The equities are 50-50, but the nutted range can make money by betting, the bluff catcher range can't. Pot equity and EV are not the same, and can be very different.
The AA/QQ range can guarantee itself EV = $75 by betting optimally. This is an equity realization of EV/equity_split = $75/$50 = 150%. The EV boost comes from having some nut hands that can get paid off by worse + some worthless hands to bluff with.
The best the KK range can hope for is that AA/QQ always bluffs, or never bluffs, in which case KK can achieve $50 by exploiting these flawed strategies.
Feb. 5, 2018 | 10:32 p.m.
In this case, the EV for both Hero and Villain is 0 (Both will win half of the pot).
This is incorrect. When Villain bets the optimal range, Hero is indifferent with KK and it doesn't matter whether he calls or folds, so to keep math simple, we can assume he folds. This means Villain effectively wins the whole pot every time he bets, which is 3 times out of 4. The 1/4 of the time he doesn't bet, hero checks back KK and wins the pot.
GTO EV (Villain) = 3/4 pot = $75
GTO EV (Hero) = 1/4 pot = $25
The player with the strongest range will capture more EV.
By the definition of an optimal strategy, when Villain deviates from GTO by overbluffing, he can not gain EV when Hero stays on the optimal calling strategy. And your EV equation for Villain overbluffing also gets the same result (you calculated wrong):
Villain EV when villain bets all combos:
1/2100 + 1/2(1/2200 - 1/2100) = 125 (wrong: it sums up to $50 + (1/2)($50) = $75)
Hero can also choose to call 100% to exploit the overbluffing. In that case Villain's EV is:
0.5($200) + 0.5(-$100) = $50
And Hero gains $25 from the exploit.
Feb. 3, 2018 | 5:19 p.m.
That's excellent, the charts really become rich in info with that extra dimension. I had the same idea, but didn't know how to do it, so would love to know. :-)
Jan. 17, 2018 | 12:07 a.m.
Great video, guys!
I've done a little range breakdown for KQ9r using Pio's PLO Calc tool with MonkerSolver preflop ranges from a full 100bb 6-max simulation (high stakes rake). PLO Calc is a good range tool that reads Monker's output and complements Monker very well:
We're a favorite pre flop with our 11%'ish flatting range.
Flop range breakdown
(Gyazo link for full-sized image)
We're a solid 54% equity favorite on the flop, and we're having a significant advantage in the nut department (combo wise we're 14% vs 11% for the straights and 16% vs 8% for sets).
Jan. 4, 2018 | 1:04 a.m.
Flop aggregation reports is a no. I asked about it, but I don't expect any flop aggregation functionality any time soon. That would be very useful, though.
Speed is determined by your accuracy settings. It's not faster for very accurate HU pre flop solving, but you can do very fast solves with reduced accuracy that give pretty decent results. I've compared some reduced accuracy levels with benchmark Pio solutions, and I was impressed.
You can node lock.
Oct. 11, 2017 | 12:03 a.m.
In February 2017 MonkerSolver was released and PLO solving became a reality for everyone (and not just owners of the fabled "Dream Machine").
Having the tools doesn't make anyone an expert, though, and for a game that is so computationally demanding as PLO it's important to stay relevant and not waste a lot of time on unimplementable perfection. It's easy to mistake information for knowledge, but if three years of NLHE solving have taught us anything, it's that access to optimal strategies does not translate directly into boosted win rate.
A couple of months ago Corey asked me if I wanted to read his book and review it here in exchange for a free copy, and I gladly accepted the proposition. I had just started dabbling with MonkerSolver myself, and I was curious to see how it was applied to PLO.
Since then I have used the program a lot, and I have decided to take up PLO again. Because I do believe PLO will be very profitable in the years to come for anyone who commits to improving their strategies with solvers. Studying this book had a lot to do with my decision, and I can recommend it wholeheartedly.
Review of "PLO 3B Pots Game Theory and Practice"
The book aims to get you started on a practical path right away. Its sole topic is low SPR scenarios (e.g. 3B pots) in PLO and how to break down their strategies into something that you can understand and actually implement. These scenarios are both frequent, important for the win rate, and they lend themselves to solver study since shallow stack scenarios are the easiest ones to compute solutions for.
This approach of treating a narrow topic in depth makes the book ideal for anyone who wishes to get started with PLO solving, but lacks a method for how to interpret results and transform them into actual strategy. What you will learn is a framework for analyzing PLO solutions and extracting practical knowledge from them. Knowledge that will translate directly into strategy that you can implement.
Since the scope of the book is narrow and it makes no attempt to cover everything about PLO strategy, the discussion is focused and easy to follow. Then it's up to you to apply what you learn to other areas of the game later. I really liked this, because in my experience (I've done massive amounts of NLHE pre flop solving), hands-on experience going deep in a specific area provides much more insight than a general theoretical overview. Once you have trained a good general method by analyzing one part of the game very well, applying the method to other areas will be easy.
One of the eternal problems of studying PLO systematically has been the presentation of ranges, since we don't have anything like the 13x13 Hold'em grid for visual aids. Cory has solved this problem with strategy charts that lets us visualize PLO postflop strategy in an elegant way:
And like so:
The first part of the book introduces the method and the framework for attacking PLO with solvers in a practical and relevant fashion. Range construction is the central topic. The second part consists of 16 detailed hand analyses. Understanding these example hands well and reproducing some of the examples (or applying the method to some of your own hands) as you go along will get you up to speed with practical PLO solving very fast.
Before you start with the book I recommend you buy MonkerSolver and get it up and running. The book doesn't provide much technical software advice (but it is my understanding that this will be covered in an optional video package accompanying the book) but the program has a 2+2 thread and there's also a very active Skype Group going.
I highly recommend this book to anyone who wants to tap into the enormous potential of PLO solvers without losing sight of the most important thing for a poker player: We play the game to get our opponents' money, and our study methods should reflect that. We want to be practical and relevant as much as possible, and we'll not waste time on unimplementable perfection.
Oct. 10, 2017 | 11:38 p.m.
The programs use different algorithms, but they give the same HU results (as they should) when accuracy is set high. HU spots are the only ones we can compare between them, since Pio doesn't do multiway.
Here's a pre flop solution comparison I posted on 2+2: The strategies are identical:
Pros for MonkerSolver are versatility (HU + multiway + pre flop + post flop for three games, Hold'em, Omaha, Omaha8) and a very reasonable price.
One thing that can be a con for some is that the algorithm does not tell us how exploitable we are (Pio tells us, and we typically choose to stop at some threshold where we are exploitable for only a small fraction of pot like 0.25%).
So with Monker, you run it until strategies are converged (as in, no longer changing significantly), and you will have to trust that the strategies it produces are strong. Since it produces the same HU strategies as Pio, I'm fine with taking a leap of faith for the multiway case (and PLO, where we don't have anything to compare Monker to yet).
Oct. 10, 2017 | 9:12 p.m.
Well done! :-)
Sept. 24, 2017 | 9:03 p.m.
Sept. 21, 2017 | 8:30 p.m.
I'm working a lot with MonkerSolver at the moment and I want somebody to discuss with, dammit. So I've started a MonkerSolver Skype group for those who use the program and for those who are curious about what it can do:
Nothing formal, and not a study group, just a place for discussing technicalities and multiway strategy.
Sept. 21, 2017 | 2:36 p.m.
If you want to exploit the pool hard, you have to make yourself exploitable in the process. If your line is very profitable, and the pool doesn't counter you hard, keep doing it. Those that go after you on the river can be marked as special cases and handled separately.
Sept. 16, 2017 | 7:50 p.m.
Hey guys. I just found the Snowie Preflop ranges, and I want to know if anybody had success with learning from Snowie's preflop tendencies? I can see, Snowie doesn't like opening SC's from EP as an example.
What does the Snowie EP range look like?
Sept. 13, 2017 | 5:28 p.m.
I am trying to decide between buying MonkerSolver and Pio. Which would you recommend for NLHE?
It depends a lot on whether or not you're interested in studying multiway play. If you're content studying only HU situations, Pio will serve you perfectly. If you would like the option to work on multiway strategy, MonkerSolver is the only option on the market right now.
You can't go wrong with Pio, and there's a lot of information out there about how to use it well. But MonkerSolver is unique in the things it can solve. Pio will release a PLO solver soon, but multiway solving is not planned.
What kind of computer specs would be required to calculate preflop ranges for 6-max NLHE with MonkerSolver?
Approximately same as with Pio, but you will need more RAM to do the heaviest solves. To solve the 4-handed pre flop game (CO v BTN v SB v BB) with decent accuracy, You'll want a 240 GB RAM setup, same as for solving pre flop HU play with Pio, using a big flop set.
To solve for 6-handed ranges with good accuracy, you will need at least 500GB RAM.
Does MonkerSolver have all the necessary features to study the game?
It solves NLHE, PLO, PLO8, pre flop and postflop, HU and multiway. It lacks one very nifty Pio tool, aggregation reports.
Sept. 6, 2017 | 11:22 a.m.
MonkerSolver is the most versatile solver out there right now. It solves pre flop and post flop, multiway and HU, and NLHE/PLO/PLO8. It's around half the price of Pio Edge, and a little more expensive than Pio Pro (which is the same as Pio Edge, minus pre flop solving).
Pio is the standard for HU solving pre flop and post flop, but after working a lot with Monker, I think Monker is overall more useful.
Also, check out CREV for a cheap user friendly solver. They have just renamed it GTO+ btw.
Sept. 4, 2017 | 12:52 p.m.
i see where your coming from but wouldnt that mean id seriously have to tighten my ranges
ie utg raise i cant play 3b or fold with my entire calling range there
You need to construct a linear 3BF range that contains the best, but not all, of your 3B + flat VPIP range.
Sept. 3, 2017 | 10:54 p.m.
You can improve your pre flop strategy (+ make it simpler) by playing 3B-or-fold from all positions except BTN and BB in high rake games. And even on BTN, there's not much to gain from having a flatting range with this rake.
Sept. 1, 2017 | 3:34 p.m.
The comments above are valid for all pre flop solvers, but there is an additional issue with MonkerSolver:
It does not measure how far from equilibrium we actually are, and the solver does not yet have any convergence criteria implemented.
So we have to be pragmatic. If we trust that the MonkerSolver algorithm produces strong multiway strategy (and as far as I know, the Poker Research Group from the University of Alberta assures us that it does), we can figure out good convergence criteria from experience.
From what I have seen, the deeper into the tree we go, the slower ranges converge. Open and 3B ranges are fast, multiway flatting ranges go slower and slower the more players are involved. For example, have not yet seen an open + call + call + call branch converge in reasonable time, even when running the sim 2x longer than the time it took for all the HU and 3-way branches to converge.
So my pragmatic stance on MonkerSolving at the moment is to run the simulations until I have clear convergence for all the ranges I'm interested in.
For those who are curious about the quality of the MonkerSolver pre flop simulations, I can report that I have benchmarked it against Pio for the SB v BB equilibrium and it reproduced an accurate Pio simulation (184 flops + tight convergence) very well when I cranked up the accuracy settings a bit.
We have nothing to benchmark it against for multiway simulations, but it's encouraging that the algorithm gets the HU case totally right.
Aug. 31, 2017 | 9:24 p.m.
Feel free to correct, but as I understand pre-flop trees include errors in the turn actions and worse errors in the river actions; i.e. checking nut flush back and other such things and other less egregious clear mistakes. In what proportion I don't know. And without Nash distance we can't know how bad the aggregated impact is, but I seriously doubt all hands are affected equally.
Preflop strategy crunching is concerned with preflop EV and frequencies. We don't need the post flop tree to be perfectly solved in order to arrive at near-perfect pre flop ranges.
Two reasons for this:
1) Preflop EVs are not very sensitive to variations in post flop strategy
For those who have used Pio, this is similar to the observation that flop EV is not very sensitive to flop bet sizing. In the sense that when we change to a different sizing, the solver chooses a different range for it, our opponent adjusts to this, and we end up with a flop EV that is almost the same.
The relationship between pre flop EVs and post flop strategy is like that. For example, if you run a pre flop solve in Pio and build a complex post flop game tree to get it perfect, you will not get much different results than from a simple tree with one size per street (but you will blow up the size of the simulation tremendously).
2) Error cancellation is our friend
For a simulation where we have myriads of error sources in the model, many of them will cancel each other, and the results we are after (pre flop EVs and frequencies) can get very accurate, even if we can't solve to infinite precision and we still have many small errors left in the post flop part of the tree.
It's important to distinguish between a pre flop simulation and the corresponding post flop game tree. Usually we're not interested in keeping the post flop part of the simulation since it will be rather crude. This is because we need to keep the post flop tree simple to keep the size of the pre flop simulation down, and we will often not solve to the point where all the post flop strategy (like river play) is well converged.
But for reasons 1) and 2) outlined above, this does not matter all that much for computing accurate pre flop strategy.
So we extract the pre flop strategy from the simulation, we save it, and for future post flop analysis we do separate post flop simulations using these ranges as input.
Aug. 31, 2017 | 9:19 p.m.
I think this is one of those moments where there won't be much future regret about throwing away some work now and redoing things.
The PLO solvers have just arrived on the scene, and they will change the way the game is studied (hopefully in a smart way). The PJ ranges will become standard tools for those who use the program, so why not use a solver to make them as good as they can be.
That way equilibrium pre flop ranges will become available also for those who can't afford to run a solver in the cloud (crunching PLO ranges is damn hard), and it should add good value to PJ.
Aug. 31, 2017 | 4:05 p.m.
1) Nick has been vetted as a coach by RIO, Jonna102 has not
2) Nick has always been open about his mediocre "MadAgenda" results, Jonna102 has been working very hard to hide the fact that he's always been a losing micro rec.
3) For both cases, price is irrelevant, since it's supply and demand, and afaik, both have offered a money-back option for dissatisfied customers.
What is on trial in this thread is integrity, not PokerStars results or price of packages. Jonna102 has misled his customers, Nick has not.
Aug. 31, 2017 | 1:26 p.m.
From the Pio blog:
Today we are happy to release our first Omaha tool: PLOCalc. PLOCalc is an equity calculator and range explorer for PLO. What is novel about it is that it calculates range vs range equity which included equity for every single hand in the range. This works on preflop, flop, turn and river. It's done without any approximations - the results are exact.
About the solver:
PLOCalc is a fantastic tool for analyzing your PLO game. We anticipate the natural follow-up question though: "What about the solver?". Short answer is: PLO solver is going to happen in the near future although it will require very powerful hardware to run.
The solver and PLOCalc are going to use the same interface for showing and analyzing ranges. PLOCalc might be more useful for some real life scenarios as it allows you to analyze ranges based on reads and assumptions while GTO solutions are going to be very hard to make sense of in the game as complicated as PLO. The future of those tools is going to be influenced by the feedback we got from first batch of our users.
Aug. 31, 2017 | 11:03 a.m.
It's as easy as setting up the AWS account. Once you're in, you will have a virtual Windows desktop that you handle just like any other Windows machine. Use Dropbox to move files in/out.