MuckMyNuts

Cool, I hope some of that proves useful. With a bit of reflection I'd like to add a bit (I tried to keep it short but apparently I'm in a long-winded mood these days).

First, I think I over emphasized bluff-catching, and I don't want you to take that to heart too much. I think a lot of players would benefit from bluff-catching wider, but what I really want to stress is making adjustments to players based on specific observations, sometimes after only a few hands. This is tricky business because it takes a lot of pattern recognition/feel which is impossible to teach and only comes after thousands of hands. It is also something which a lot of players mess up by using HUD stats, or similar simplistic information, to make huge adjustments.

Gangsta shit can mean making a hero fold too. A few months back, I folded KK on KT3 Q (rainbow) facing a turn shove from a LAG with aggro postflop stats, which I still don't believe I did. I thought it was the right fold because of what I know about his play, and the stack dynamics (8 handed at a final table I was one of 2 players that covered him). I still ask people about this hand, and I can't say that I think it was anything but a timid fold, but, I'd probably do it again against the same villain (I hope he doesn't read this). If you'll allow me to be results oriented, I finished 2nd instead of a 77% chance of going out in 8th if I was behind (I had less than 3bb more than him).

Second, I want to emphasize how much board texture/range study matters more than what you can learn with a solver. I may not fully understand how PIO is different from other solvers, and I am certain that I will eventually get a copy (I hear great things), but I want to deepen my understanding of the game before I look to a program to tell me what to do. If you don't thoroughly understand the differences in ranges on a board of, for example, KT6 vs a board of KJ6, a solver may not be your best route to progress.

I might just be old fashioned, but it seems to me that getting a program to tell you what to do has the same drawbacks as watching a video that tells you what to do. Not that you can't learn a lot, but its more a question of what knowledge you can have access to while playing, and for that, I don't know if there are any shortcuts. I think it's a lot better to reach 100% of your potential as a player in 2-5 years than to reach 90% of your potential in 2-5 months and never go beyond that.

Finally, If you feel like your mental game and approach sucks, my only advice is to write it out. Put down on paper exactly what mental game problems you think you have. Write out details of what seems to trigger them, how each problem hurts your ability to succeed, how you would prefer to think and what advantages those different thoughts may have. Hell, write anything.

Just getting those thoughts out of my head, and reading them from time to time, helped me a lot. It's a long ass road, and I'm probably way less than halfway to the finish line. I still get desperation tilt (why can't I afford high stakes yet?/where's my porsche?), lack of confidence (maybe my results are all good variance?/what if I can't support myself and my gf leaves?), and downswing tilt (if I've lost ten days in a row, I don't even want to look at my PC). I still look at my $$ results too often, and my motivation to put in hours is still sub-par when I feel like I'm not quite on my A game. I regularly struggle to focus in the early levels of tourneys, especially if i just busted close to a final table. I am slowly getting better at all of these things.

The scary part is that every day you put off working on your mental game, the habits get more ingrained, and the finish line gets further away.

I haven't used PIO or any solver (aside from some light messing around with CRev), so I hope my post isn't many levels below you. If so, feel free to point and laugh.

In my opinion there is no right way to build a study habit, the most important thing is that it becomes a habit. I'm still not great at honouring my schedule so I manage to spend at least 5 hrs a week studying by setting aside 10-15 hrs as study time, and following through on at least half of it. I think you've got the right idea by not cramming in sessions around your busy work schedule. Should free up some mental energy for studying, and hopefully lower your stress levels in general.

As for identifying topics... play some poker, get in a spot where you're not sure what to do, study everything related to that spot, rinse, repeat. You can also go through your database and pick an old session that you don't remember well. Replay some hands but before each action think about what you would do, and see if/how/why it's different than what you actually did (make sure villain hole cards are hidden).

I mean, if there are fundamental things that you know you still need to work on, then those would be top priority, but I get the sense from your post that you are a fairly experienced player looking to shore up some small weaknesses and mostly just keep your blade sharp.

I'm not sure what you mean by meta skill, but mental game is hugely important. I stopped tilting years back (or at least I stopped the angry monkey spew tilt) but, since turning pro last year, I've found a whole bunch of mental leaks/mini-tilt in my game/approach. I'm planning to work with someone like Elliot Roe within the next year or so (once I'm not using 100% of my profit to pay my strategy coach lol), but just by working through some parts of Jared Tendler's books (especially TMGP 2) and experimenting with a bit of meditation, I am making huge strides. Everyone is different, as are our mental game challenges, but I can't believe there is a single poker player on earth that wouldn't benefit greatly from taking a long hard look at their mental game, unless they've already put a lot of time into it (and continue to).

As for quantifying how much better we get, that is a difficult question, and you're not alone in wondering that. You'll never know how much 50 hrs of studying changed your bb/100 or ROI in any real sense.

There is a big difference between efficient and inefficient studying. As human beings we naturally enjoy the process of learning, especially in areas we are passionate about. If you're not finding what you are studying interesting, and if you don't occasionally get a little bit excited by something you figured out, you're probably not studying the right thing/way. Stop, and head in a different direction. The beautiful thing about poker is that there is always something else to study. With a little curiosity, you could spend many hours studying a single hand without wasting any time, if you go deep enough into all the possible lines/ ranges/ future cards/ villain types/ differences compared to similar boards/etc.

I think the most important thing to consider about studying is: Are your opponents doing it?

In a zero-sum game like poker, you only get money from being ahead of your competition, and the player pool is getting incrementally tougher every single day.

My best suggestion for improving post-flop play is a very detailed study of how preflop ranges interact with various board textures. I like to use Flopzilla to get started. Once you see what hands are most likely for each preflop range on a particular board texture, you can get a very precise sense of which parts of your range you should bet/check/call/raise/fold. You can do some 1-alpha or similar calcs to figure out some rough minimum frequencies you want to have for each action in each spot. Knowing precisely when A-high is a very strong part of your range, or when TPTK is (at best) a very weak bluff-catcher, is invaluable. Getting a clearer picture of how you want to play each part of your range in various situations will also allow you to predict (and abuse) how villains may behave in similar spots. Also, study removal/blockers and their effect on bluffing/bluff-catching.

If you can stomach a bit of reading (okay, a lot of reading), I can't recommend the book "Applications of NLHE" by Matthew Janda enough, although I also can't pretend to have mastered even a fraction of its content.

I think another big thing to consider for postflop play is that you don't win tournaments by folding. I'm not saying make every hero call or 3 barrell-bluff that you can, but once you spend enough time studying ranges, you'll realize that most half-decent players (at least online) are wayyyy too bluff heavy in a lot of spots. Obviously, there are a bunch of players where the opposite is true, and some players who will adjust to you very quickly. I hope it goes without saying that you must be cautious in choosing your villains, but I regularly stack people by bluff-catching with bad pairs or high-cards just by knowing that they rep a very narrow value range on certain run outs. They don't call MTTs donkaments for no reason: you gotta do some gangsta shit that can end up looking pretty foolish (to the uninitiated) if you want a half decent chance of winning.

We dont need an edge on 90% of field to be +ROI. We can be average compared to field but be good at exploiting fish, while forcing better players to play big pots when against us, and still have positive ROI in field where we are not inherently a favorite.

Pretty cool formula though, definitely food for thought.

I think getting Nash ranges down is essential but there are a ton of spots where adjusting them is a good idea. On bubble we should shove wider than Nash vs those we have covered if they don't seem prone to gamble (sometimes ATC vs midstacks when there are a bunch of shorties left in the field), and should be calling way tighter than Nash vs those who cover us (assuming many players shorter than us).

Early ITM I think we can shove a bit wider than Nash with shortish stack in big field tourneys (like when 400+ paid), because laddering up is worth way less than chance to go deep, even if we make slightly -chipEV shoves (may be wrong here but it is my approach). Final table bubble plays a lot like bubble but knowing villains is even more important. Some players play very tight with mid stack trying to make FT with low risk, others are 'going for the win' and very happy to flip for their stack, so will be calling pretty wide. Adjust accordingly.

I think ICM dictates we should be pretty hesitant to call off our stack with less than 60% equity vs range on final 2 tables, but I'm just starting to learn the math so can't say I'm sure. We should still be shoving pretty close to Nash, but tighten if we know that someone left to act is calling especially wide. Every chip we can lose is worth a lot more than chips we can win, and we'd really prefer not to gamble without a good edge.

Especially if we are midstack and there are many shorter stacks, we should be very risk averse on final table. Laddering up is meh, but busting in 8th when 3 people had way less chips than you is lighting your ROI on fire.

Also consider that a lot of great players will minraise weakest and strongest hands in Nash ranges, even at stacks as low as 10bb. It's a more difficult strategy than open shoving, but likely higher EV if you pick right spots and you've got good ranges for R/C and R/F.

You can look at Nash shove ranges and figure out what would be profitable calls with a program like Equilab. It has a cool feature (can't remember exact name but it functions like goal seek in excel) that tells you exactly what hands have at least X equity against certain ranges. You can also widen or tighten villain's range depending on reads.

I'm barely scratching the surface of MTT math and ICM calcs so not sure what kind of equity we should be looking for vs. various stack sizes, and I think it would change significantly based on stage of tourney and our own stack size (and structure, need much less equity in a turbo).

Rough guess is we standardly want >=57% vs 18bb+ shove range when we are big blind, and more if there are players left to act/we have less invested. As villain's stack shrinks we can likely take some spots where we are as low as 40% vs their range, and vs <5bb I think we call any two in BB (assuming antes are in play).

Keep in mind I've only started learning this stuff so may be wayyyyy off, and would be interested what better MTTers have to say on the subject.

AQs is super awk here, I think fold is fine. Before antes unlikely an 11/11/0 (even over small sample) is getting too frisky. You're ahead of much of both ranges but if you 4bet and face a shove you're almost always way behind, but roughly priced in to call. You could 4b very small and fold to shove, but it gives villains great odds to peel in position with whole range (which is no bueno). Even when a normal size 4b gets flatted, can't assume villain doesn't have some AA-QQ and AK in their range, bad regs at these stakes love to 'trap' here. Mini pacific rim (its $16.50 BI, right?) and similar deepstack low BI tourneys we can usually find better spots to GII before getting short.

That being said I don't hate a flat either. Sure, your range is pretty face up against good hand readers, but with little history they'll at least consider that you may just be bad when you cold call in the BB. Need to call 1187 when MP is rarely 4betting but calling often, so you are usually getting around 3.8:1 on your chips. AQs flops pretty well, and many villains will play straightforward postflop fearing you might be really strong, so this can't be that bad even OOP.

Still, you are somewhat frequently dominated so A or Q high flop can mean bye bye stack more often than we'd like. I'd probably be folding with no real reads. If field is really tough you probably can 4b GII here as standard, but in low-mid BI deepstacks I don't think this is the case.

Grats on shipping it! Well done sir :)

I think if you have pretty strong population reads then for sure your assumptions make more sense than my general approach to unknown fishies.

I completely agree that we can drive ourself crazy and accomplish nothing by overanalyzing spots against rec players. If they think about the game in a much different (and likely convoluted or overly simple) way than us, it will be hard to gain much by using logic that assumes a well reasoned approach to predict the meaning of their plays.

For example, I recently played a drunken home game with some friends. At heads up I 3bet pre with KQ. Flop comes QT7 and I made a ~1/3 pot bet with <2SPR (he has me barely covered). Buddy looks me right in the eye and says "What do I do with trip 7s here?" He tanks and then shoves. I figure he is trying to level me in some weird way, and am pretty happy to call. He of course shows 77. Like, wtf right?

Fair enough, that is a good point. Sorry for the tone of my response, I think someone pooped in my cornflakes that morning.

Great Read!! Forgot about this one :)

Also there is no 'breaking' of Nash Equilibria three-handed.

Wrong. If the presence of a player making mistakes provides incentive to diverge from a previous Equilibrium strategy, then by definition you have broken the equilibrium.

I can't copy the formula here (its just a bunch of html code), but they define a Bayesian game as G=(...), and then define a Bayesian Nash Equilibrium as Gprime=(...). In theory, if we could calculate they Bayesian Nash Equilibrium it might give us a more accurate/ detailed model of a poker decision than a simple Nash Equilibrium. The example of the sheriff game at the bottom, as well as the example of the chicken game in the related article about correlated equilibrium, illustrate situations where simple Nash Equilibrium achieve less than optimal results.

I again didn't word what I was saying very well, or think it through well enough. People in the community always seem to compare GTO play and exploitative play as if they were polar opposites. My original understanding of a Bayesian Equilibrium was that it described a state where we were maximally exploiting our opponent, but of course this is wrong because for it to be an equilibrium our opponent would need to be maximally exploiting us, and therefore it is actually just a typical formula for Nash Equilibrium when we have imperfect information. So I hastily jumped to some incorrect conclusions.

What is quite interesting to me now is the idea of Bayesian-optimal mechanisms. They are typically used as an approach for setting prices with imperfect information about the market or potential consumers.

If we assume that our opponent's willingness to call a bet is represented by a single-parameter utility function (fancy speak for he will call anything less than a certain amount and fold to anything more than said amount), this approach could be a useful way to look at bet sizing. I haven't actually played around with it, and it may be quite clunky and not the most efficient way to study/build a strategy, but always fun to find new ways to think about poker decisions.

Thanks! That article describes what I'm struggling with pretty well, although my problem I think is that I am agonizing too much about the very common decisions: BB defense, reacting to 3bets after raising the button, how to size my c-bets and which players I should be less likely to cbet, etc...

I think my problem is that I thought I was good, and my results at micro/low stakes have been good over a smallish sample, but as I learn more about the game I realize a lot of my fundamentals are flawed. My reaction has probably been to over-adjust my strategy, and now I am trying to work back towards the middle ground.

I'm working through a lot of mathematical analysis and taking a few days off from the grind. I need to remember that as much as my strategy was flawed, it was still winning me money against players with bigger flaws, so I can't forget what I know has been working as I strive to make improvements.

My ultimate conclusion is that I just need to chill-out, and as you say, work on one common spot at a time rather than trying to overhaul my entire strategy at once. Mostly I just need to chill out lol

With regards to the algorithms, would they be along the lines of solving for multiple actors in a Bayesian game? I only took an introductory game theory class as part of an econ degree so I don't really have a firm grasp on how to learn about more advanced topics. Do the formulas on Wikipedia hold up?

https://en.wikipedia.org/wiki/Bayesian_game

A Bayesian Nash equilibrium is defined as a strategy profile and beliefs specified for each player about the types of the other players that maximizes the expected payoff for each player given their beliefs about the other players' types and given the strategies played by the other players.

If the variables could be accurately defined (which would be infinitely hard), it seems like this is, in theory, a formula for maximum exploitative play. Would this be the exact opposite of GTO play (in that it accounts for our beliefs about each player) or are the two relatively closely linked?

Yay! People smarter than me are talking. :D

So much so that some are already coming up with ways to exploit "GTO players" who misunderstood concepts.

Yeah, I think GTO strategy is misunderstood by most who try to practice it and thus can be manipulated, if you can figure out the individual misunderstandings and where they create repetitive errors. Myself, if I were to attempt to base my play off of some GTO strategy, having not put in any work with CREV/PIO/GTORB other than watching videos, would just become a huge fish and easy to exploit by any semi-competent player, even those with no concept of GTO play.

I do agree that it is a very useful concept for building our strategy around, and am planning to purchase PIO to do some work once I can wrap my head around the $250+ price tag. I'm a nit with my life bankroll.

Thanks for this. Interesting to me that in three-handed you could break a Nash Equilibrium but when six-handed it would not be so. I guess it does stand to reason that unless the Nash players diverged from their strategy to play an exploitative strategy to account for your presence, you would just slowly (or quickly) lose money based on your play. If one did diverge to exploit you, then I guess all players could benefit from diverging, but otherwise they would just all happily collect the dead money in the game while sticking to their pre-established strategy.

I imagine that, while 3-handed the presence of a player making mistakes will make one player sticking to his GTO strategy -EV compared to the other GTO player, simply by relative positioning, in 6-handed game this effect would be diminished such that even if one or more players' EV diminished relative to the other GTO players, the player playing a new strategy would by far have the lowest EV, and the other changes in EV would be minuscule.

Funny that you made this post (which inadvertently answered some of my further thoughts) while I was writing the above post.

It was this part of the article that made me particularly curious:

Some games may have Nash equilibria that are not ESSes. For example, in Harm thy neighbor both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either. However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B. This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B).

If you look deeper into game theory there are more situations where Nash Equilibrium can be disrupted by adding additional actors. Specifically for poker:

http://blog.gtorangebuilder.com/2014/03/gto-poker-outside-of-heads-up-what-it.html

If you scroll down to the section entitled GTO 3-handed The author argues that even if two players are playing different strategies at Nash Equilibrium, adding a third player to the game who is playing less than optimal and making mistakes will cause one of the original players' strategy to become -EV.

Nothing about the definition of a Nash Equilibrium guarantees that the button's change in strategy won't also decrease the hero's ev.

If you imagine that the Big Blind player is a smart reactive player it can get even worse!

It is important to note that the above are not due to ICM, they appear even in cash games. In SnG situations where ICM is a factor there are even bigger and more obvious instances where the presence of a fish can make a nash strategy -EV.

The author only analyses instances of push/fold but it seems to me his reasoning is sound and would extend to other poker situations. I'm curious if other people have gone beyond his study of GTO in these situations, considering this post was made in 2014.

I don't disagree with anything you say. I guess I didn't word my question well. I'm wondering if this theoretical situation can occur at a poker table, specifically what is described in the section "Nash equilibria and ESS."

https://en.wikipedia.org/wiki/Evolutionarilystablestrategy

I'm wondering if this concept applies to something as complex as poker. It's purely hypothetical and not of any strategic value, but it makes me wonder, if you were forced to play at a horrible table with 5 other players playing exactly the same GTO strategy for every imaginable situation, would you have no choice but to emulate their strategy, or automatically become the biggest fish in the game?

In nature my understanding is that there are certain things that can disrupt ESS states that have existed for generations, often due to human shortsightedness (eg. introduction of foreign species or bacteria/virus). Got me thinking about whether there could be a strategy that would break an ESS poker table, if such a table could even exist, and what that strategy might look like. My mind goes to strange places when I am trying not to go crazy around my family (Canadian Thanksgiving).

Yes, I could have worded it better, lol - if it was actually learned it wouldn't be tripping me up. Thanks for the advice. I've tried to be conscious of changing only a few things at a time but I'm probably working on new things before spending enough time playing with what I've recently learned.

I definitely need to spend more time thinking about why plays are working or not.

I was thinking about this a bit more and I want to recommend a book. Excelling at No Limit Holdem by Jonathan Little. Many very talented players contributed chapters, and it has a lot of sound advice about strategy, life balance, and the mental game. The price is higher than most Poker books, but after a chapter or two you will see why.

You may find the chapters by Evan Jarvis (AKA Gripsed), Dr.Patricia Cardner, and Ed Miller particularly relevant, and there is a TON of really good strategy for MTTs in the second section. Alex Fitzgerald's chapter helped me a lot - he strives to simplify a bunch of MTT strategy and show that a big portion of winning poker can be understood through a relatively simple approach. He breaks down a lot of common spots mathematically and provides you with simple tools to do the same with any holdem situation. I will caution that some plays he suggests are very opponent dependent, and you're just burning money if you're regularly making them in the wrong spots. Even if you use none of his specific strategies, he teaches a really useful way to think about the game.

I think you can explain the time commitment to your friends and family in terms of working really hard to get better so that you can make good money in the future, rather than telling them about X $ made per hour/week. Your passion for the game is a much better reason to devote a lot of time to it than how much money it might be making you at this point.

Unless you are already beating your games at a healthy clip, I don't think it is wise to rely on being able to turn 1k into 15k in a year. If you need the money you're almost certainly better off getting a normal job and working on your game during whatever free time you have. You could get a part-time job and focus 10-25hrs a week on poker around your work schedule. There is no rush to dive right into chasing your poker dreams right now. As long as your passion for the game remains strong, and you're willing to work hard to develop your game, there is no reason why you can't chase the dream 5 years from now, after college. Poker isn't going anywhere.

I think passion is the answer to a lot of your questions. If you really enjoy poker, especially if you enjoy analyzing hands away from the table, it won't be as hard to motivate yourself to put in the work to get better, and to put in the hours grinding. If you're not already playing 8 hrs a day, but imagining how hard it will be to do so (rather than being excited about it), you may want to ask yourself: "Why poker?"

There are many easier ways to make money. Are you chasing the dream of making lots of money and having the freedoms of the poker lifestyle, or are you interested in poker as a career because you expect to start your day excited to play more often than not. Any skill is much easier to develop to a high level if you enjoy practicing it. It's going to be a lot harder to study the finer points of strategy if you're not at least a little fascinated by the subtle intricacies of the game. It takes A LOT of work to become very good at this game. I've got a tons of work to do before I'd consider myself a very good player, and I've been passionately working on my game for more than 10 years.

There are many successful players that grind out a great living from poker without being very passionate about the game. However, if you were to take a survey of all the biggest winners at medium to high stakes, I'd be willing to wager at least 90% of them started their career because they loved playing and were fascinated by what they learned as their strategies progressed. Many of these greats have been playing for years but still get excited to analyze hands and/or situations, especially if they're able to bounce ideas off other great players. Getting ready to play rare events like the WCOOP or other series that only come around once a year is something these players relish. Can you see yourself feeling that way after 10+ years of playing?

So... Why poker? Ask yourself, write it down, keep the paper. Look at it from time to time and add to it, or cross out what's there and start all over. Your 'why'.will lead you to more success than you could ever dream of... If it is strong enough.

I think pre-flop hinges on what category of loose and fishy our villain falls into. I think we need to find a fold if he is habitually very aggressive. Our hand hits a lot of flops hard enough that we'll often want to continue, but it rarely hits hard enough that we're excited to play for multiple big bets OOP. Being two seats to the left of this player, we'll have plenty of chances to abuse him with position on our side. Why get involved OOP?

I can't assume he was hyper-aggro based on one hand. Anyone who's played enough poker has seen more than one passive fish suddenly play a hand this way for no apparent reason. If villain won't pressure us very often, playing a middling ace out of position can't be that bad when we can exploit frequent post flop errors. I will say that 4x is pretty steep, especially considering villain had less than 40bb to start the hand (if I counted right). If you believe villain might be easy to read because of tells or an obvious lack of emotional control than I think calling is great. Otherwise it's pretty marginal unless BB is overly tight, or seems very conscious of the approaching bubble. With our big stack we can afford to take less than optimal spots, and to make deep runs we want to give ourselves every opportunity to take weak players' chips (before someone else does), so I really don't hate the call if villain is on the passive side.

Regardless of open size, I only like 3-betting if we've seen villain fold to a flop cbet in multiple 3bet pots. If he is folding preflop it's obviously fine, but not sure loose fishy players are doing that very often, unless we make our 3bet really big. Aside from hand selection, which we aren't really using here, we probably gain most of our edge with superior post-flop play, so I don't see why we would inflate the pot OOP. I guess it is useful to make sure BB isn't likely to get involved, but I don't think that's a good enough reason when we can expect fairly straightforward play in a multi-way pot this close to the bubble (assuming that we have BB covered).

I think your decisions post-flop are okay, but I do want to highlight some potential problems:

1)You might be defining villain's value range too narrowly. Why is villain not allowed to have J9s, QTs, TT, 44 or AT? Is he limping cutoff rather than raising with most of those hands?

2) Your numbers re: villain bet sizing seem inconsistent. With two callers pre, the pot would be 36k (+ antes if there are any) on the flop. After an 18k flop bet, pot is at least 72k on the turn, so a 29k bet is pretty small. By your reasoning, this is right around the size a scared overpair and/or set wanting action would pick. Although I think regs will bet big with sets (and check back a lot of overpairs) considering all the draws, I agree that weak players often tend to pick small sizes when they desperately want to get paid, regardless of board texture, or when they feel they have to bet an overpair but are kind of scared by the board.

3) You mention tells that indicated insecurity, but even with those I think peeling the turn is very questionable holding 3rd pair. We can't assume a fishy villain wouldn't bet a hand like AT or JJ (or 99) despite the overcard coming (and might feel pretty insecure doing so). When you are ahead, villain must have outs. There's a lot of river cards you will really hate. Effective stacks make a river shove pretty likely, and even when our hand improves we will lose a non-zero percentage of the time. Even with a pretty good price, you'll find way better spots to commit a big chunk of your stack. Don't fall into the trap of thinking that villain reps so few value hands that he must be bluffing too often. Unless you think he is betting 100% of his air, how many hands flop enough equity to bluff on this board but are still behind A8?

4) I flat out disagree that QQ and TT won't shove the river, unless you are pretty certain that a min cash meant a lot to this player (which in your reply to Ralphy you seem to be saying the opposite). I think a lot of recreational players aren't even considering ways they could be beat when they have a hand as strong as a set (unless a 3flush/4straight hits the river).

Either way, there aren't a ton of value combos that beat us. Once we get to the river and see one of the best cards possible I think we are priced in to call. We have enough chips behind that we shouldn't be at risk of bubbling when we lose this pot, and winning it puts us in a great spot to make a very deep run (which I hope you did!).

I hope this was helpful. Some of my reasoning is likely flawed and I'd be interested to hear what you think.

Wow, just wow. Introspective mind activated 100%.

Yeah I agree that 23 worse combos calling is very optimistic. I didn't bother breaking down which hands call, I just discounted the numbers a bit for both outcomes when called, to reflect that I made a lot of assumptions throughout the analysis.

Agree 100% on sizing: 30-35% is probably the biggest we want to go, likely best for every street if we plan to three-barrel. As played we could even bet ~15% on the river. I don't think enough villains are bluff-raising small bets to worry about that, and we might even get thin value from a stubborn A2.

I had a bit of trouble analyzing this pot. I can't remember the last time I double barrel AJ OOP vs unknown on this kind of board. I'm mostly checking turn or sometimes flop and treating it like a strong-ish bluff-catcher after that, probably looking to call one reasonable sized bet on either turn or river. Probably making a 2/5 pot bet on river when villain checks back turn.

I got caught up with the assumptions OP and some comments made about villain's ranges, aside from the few adjustments I mentioned. Although I don't agree that only the worst players are calling with worse Aces, I think you are right about this being a losing bet as played. I often see call downs for three <1/2p bets in <$10 MTTs across multiple sites. Some players happily call their entire stack here with A8s... However, the average unknown, even in the weakest fields, is not calling enough weak aces to make a river bet profitable. We're more often value owning ourselves against AQ/A6/87 or getting raised by nutty hands.

Against known stations I think this line is fine but would advocate larger bets. I think we should never be in this river spot without reads because checking on an earlier street plays better.

I still think check-call is the worst possible line as played. Not enough missed draws to assume players at this stake will be bluffing often enough after we bet twice. I don't think sensible villains often bet for value with a hand worse than ours (many check back AK/AQ here - whether they should or not is up for debate). Long run you'll more than make up for the times you fold a winner by not paying off when beat. Check-fold and move on if you don't want to bet-fold.

Duuuuude... I've been mulling over thoughts along these lines for the past few weeks and reading this instantly brought everything into focus. Sharing from a place of true wisdom indeed. Thank you!

I played around with Equilab some and I'm a little surprised by the results. This post will get pretty long I fear, but I hope someone can get something useful out of it. I definitely did.

Before I get into that, I want to address something:

I think I made a sizing mistake here. What should I be considering here? If he has an ace, I'm not worried that it beats me. Because he has so few hands that beat me, do I size smaller to get value out of his marginal hands that are drawing very thin right now?

Are you really saying that you want to bet smaller because he has less hands that beat you? Or do you mean he can't have many draws? Either way, I mainly try to consider four things for flop bet sizing (in order of importance): Board texture, reads on the villain, what I am trying to accomplish, and if I am in position or not.

In this hand you have a very dry Ace high board, a big reason for sizing small. You have no reads so we can ignore that. Your hand is way ahead of villain's range but the top of villain's range has you crushed, so what are you trying to accomplish? --> You want to extract value from marginal made hands, which tends to suggest sizing small. You are out of position: on a dry board this is another reason to keep the pot smaller.

So we seem to have a lot of reasons to bet smaller. I think about 35-45% with both value hands and air is about right. This lets us extract some value from marginal hands like 88, 76s or even 98s (GS+BDFD). It's okay keeping those hands around when we have air because they often won't be able to call a second barrel (and on dry boards we usually want two bullets ready unless the turn card is awful).

The difference between a bet of 90 (40%) and 150 may seem trivial but bets in NL grow exponentially by street. 225 + 2(90) = 405 in the pot on the turn. Turn sizing I tend to go bigger, but on this board there's not much reason too. Around 165 seems good to me. This would get us to the river with 735 in the middle and 1115 in the effective stacks, roughly 3 : 2 SPR.

This leaves you with more room to bet - fold the river which -spoiler alert- is the play that my Equilab analysis greatly favors.

Speaking of which, I'll start by assigning villain a button flatting range. Something like:

TT-22, AJs-A2s, AQ-A8, K9s+, KJ, Q9s+, QJ, J9s+, JT, 1-gaps 75s+, connectors 54s+.

This is pretty wide, but not unreasonable. We don't need to be too concerned about getting villain's range perfect, especially because we have no read on this villain. As I mentioned earlier I think villain will sometimes have AK/AQs/QQ/JJ in their button flatting range. To account for this I will include half of the combos of AKs (1), AQs(1), AK(3) and one third of the combos of QQ (2) and JJ (1).

Not accounting for blockers, villain has 286 possible starting hands (21.57%) Considering our hand and the flop cards that shrinks to 208 combos. If villain calls a 2/3 pot bet with any OESD and any middle pair or better there are 97 combos that reach the turn, namely:

49 Top pairs, 27 pocket pairs QQ-77, 6 middle pairs (86s/76s), 6 sets, 5 two pairs (2 A6s, 1 A5s, 2 65s), and only 4 OESD (87s). It's worth nothing that we beat 35 of the top pairs, lose to 9 and chop with 5. We should probably add a few more combos for floats like KQs or 98s w/ BDFD but I'm not going to bother with that in this example.

We don't want to assume our unknown villain is a fish, so after they call flop and turn I think it is wise to remove some of the weakest Aces from their range. We block all of the A high flush draws, so I'm going to proceed as if villain dumps any hand worse than A8. It might actually be wiser to go tighter but considering our assumptions about the player pool I think this is fine. Let's also assume his middle pocket pairs and all of his 6x get dumped too. Although the board pairs I think 8h7h is never folding, and we should probably keep 1 more combo of 87s too.

Once we see the river 4, we're looking at 52 combos: - 1 four of a kind, 6 full houses (66, A5s, 65s), 2 straights, 2 three-pairs (A6s), and 41 Aces.

That means we lose to 20 of villain's combos, chop with 5 of them, and beat the other 27. However, we should probably discount the nutted hands and A6s slightly because at least some of the time these will raise either the flop or turn. I think we can safely eliminate 1/3 or 3 of those combos. We now have 17 combos that beat us.

For a profitable value bet we need to be called by worse at least 50% of the time. If villain is getting this far with his weak Aces he is probably not folding them to a reasonable sized bet. I think we can safely count on 23 combos that we beat calling us. We can ignore the 5 chops so 23/(23+17) = 57.5% of the time we win when called, so a bet here is almost certainly +EV (again, this is only against random typical player in micro/low MTTs). As for sizing I would say sticking to roughly 40% (~380 as played, ~300 in my fictional example) is a good plan.

There's an even better reason for bet/fold being preferable to check/call. If we look at the breakdown of villain's range, most of the hands that we beat will check for a free showdown while most of the hands that beat us will be betting. Backdoor hearts is the only reasonable draw that bricked, so for check-call to be profitable, villain would need to be value-betting all of his weaker aces and/or getting to the river with a lot of weird holdings which he then decides to bluff with. Although we've all seen villains do both of these things many times, I don't think we want to plan our strategy assuming that unknown villains do this frequently. In the long run, check/fold might actually be preferable to check/call in similar spots.

* TL;DR *
I think Bet/Fold is by far the best play on this river. It sucks committing a big chunk of our stack to fold (you can mitigate this by adjusting your flop sizing), but we need to be hunting every scrap of value we can find and I don't think this spot is even very thin.

For me, with no specific reads, it really depends on the buy-in of this tourney and what we know about the player pool in general. A $5 tourney on 888 is a lot different than an $11 one on stars.

I don't think we can safely assume villain never flats with AK and AQ on the button with 47bb effective. I personally flat both hands on the button around this stack depth vs many EP, and some MP, raises. I'm not really excited about playing for stacks but can't really fold to a 4-bet with the top of my range, so I like to take advantage of my guaranteed position. This also helps to balance all of the speculative hands in my flatting range.

I'm going to have fun and do some work in Equilab with this spot. I'll post my results here when I'm done.

The simplest way is click on menu Hud -> Edit Hud Options. On the right side of that popup you can set filters for various stack sizes.

There is also a way to set up your hud so that you have separate stats for various stack sizes, so that you can see how they play their current stack size but also see general stats and stats for other stack sizes at the same time. I haven't figured out how to do this yet but when I do I'll try to remember to post it here.

Make a free account at max-value.com you can download Nash charts for push/fold free. They have one for 10% antes, 12.5% antes, and no antes.

Some of the hand ranges have small errors, but the percentages are at Nash equilibrium, which means there is no possible combination of plays by the players left to act that could make pushing that range worse than breakeven. If you plug the percentages into a program like Equilab and use a bit of common sense to adjust the ranges you'll have an unexploitable push/fold strategy.