Great! Equilibrium is a constantly moving target, a downward spiral to a 0 EV state where luck reins supreme.
Level 61: Components of Range Advantage
So what makes up a range advantage, and how should I usually use it?
- Equity advantage: we can use solvers and equity calculators to determine how ranges far against each other in a situation were no one bets
- Polarization advantage (largely the same thing as what some refer to as a nut advantage): even if we have an equity disadvantage, if we have more of the strongest hands, we can usually over realize equity by betting large with our nutted hands and a mix of appropriately selected lower equity bluffs; flipping that, with a condensed range (not much that is very strong or very weak), it becomes difficult to make larger bets profitably, even with a large raw equity advantage
- Wetness of board: wetter boards make most of our holdings more vulnerable to being outdrawn
- Position: having a positional advantage will allow us to bet a larger portion of our range profitably, while being out of position will push us into playing more defensively, and usually assigning more strong hands to our checking range
- Stack depth: deeper stack depths introduce reverse implied odds for many of our made hands, and greater implied odds for our draws, and again can change what constitutes a range advantage
Still not really sure how to balance all of these against each other, and decide how this really means I should play with a given hand on a given board… but hey, maybe practice will make that easier.
LOL… yeah, I’m not sure how strictly useful it is for us mere humans. I almost included some of the math, just to make all of us feel really obsolete (myself included). Still, I think understanding that there is an equilibrium state in poker (proven), even if it has not been discovered, means that, if you know exactly what your opponents strategies are, there is an optimal, mixed strategy response.
Level 62: The Mental Game
- Avoid tilting
- Feel positive about your play
- Focus on quality decisions; results are a quantum cloud and you’ll see every possible result over time
- Enjoy playing, or take a break
- Try to understand what principles are guiding your opponent’s play
- Don’t be afraid of taking risks: if it is +EV, do it
- Mix up your play; don’t always take the same kind of line in similar situations
- Work on your game; if it is worth your time, gaining new tricks and skills will probably deepen your appreciation for it
- Don’t neglect your health, it’s a vital component of your ability to think clearly and play well
Level 63: Synthesis and Integration
So many different things to consider, and many of them often pushing you in contradictory directions. Figuring out the balance between the different principles, their relative priority, and what the overarching strategic themes are. It’s one thing to know dozens of poker principles, and it is another to be able to know what they mean when you have a given hand on a given board after a given series of prior actions. And even if you can do that part off-table, it’s still entirely something else to be able to do it in a few seconds, in the face of the emotional rush that poker often provides.
There’s a long road between learning something and being able to use it effortlessly as a balanced part of all the other things you understand. Think of your golf swing, or a new martial arts move, or early work on a new and very difficult song. It will take practice and repettion.
I think I’m probably finished with this thread. Hope you find some value in it.
There are of course a lot of skill levels left, and so I’ll throw out a few other things to think about… but I’m not really a GTO style player, and I think most of the more advanced heuristics about the game are mostly trending in that direction, and so I feel a bit out of my depth discussing them.
But things I hope to improve on myself:
- What do different player’s ranges really look like in different spots?
- How does my range and my opponent’s range really break down into different equity buckets on different boards?
- How do I find the last few bluffs to get to my ideal ratio, without losing my balance altogether, and moving into territory where I’m wildly over bluffing?
- How can I identify more spots where I can extract thinner value?
- What are the right bluffing ratios in multi-player pots, and does the nature of the hands you want to pick change?
- How can I continue to deepen my tool kit of exploitative adjustments to frequency and range errors I observe?
Best of luck on the tables!
That took a lot of your time and i for one appreciate that and your knowledge. Many many players are going to benefit from this thread. I certainly learned valuable information.
Yeah thanks for taking the time to lay this out. I’m sure it will be useful to many players.
I have tried to restrain myself from commenting because I didn’t want to break your flow, but now that yer done…
In Level 42: Polarization, you talked a little about making polerized 3! and 4!, but for most of us, I don’t think there is such a thing. In the tournaments I play, a 3! is almost always pure value, and the only 4! bluffs I have seen were the ones I have made myself.
So yes, against better players at the higher stakes, you will see more 3! and 4! bluffs, but at the stakes/buyins that 90%+ of us play, 3! and 4! aren’t really that polerizing. Of course this means that 3! and 4! bluffs can be more effective if used correctly. (haha)
Anyway, I would be interested to hear your thoughts on how stakes affect this, and the differences between ring and tourney if you feel up to it.
Thanks again for a great thread!
This (mental game) is the most important level of all!
The whole series is excellent and a lot better than many poker books. Well done!
I think I might have started tracking pre flop frequencies around the early part of medium stakes on this site. Here are stats below for a strong player that is on the looser end of the spectrum, over a fairly short number of pre flop hands. The first number is position (6 = UG on a 9 hand table, and 0 = button). The second number is pre-flop raises, then limps, then folds.
- S 0 4 0
- 0 3 3 2
- 1 1 1 3
- 2 1 2 5
- 3 3 1 3 *2 A9r
- 4 3 5 1
- 5 0 5 2
- 6 2 2 3 JJr
Even over a short sample like this, you can see that this player is opening a relatively high frequency of hands from almost every position. Against players where the second number is almost all zeroes (indicating an extremely low frequency of pre flop raises), you can’t 3 bet that often, as with some their raise is almost always AA. 3 betting in general is rendered almost useless here, let alone 3 bet bluffing. Their range is just too nutted.
At low and medium stakes, honestly, I’ve never bothered to polarize my 3 betting range (very much anyway). I just make an estimate for the percentage of hands I think they are opening from a given seat, and then 3 bet with a range about half that size initially. If they fold a lot, I start broadening that range.
Beginning with high stakes, I started experimenting a little with polarized 3 betting ranges, but gradually felt that here too I preferred mostly linear ranges.
Now at elite stakes, I’m still mostly 3 betting purely linear ranges, or merged ranges. Against some of the most aggressive players is the top 30, I will start to polarize a bit more often, but in seats were I feel I’m going to mostly 3 bet or fold (meaning I don’t have a calling range I feel a need to defend), I’m again using a merged range rather than a classically polarized range.
I think polarized 3 betting and 4 betting ranges were introduced about 15 years ago or so, and really put to use by players like Tom Dwan, and were essentially part of the move to 3 bet and 4 bet light, to capitalize on players over folding against these bets. But interestingly, solvers and strong AI programs don’t seem to polarize their pre-flop bets very often, and so in general that has resulted in professional play moving a little away from polarized pre-flop bets, and more to merged ranges.
But still, against humans, especially in normal play, I think it just becomes a question how broadly people are calling or raising your 3 bets and 4 bets, and if they are over folding, using some trash hands with nut blockers (to improve the fold rate you’ll see) can be a rather effective tactic.
In ring games, you don’t really care about volatility, so long as you are properly bank rolled for the stakes you are playing at. In tournaments, 3 betting and especially 4 betting light will expose you to a lot more volatility… but that volatility, while usually something people seek to avoid, will also push you into the top few places more often, especially if you take some effort to manage it, and are selective about your spots.
Thank you sir.
Level 64: Post Flop Decision Making Sytems
There were really quite a few things I never covered in this thread, and a more systematic approach to post-flop decision making was one of them. If you watch strong pros talking about their decisions on the flop, turn and river, you start to see that many of them have some kind of process for making their decisions, and so I thought I’d share one possible 3 step process for making post flop decisions.
- Compare the overall strength of your range to your opponent’s range.
- Decide on how various hands within your range should be bucketed.
- Consider attributes of your specific holding.
Start with step 1, and proceed to the next steps if needed. At step 1, you are first trying to decide which range (yours or your opponent’s) has the highest density (as a percentage of their total range) of the strongest holdings. Then you consider how equity is distributed across the range (how does top of range match up with top of range, middle of range with middle, and bottom with bottom). With this examination, you’re trying to decide how you want to play your whole range. For example, with an equity advantage for much of your range, but lacking a nut advantage, you’re often going to want to bet small with a large fraction of your range, or even all of your range if the equity advantage is large enough. With a strong nut advantage, but lacking an equity advantage, you will often make very large bets with a small part of your range, adding in bluffs with enough of your weak hands to achieve balance.
If at step 1, you feel every card in range should be played the same way, then there is no need to move any further. Many players often like to simplify strategies: the old advice of always making a half pot continuation bet on the flop as the pre-flop raiser is an example of such a simplifying approach that skips even step 1 (it doesn’t consider whether or not our range actually has any kind of advantage on the current board). Making a smaller flop bet on some boards with 100% of range as the in position pre-flop raiser is similar, in that we’re now not going to bother with steps 2 or 3, as we’ve decided we have a large equity advantage, and that the opponents will have a lot of cards that just won’t have any desire to continue.
But most of the time, you won’t want to play every holding in your range the same way, and so at step 2 it is time to group your holdings into various buckets. I’d usually recommend at least 3 buckets, and honestly typically go with 4 or 5. A 5 bucketed approach:
- Your strongest hands that will sometimes want to make overbets of the pot
- Your strong hands that will sometimes make normal bets (half pot to pot) for value
- Your marginal hands that might be able to make smaller bets for value
- Hands with showdown value
Here, you’ll also want to consider if you want to go with a 100% approach for each individual bucket, or if you need to split the bucket between different strategies. If you feel that all hands in the bucket you find yourself in should be played the same way, then there’s no need to go on to step 3. Assuming you have any kind of range advantage, trash is usually split, as it will be where you’ll source many of your bluffs. You also often need to find at least some hands in the top 2 classes to check or bet small in order to protect your lower buckets, except when you have a very large equity advantage. If you do find yourself in a bucket with a mixed strategy, then it is time to continue on to step 3.
In step 3, you consider the characteristics of your specific holding. Is the hand, relative to other hands in the same bucket, more or less vulnerable to future cards? Does your hand block key parts of your opponent’s range, or unblock them?
As an example, if you have a holding in the strongest bucket, if it heavily blocks combinations in your oppenent’s range that are likely to want to continue (top 2 pair or top set on a dry board comes to mind), and is also not needing protection relative to your other strongest hands (AQ on an AQ3 rainbow board, as opposed to JT on a JT7 board), you’ve likely got a candidate to trap or bet small. Do you have complete trash with no equity and no showdown value? Does it also unblock many weak holdings in your opponents range, or block many of the hands that would call a large bet? You may have a candidate for a large bluff if your range also has a reasonable density of the strongest holdings.
This is obviously somewhat hard and takes practice. Just roughly understanding what your own range and your opponent’s range probably looks like is no easy task, and to then decide at step one if you have an equity advantage or a nut advantage is that much harder. By the time you’ve gotten that far… *****, I ran out of time!*. Still, with practice you’ll gradually get both faster and more accurate at doing this, even if you never approach what a solver can do. And if you’ve mastered many of the levels discussed earlier in this thread, it may be time to consider some kind of systematic approach to post flop decision making.
Level 65: Bet Size Diversity
Back when I started playing poker more seriously (roughly 20 years ago), I went through a phase where I greatly restricted the number of bet sizes I used. I remember often only making 40%, 70% and full pot bets (usually rounding those to the nearest round figure). Sometimes I would even go for long stretches where all my bets were half pot, or all of my bets were full pot. I did this in an effort to keep my bets from providing too much information about my ranges, in the same way that most strong players don’t modulate their pre-flop bet sizes based on the strength of their hand. Another reason I did this: my play was fairly straight forward. If I raised preflop, I’d almost always fire a continuation bet. On later streets, if I had a value hand, I’d almost always bet for value. And by the time I got to the river, I made almost no bluffs.
But one of many beautiful things about balance is that it reduces the ability of your opponents to narrow down your holdings based on bet sizing, and helps keep your range relatively mixed. Any bet size will usually contain a variety of hand types:
- over bets will mostly be a mix of very strong hands and very weak hands
- middle sized bets will have a few very strong hands, many strong hands, some bluffs, and a few other hand types now and then
- small bets will have a small number of strong and very strong hands, a small number of bluffs, and a lot of everything else
This freedom to use a greater mix of sizes means you can choose sizes that better maximize the rate of return. For most players this means that your small bets aren’t small enough, and your big bets aren’t big enough. A smaller bet size allows for value betting with a much larger part of your range, and provides extra value relative to a check. Larger bets allow for a higher bluffing ratio, and maximize your share of the pot when you have a significantly more polarized range than your opponent. Both allow for extra value extraction in appropriate situations. (Note that we’re not saying that all bets should be either microscopic or massive overbets of the pot).