see three cards, with AA UTG gets to see 5 cards, so my 12% for a set is reduced by 2%. So I have 10% chance of winning 40 and 2% chance of losing 100 so my EV is just 2 and I have paid 3.5 pre flop, so even if I was in big blind I can’t set mine. So what hands can I call in position with? Do good players either 3-bet or fold? Presumable when a good player calls it is with the idea of floating or bluff raising a c-bet.
Strangely, it seems to me that set mining in a 3-bet pot has better prospects. Say now UTG has 22 and button 3-bets to 12 with AA. Button can’t pot control with AA in a 3-bet pot so UTG EV is 10% of 112 less 2% of 96.5 or about 9 compared to the additional outlay of 8.5. Of course 3-bettor does not always have a hand to stack off with but if they are going to check-fold a significant number of flops then this might make up the difference. But everybody writes that shouldn’t call 3-bets with 22 – 77 and even with 88 it is necessary to bluff raise or float to make it profitable.
After playing a little on-line I am trying to develop some basic strategy for opening, calling, 3-betting etc. Trying to reconcile all the conflicting opinions and get it to make GTO sense is making my head spin!
A: Very good question. Your first instinct is correct: it’s not profitable to play a pure set-mining strategy (meaning you give up 100% of the time that you don’t flop a set) against a player capable of pot controlling and/or getting away from strong one-pair hands such as overpairs. Sometimes you’ll flop a set and he’ll have nothing, sometimes you’ll flop a set but win only a medium-sized pot, and sometimes you’ll flop a set but lose anyway. There may even be circumstances where you flop a set and end up folding to a bluff (ie you hold 55 on a 5d 6d 7d board and he triple barrels Ad K or something). The point is that, as you say, the implied odds aren’t there unless your opponent simply can’t fold a strong pair no matter how obvious that he’s beat. A few things follow from this.
Against a player who can fold a hand like AA, you should sometimes represent a set when you don’t have one (though not necessarily with a whiffed small pair). Suited connectors or other draws are generally the best candidates for doing so. This general strategy actually goes all the way back to Doyle Brunson’s Super/System: play your draws aggressively, and you’ll either get lots of fold equity with them or get more action for sets and other big hands (or ideally both). My recent mailbag post about suited connectors, which was actually the impetus for this question, may be of some help with this.
Secondly, you can’t afford to fold every time you miss a set. The more resilient your pair is unimproved, however, the more you can justify calling with a strategy that sees most of your value coming from sets but some coming also from picking off a bluff or two and/or running a bluff of your own. This, I assume, is why you distinguish small pairs (22 – 55) from the larger ones; the larger your pair, the more boards there will be where you can profitably call a bet or three. My recent mailbag post about chasing a gut shot explains the more complicated implied odds involved in such a calculation.
The important thing to remember is that your opponent isn’t a god. If you have the advantage of position, then he shouldn’t be able to win the pot every time you don’t flop a set but also get away cheaply every time you do. If he bluffs a lot, you’ll call down unimproved more often, sometimes losing to bigger pairs but overall showing a profit. If he gives up big hands to resistance, then you’ll give up pocket pairs unimproved but bluff often with a different set of hands. And if he simply doesn’t give up, then you can indeed show a profit purely with set mining.
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Thank you Andrew. A very good reply. Of course Villain does not need to fold AA – he can pot control. This can be harder out of position, but still possible in a single raised pot. I suppose another question arises – should a player pot control with AA or is this giving up too much value. Depends on the board texture, opponent and game flow I suppose.
Which leads on to the second part of my question above. Villain can’t pot control holding AA and stacks of 100 in a 3-bet pot so small pairs could be marginally profitable for calling a standard 3-bet.
It’s not that easy to just “pot control” in a no-limit game. For the sake or argument, we’ll even give Villain position. He raises with AA, and you call out of the BB. He bets the flop, you check-call. Turn checks through. You have the option of just moving all-in on the river. You can and arguably should do this with a mix of value hands (sets, completed draws, etc.) and bluffs (busted draws, pairs that called the flop but now want to turn into a bluff). If you get a read that Villain will or will not call predictably with whatever he was pot controlling, you can adjust your bluffing frequency accordingly. Of course it would be even easier for you to disrupt his pot control plans, with both bluffs and sets+, when you have position. This is why it’s so dangerous to take a line that turns your hand face-up as something medium strength.
Why do you assume Villain can’t pot control and/or fold AA in a 3-bet pot? It’s still a game of assessing the board, assessing your range, and determining how much equity he has. To the extent that he’s less likely to fold AA in a 3-bet pot, it’s because he got so much more money in pre-flop that your set-mining is less profitable. Also as long as he 3-bets a balanced range, then he can often afford to stack off with AA because he won’t always have it. If you’re pure set mining, then he reduces your odds by sometimes bluffing you with his AK or whatever when you fold your pair unimproved and also cutting down your implied odds by not stacking off with AK when you make a set.
I see your point. But strictly set mining was the object of my post, arguing that the set miner should employ GTO skills avoids the issue. Players engage in a set mining strategy often for the very reason that they believe they lack such skills. For example I am such a player, hence my post
When the SPR is large it is difficult for the set to get it in without a massive over bet. If the set peddler only over bets with sets then AA has an easy fold, if the set peddler sometimes over bets with other hands then he loses value on these unless he is very GTO skilled and in any event he is not then a set miner, and that was the point of my post – the profitability of calling just a few blinds with the object of set mining.
Using your example the pot pre-flop is 7.5, AA bets say 6 on flop, pot now 19.5. Check-check on turn, still 90 behind. The set peddler now leads out for 90 into a 19.5 pot. Mmm not sure what I would do if I was holding AA. But then I am a pathetically under skilled cash player and would fold.
Regarding 3-bet pots, my central point of set mining still remains. The 3-bet by AA reduces or eliminates the overall profitability of the 22 hand, but that’s not my point. I was addressing the profitability of the call of the 3-bet.
Once again using your example in a 3-bet pot. 22 open raises to 3.5, AA 3-bets to 12, 22 calls 8.5, pot now 25.5. AA bets 24 , 22 call 24s, pot now 73.5. Check-check on turn, still 64 behind. Set peddler leads out for 64 into a 73.5 pot. Mmm, even this under skilled player holding AA knows I can’t fold here, otherwise I get pushed off every hand I play.
Sorry Andrew, I didn’t address you point about sometimes having AK. Suppose my opponent 3-bets with any value value range such as {QQ+, AK}, the exact range doesn’t matter as long as there are say 50:50 of big pairs and unpaired cards. If the 3-bettor has in addition a bluffing range containing hands such as 67s it alters things. But if he is going to 3-bet bluff and not bet the flop with a high frequency and considerable GTO skills then maybe even I can exploit him. So lets say that no matter his 3-betting range he is going to c-bet fairly frequently.
As set out above we will pretty certain get his stack if he has AA unimproved. A little bit less often when he has KK because sometimes the flop will be Axx, but we will still get some of it on Axx. QQ even a bit less and so on. With AK he will surely see a turn a fair amount of the time (the set peddler can help him do that), so with AK there are two cards on the flop (the set takes up one) and one on the turn with which to hit an A or K. When we work through all this (trust me I have) we see that a range of say {QQ+,AK} doesn’t cut into the profitability of set mining compared to a range of {AA} . Why? Well mainly because AK can’t over set us, but AA can. And secondly because we are often getting at least a c-bet out of him.
Now I am not trying to assert that set mining in a single raised pot is abysmally unprofitable or that calling a 3-bet with the object of set mining is particularly profitable – in fact my assertion is that both activities are marginal in one direction or another at best or worst. But if an activity is marginally unprofitable it may still have a place in a balanced strategy.
I think I agree with your central assertion that pure set mining, at least against competent opponents, is marginal to unprofitable. I do think, though, that these players will usually have much wider 3-betting ranges than you’re assuming here, ranges that will include hands like suited connectors and will definitely not be 50:50 paired:unpaired. To call a raise or 3-bet with a pocket pair, I generally need to believe that I can win the pot at least sometimes without improving. That requires at least one if not both of the following:
a) position;
b) a pair large enough to call one or more bets and still win often enough on the river.
The relative importance of implied odds from set-mining vs. equity won from showing down unimproved will change depending on the opponent and his range. So against an extremely tight 3-better, I might go for a pure set mine (I’ve done this with hands as strong as QQ), especially if the 3-bet is small. I can rarely if ever continue unimproved, but my implied odds are very good. Against a wider 3-betting range, my sets won’t win as much, but I have a better chance of showing down a winner unimproved. The key is that I need to know which I’m up against before deciding whether to call and what my plan will be on various flops.
I should add one more point to explain my interest in this topic.
My main interest in assessing the profitability of set mining under various circumstances is because I am interested in the intrinsic value of each hole card hand and I want to separate (as far as possible) this from the value derived from the skill set of a player. With many poker hands the winning player could, in theory, have had any two cards. In reality we know that for a hand to get to a certain state of play it is very unlikely he has any two cards, but in theory he could, and the value derived is entirely dependent on the skill set of the player, not his hole cards.
When I am constructing a strategy for myself, I need to have a good idea of the value of my hole cards under the circumstances that I will play my hand in a fairly lacklustre fashion. I then can assess how much further skill (e.g. GTO maneuvering) I need to add in order to reach my desired level of profitability. For example it would be foolhardy for me to construct my strategy on the premise that I was a brilliant hand and player reader. I am not and a strategy built on this foundation is doomed. But a strategy built on carefully selected hole cards plus a few well rehearsed and disciplined plays might show a modest profit and provide the foundation to build further.
I am not concerned about arguing for any particular point of view, but I am interested in gaining a deep understanding of the game.
For example I put up a post regarding the relative merits of 53s versus AJo, not because I want to argue for either hand, but more to gain an understanding of what is required to be a winning player and which hands are a better starting point.
After reading your post about implied odds and chasing a gut shot I started to think about an idea that has been bothering me for some time.
It is this – do odds (implied or explicit) work the same way for MTT (SnG are already a solved game) tournaments as they do for cash games.
If all participants have the same skill level then each person’s chance of winning (or tournament equity) is linearly proportional to current stack size – we can demonstrate this mathematically. This should cause big and medium stacks to be risk averse and small stacks to be risk seeking.
If all participants have the same skill level then a player will only offer wagers that are fair or better than fair to himself (in terms of chips) and another player will certainly decline wagers unfair to himself. But wagers that are fair in terms of chips may not be fair in terms of equity.
Suppose a 1000 stack is offered a fair 2:1 wager for 500 by a 2000 stack. The 1000 stack should decline this 33.3% chance to double his equity and instead wait until offered a 1:1 wager for 1000 so that he has 50% chance of doubling his equity.
The 2000 stack was unwise to offer the wager as he has 66.7% chance of increasing his stack by 25% and he needs an 80% chance. This paradox is resolved by observing that both players are not playing this hand against each other in isolation, the hand is also being played against all other tournament participants.
So what should these medium and big stacks do? They should let the small stacks fight it out among themselves.
Suppose the 1000 stack takes the wager and loses. He is immediately offered a another fair 1:1 wager for 500. Because he is betting all his chips then a fair chip wager is also a fair equity wager (to him) and he should accept regardless of the fair chance.
The effect of both wagers combined is a 33.3% chance of losing all equity, 50% of coming out even and a 16.7% chance of increasing his equity by 150%. Lets say a casino offered you 33.3% chance of losing, 50% chance of ‘push’ and 16.7% chance of ‘BJ’, Your EV would be 0.5×1 + 0.167×2.5 = 0.92 so you lose 8c for each $1 wagered. I analysed a number of casino games and concluded that they maintained a house edge at the same time as appearing to be fair or better than fair by having a significant ‘push’ element, Blackjack being a good example.
Now we can see why a skill disadvantaged player can offset this disadvantage by getting ALL his chips in pre-flop. Once this player sees a flop the skilful player will offer him unfair wagers, which by definition the unskilled player cannot adequately assess. Pre-flop the unskilled player is rarely making a big mistake. However the skilful big stack must be careful to offer seriously unfair wagers as a moderately unfair wager in terms of chips may be just as unfair in terms of equity to the big stack as to the small stack.
I played every tournament at my local live casino for a calendar year. At the end of the year I won “Player of the Year” with 50% more leader board points than the chap who ran second to me, who had won the previous year and had also run deep in WSOP that year. But when I played $2/$3 (or even $1/$2) deep stack live cash game at the same casino (against cash players not tournament players) the table welcomed me profusely and took all my money – every night. The tournament players thought I was a lucky loony – which had some truth because the only words I knew were “I’m all in”, the whole table would groan before I even got the words out “Oh no, not again”
I don’t know much about ICM but it is likely that what I have described is at the heart of ICM. Andrew, I seem to remember that you built your bankroll grinding SnG so you would know something about ICM.
I also can’t guarantee that I haven’t slipped up somewhere in all this. I am surprised myself by the final conclusion – despite having some niggling idea that tournament equity was different from chip equity. So please – everyone – have a good look and find where I am wrong. I have just done all this on the fly while writing this post.
Just reading through my post.
All participants having the same skill level does not imply that a player will only offer wagers that are fair (or better than fair) to himself, but do we still have to assume (because of equally poor skill level) that the player receiving the offer is just as oblivious of true value as the player making the offer.
Actually no. The player receiving (despite poor skills) is in a better position to assess the offer. For example if the player receiving has the stone cold nuts, he needs little skill to assess the wager. So these wagering negotiations are asymmetric in that the person being offered has an inherent advantage in that he has more information – his own hand.
Even in WSOP it is likely that many hands are played between two players possessing seriously inadequate skills. The under skilled player may not be as disadvantaged as we think –
* poor skills result in small stack – so he is offered wagers for his entire stack, which as we have seen are more likely to be fair in terms of equity
* if his poor skills result in passivity then he is more likely to receive offers than him doing the offering – he is often offered tempting equity wagers that despite his poor skills he can sometimes adequately assess
* if his poor skills result in rash excessive aggression – this is not so bad in poker especially pre-flop, he is often not making a big mistake getting it all in pre flop.
So we have an asymmetric consequence of poor skills. When the poor player makes an offer he often does so in circumstances where his lack of skill is not such a disadvantage – all in pre-flop. When he receives an offer the poor player is sometimes in a better position to assess the offer than the offeror.
So the under skilled player may not be as disadvantaged as we think – the young daughter of a casino magnate that Sklansky tutored to play in WSOP despite the young lady not having previously played a single hand of poker comes to mind.
Sorry Andrew, despite your good intentions to improve my poker, I think my lack of skill gives me an intrinsic advantage over your superior poker skills if we ever meet in a tournament.
Haven’t had time to give this the consideration it deserves, but the first thing that jumps out at me is this:
“If all participants have the same skill level then each person’s chance of winning (or tournament equity) is linearly proportional to current stack size – we can demonstrate this mathematically. This should cause big and medium stacks to be risk averse and small stacks to be risk seeking.”
It’s not clear to me why the second point follow from the first. Conventional wisdom holds that a player should be more risk averse with the last of his chips in a tournament, even in a scenario where there is no skill differential. This felt like a big jump in logic to me, on which the rest of your argument is predicated…
Fair point.
But no, it is not a jump in logic, and the rest of my argument is not predicated on it. I was actually summarising the conclusion drawn from my logic before presenting the arguments leading to those conclusions. You are perfectly correct to note that the second point does not automatically follow from the first. But it does follow, possibly in a qualified sense, from the arguments presented.
You are quite correct in stating that a player, regardless of skill differentials, might benefit from carefully choosing the spot to commit the last of his chips.
But a skilful player with a big stack needs to use his skill to persuade his less skilful (and stack challenged) opponent to accept wagers that are extremely unfair to the opponent. This is possibly not difficult for the skilful opponent, but he needs to take care that the wagers are not just slightly unfair. This is because a wager that is only slightly advantageous in chip terms for the big stacked skilful player might in fact be disadvantageous to the skilful player in terms of tournament equity.
I agree that my conclusions are radical (and possibly only a theoretical curiosity) but so far I cannot see a flaw in my reasoning. But that is the purpose of the post – find the flaw.
Patrick, I disagree with your assumption that skilful players have to seek only “extremely unfair wagers”. At almost any tournament I play in, I am willing to accept almost any edges so long as they don’t hurt my overall tournament equity.
“Now we can see why a skill disadvantaged player can offset this disadvantage by getting ALL his chips in pre-flop. Once this player sees a flop the skilful player will offer him unfair wagers, which by definition the unskilled player cannot adequately assess”
This quote kind of illustrates where you are going wrong, in a way that many amateurs tend to. You have for some reason assumed that “skill” becomes a factor only once the flop is dealt. This is absolutely untrue, and I’ll go as far as saying that the main skill tourney experts have is their understanding of pre-flop betting. It seems that you have decided you are bad at poker and therefore your best strategy is to keep going all-in preflop at appropriate moments. In general going all-in a lot preflop can be +EV…what you are missing is that good players can choose to do a lot of what you are doing and ALSO play well on flops. Being a good player doesn’t mean I am forced to handicap myself by refusing to accept small edges and accepting only “extremely unfair wagers”. This seems to be the approach that Phil Hellmuth type players adopt, but its quite clear that in recent times young players who adopt massive pre-flop aggression and a willingness to pursue small edges are doing extremely well. I am not giving up my skill advantage by taking small edges…taking these edges IS my skill advantage.
It is only on the final table or close to bubbles that there is a divergence between chip value and dollar value, as a consequence in the vast majority of situations I would accept a moderately favourable wager. To provide an extreme example, on the first hand of the WSOP if someone shoved and accidentally exposed AKo, I would make the call with QQ and take my race as a 54% favourite. I think that at least part of what makes me “skilful” is that I would take these and similar edges rather than be overly cautious.
I am aware that Andrew would actually fold here, but I am not Andrew Brokos and unlike him I don’t think I have a 80-85% chance of doubling my stack anyway by outplaying weaker opponents (which he almost certainly has). My reasoning here is that I am almost certainly going to have to risk my tournament on a coin-flip at some stage or the other; I don’t think anyone has ever made the top 100 of the WSOP Main without doing so, let alone win the event. As a consequence I would rather take my flip when I know for sure I am good and when doing so allows me to take further and possibly even more +EV coinflips at more critical stages WITHOUT risking my tourney life.
Thank you Prabhat, you have set out some very useful observations.
But my “extremely unfair wagers” is not an assumption, it is a consequence of a chain of logic – which I am hoping will be challenged. I think I have laid out all the assumptions I have made as a precursor to my logical chain.
Oh I forgot to address your example of AK v QQ. The logic I have set out clearly leads to you accepting this wager. You have 54 to 46 advantage in both chip equity and tournament equity because you are wagering all your chips.
But say it was the second hand and your opponent only had half your chips. Would it now be correct to accept? Superficially our reaction would be “what’s the difference – if it is good for all my chips then surely it is good for half”. I have a great deal of sympathy for this reaction – but that does not mean it is correct, and I have set out some reasoning that might lead us to challenge our natural instinct.
As usual, it took me a while to assess your example.
With the AK v QQ, clearly your villain has offered a wager that is unfair to the villain, and this unfairness is not offset by any other factors such as chip equity versus tournament equity. It is also a very good example of a deal that might be offered to a skill challenged player. Clearly in this situation you are in a very good position to assess the true value of the offer regardless of your skill level.
If you were offered the same deal for half your chips then I think pretty much the same reasoning applies, but I would need to work through this in detai.
But what would be of more interest to me is should the villain be offering such deals or even 46:54 (he has the QQ you have the AK).
A 46:54 for half his chips and all your chips would unfair for you but might be just as unfair in tournament equity to the villain. This still needs working through in detail but the example given in my original post is not far removed.
Patrick, let’s look at your example this way.
Let’s say I make my call with QQ and I hold up. I now have 60,000 chips. On hand 2 of the Main Event, some other clown shoves and I see AK again, and I have QQ again. I can’t for the life of me imagine why I wouldn’t make the call again. My chances of winning the hand are the same. I can’t be knocked out of the tournament now, and in any case there is no need to be risk averse because 60,000 chips is very far from the kind of figure i need to win this tournament or even go deep. I called in Hand 1 precisely so I could take this kind of risk later on. (Please note that calling a shove for 15,000 chips with 30k in my stack is quite similar to calling 30k with 60k in my stack. More importantly both of these calls are very good.
I am very unsure as to why you are so fixated on whether the bet constitutes half of the bigger player’s stack. As long as the bigger stack still has enough chips to play with, the equity he has in the hand is far more important than what percentage of his stack the bet constitutes.
Edit: I’d go as far as to say that I can perfectly understand why some players, Andrew for example, would choose to fold QQ in Hand 1. But if those players doubled up on hand 1 (in some other manner) and then faced this same shove, I think it would be terrible to fold QQ to AK when you have 60,000 chips. In other words, the 2nd hand is a much easier call than the first one.
“the 2nd hand is a much easier call than the first one.”
-Agreed.