Player Levels

Level 48: Thin Value

Need more of this… need more of this… need more of this.

I’m starting to notice that, as I get more aggressive, I get lighter and lighter calls more and more often, and given that, I think I need to expand the bottom end of my value betting range. Too often I’m checking down the river after taking one or two streets of value earlier, and showing up against a hand that would have probably called another medium to smallish bet.

This will get a little dicey, as I’ll start getting called and beat more, but even if these bets exactly break even, I think the fact that this will increase my betting frequency will lead to people feel more pressure, and will generate more mistakes that will benefit me, and should also generate some additional cover for smaller sized bluffs in various spots (further upping the pressure).


Level 49: Reverse Implied Odds

Many authors use this term in a relatively narrow context, when certain drawing hands like a non-nut straight or a small set run into the nut straight or a higher set. I’ve run into a few authors that use it in a broader way that I think has more importance in poker generally, even if some might disagree as to whether the term “reverse implied odds” is supposed to cover these broader situations.

Implied odds looked at the possibility of winning a pot bigger than the current pot when drawing to outs to decide whether or not to call on an earlier street. Traditional reverse implied odds is an offset, as without drawing to the nuts, sometimes that bigger pot will be a pot you lose, rather than one you win.

But many hands suffer from a related type of reverse implied odds that mostly applies to medium strength made hands: they tend to win small pots and lose big ones. And just as thinking only of direct odds when deciding whether or not to call when I have a hand with strong outs would clearly result in over folding, failing to consider with made hands how many small pots I’ll need to win to offset larger losses will lead me to take lines that will show negative value over the long run.

The classic examples here are medium and top pair type hands, especially with many over cards that made hit on later streets, as then in addition to all the normal draws you might be up against, any card higher than the board is often also an out for an opponent.

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Level 50: Range v Range
I’ll probably have to come back to this one a few thousand times… but it seems that my normal approach of playing my specific hand against my opponent’s range is often not the way professionals approach play on the flop (or later streets often). So I need to start thinking about how my range compares with my opponent’s range on given boards.

This seems so hard… off table, given 30 minutes or an hour, I can probably say which flop favors which player, though even there I’m likely to make big mistakes on what my opponent’s range really looks like. What I’ve read doesn’t make it perfectly obvious exactly why we’re doing this, either, except that it seems like this helps to explain the way solvers pump out solutions, and the way various advanced programs play the game at what seems to be a super human level.

OK, so I’m going to have to start getting better at figuring out who has range advantage, and what I’m supposed to do with it when I have it on various types of flops.

Level 51: The Wrapper Bluff

I don’t really know if this has any kind of name, but I’ve seen pro’s make this kind of bluff on many occasions, and if you are heads up on the flop, against someone pretty strong where you feel like you need some extra bluffs to stay balanced, this is a great bluffing hand with effectively almost no outs (well… you have lots of outs to outs).

Let’s say we have QsTs as the big blind, and defend against a normal sized $3k cutoff raise, with 200k effective stacks. Pot is 6.5k.

Flop comes Jh6d2s. Kind of a brick for both ranges. We check, and CO bets 2k. We think he’s betting with most of his range here, assuming he has a degree of range advantage on this dry board. We check raise to 12k. Wait, what are we doing and why? We have no part of the board, and no draw!

The beauty of this? We’re blocking some of the CO’s value range, blocking QJ and JT, and the board is relatively unlikely to have hit either player. What’s more, we have clear conditions on the turn for either standing down, or continuing the bluff. Any K or 9 gives us an open ended straight draw, and any spade gives us a flush draw, allowing us to bet aggressively on the turn for a large size a fair fraction of the time, with a very disguised holding if it hits on the river. A queen or ten would of course be ok, too, though we’d want to play that quite a bit more cautiously.

On the turn, if the flop check raise gets called, we’re looking at a pot of 30.5k. If we get a K, 9 or spade, blast an over bet of 40k to 50k.

A call on the turn and we’ll say the pot on river is 125k, with stacks behind a little larger than that. Hit straight or flush? Then ship it. Miss? Give up 75% the time, and ship it the rest, perhaps modifying your percentage of river bluffs based on how sticky you think your opponent will be to the final over bet. I’ve driven the river bluff percentages down assuming that a lot of players will be a bit sticky after calling the bets on earlier streets, and also to target moderately close to 2 to 1 value to bluff ratio (though since you are over betting the pot, equilibrium will have a slightly higher level of bluffs than that).

Seems like madness. I guess that is why they are pros.

Level 52: Board Types

OK, I’m recalling this from Modern Poker Theory, though I don’t know if all of this originated there (or if I’m even remembering it right), but I thought this was a kind of nice way of breaking out some relevant components of different flops.

  • A: an ace
  • H: K, Q, J, or T
  • M: 9, 8, 7, or 6
  • L: 5, 4, 3, or 2

So AK6 would be AHM, and QJ4 would be HHL.

Then we have monotone, two tone, and rainbow for suits; trips, paired or normal; 3 possible made straights, 2, 1 or zero.

So HMMr (high, high, middle, rainbow) could be Ks9c7h, and AHL2 could be AhJh3s. I don’t remember clear notation that made it visibly obvious how many straights were possible, or if the board was paired… I think the key point there was that these factors also often impact who has range advantage, the nature of that advantage, and what kind of lines are often optimal. I think different pages or columns were often used to break some of these differences out.

Some general observations:

  • Axx almost always favors the pre flop raisers range (BB defend)
  • HHx and Hxx boards favor the raiser again, but not usually quite as strongly
  • rainbow boards allow more aggressive betting lines more of the time
  • monotone boards seem to result in smaller bets and less betting in general
  • paired boards see more bets, but smaller bet sizes
  • small card boards, like MLL and LLL, especially rainbow and with 2 or 3 possible straights, level the playing field between BB and the raiser, and are the boards where donking can sometimes actually be a good strategy

Level 53: Equity Buckets

Supplementing the board type idea was four classifications based on range versus range equity. I don’t remember the labels, so I’ll just use: strong, good, weak, and trash (might be the same).

So inside your range, you’ll have some hands that hit the board for strong equity (think your monsters, 2 pair and up), some for good equity, some with a realistic chance… but don’t get too hopeful, and some that just won’t have much showdown value, or likelihood of improving to even a good hand. Your opponent will also have hands that can be categorized into these buckets.

As you compare the way your range interacts with the board to the way your opponent’s range interacts with the board, you want to consider how big of a slice is landing in each category. You also want to think about whether either of the ranges are capped or compressed, and if one side has a polarization advantage (which would support larger bet sizings for the player with that advantage).

OK… give me a few years and I think I’ll have digested these well enough that they might actually start improving my play…

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Level 54: Expected Value

I forget exactly where I ran into this, but presumably it is from another of those poker databases out there (I’ve had it floating around on a note for a few months I think), and lists the overall expected value (EV), averaged for all positions, of each starting poker hand, and then places them in tiers (with hands also listed in overall EV order).

Tier 1. EV 2.32 - 0.78: AA, KK, QQ, JJ, AKs
Tier 2. EV 0.59 - 0.38: AQs, TT, AK, AJs, KQs, 99
Tier 3. EV 0.32 - 0.20: ATs, AQ, KJs, 88, KTs, QJs
Tier 4. EV 0.19 - 0.15: A9s, AJ, QTs, KQ, 77, JTs
Tier 5. EV 0.10 - 0.08: A8s, K9s, AT, A5s, A7s
Tier 6. EV 0.08 - 0.05: KJ, 66, T9s, A4s, Q9s
Tier 7. EV 0.04 - 0.01: J9s, QJ, A6s, 55, A3s, K8s, KT
Tier 8. EV 0.00 - 0.00: 98s, T8s, K7s, A2s
Tier 9. EV -0.02 - 0.03: 87s, QT, Q8s, 44, A9, J8s, 76s, JT

Interestingly, all of these hands combined make up less than 1/4 of the possible hand combinations (24%), and if you get rid of tier 9 that actually aren’t profitable overall (though they will probably be profitable with better position), and also tier 8, which only break even, it is only 18.4% of hands.

I suppose I need to remember that this will morph a bit at different stack depths, with high card hands gaining value short stacked (and suited or connected small card hands losing value), and the opposite happening at greater stack depths.

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Level 55: Max Value

OK, I’ve watched some of the strongest, most aggressive players on the site a few times now. It feels at first glance like they are unbalanced with too many bluffs. But wow, do they ever get full value from hands like top pair. In fact, I can’t believe how often they stack people with just top pair… it’s like magic.

I suppose that is a benefit to being perceived as very aggressive and bluff heavy. They really seem to be able to get more streets of value, and so much more of their range seems to be so much more effective at chip extraction.

I imagine there is a lot of volatility associated with that kind of play… but it does also remind me of watching the older clips of Tom Dwan or Phil Ivey back when they were at the top of the poker world.

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Level 56: Value to Bluff Ratios 2

OK, we used MDF earlier to establish optimal bluff ratios for various sized bets when our range is perfectly polarized and the defender has only bluff catchers… but does all of that even apply to real poker? How often should I really be bluffing on each street?

Hmmm… yikes… that much???

  • Flop: roughly 1 value bet to 2 bluffs
  • Turn: roughly 1 value bet to 1 bluff
  • River: roughly 2 value bets to 1 bluff

Errrr, hmmm… ok, I don’t think I’m bluffing that much. Can I really do that?

  • Flop:
    • On boards that favor my range, I’ll mostly be betting small with a large chunk of my range… easy to get a high ratio of bluffs here
    • On boards that are more neutral, or that favor my opponents range, I’ll want to take a lot of my good hands that usually can’t get 3 streets of value, along with most weak hands and trash, and check, and then bet larger with my strongest value, and then a ton of draws of various sorts (including a lot of gut shots and back door flush draws)
  • Turn: I’m mostly going to keep betting with my strong hands (including draws that hit), and will be dropping about half of the trash I was betting last street
  • River: Keep betting the best hands, and now use blockers to identify the hands to keep bluffing with (want to block the natural calling hands, and not block the give-up range)

Gee, this seems a bit wild. I think I also need to consider whether a given opponent over folds or not in various spots. This doesn’t seem like a wise plan against a true call station…

Further, I suspect that a lot of the people I play with over fold on the flop and turn, but if they get to the river, their range is strong enough that they will naturally seem to under fold. And then actually hitting anything close to whatever target ratio I decide to aim for… how do I really do that? This isn’t going to be straight forward, is it…

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Level 57: Flop Range Construction

OK… let’s try and decide how we might play in a given spot with our full range. OK, there was a hand yesterday, where I raised from the high jack and got called by a strong player on the button, and everyone else folded. I was playing a slightly tight RFI range of just under 20% with the following hands, over 200bb effective:


The flop comes Kh9d4h. I think I have a slight range advantage here (though it is pretty close), and also a nut advantage and a polarization advantage, as I think the button’s range is slightly capped, as I have more combinations of the strongest hands (AA, AK, KK, TT), even though he will have some of these in his range also. So I think I’ll want to bet less frequently, for a larger size, polarizing fairly early.

What to do with each hand on the flop:

  • check and defend hands:
    • KK: this could clearly go into the raising range also, but it blocks combinations that will continue more strongly than the other nutted hands
    • KQ (except KhQh), QQ, JJ, TT, A9, K9, Q9, J9 and some of the smaller pairs
    • my Ax flush draws
    • pair with draws
    • other combo draws not bluffed
  • 3 streets of value hands: AK, KhQh, A9, A4, 99, 44
  • bluffing hands:
    • all flush draws except my Ax of hearts
    • all smaller open ended straight draws
    • JdTd, Td8d, 8d7d (back door flush draws with back door straights)
    • do I need some more… maybe gut shot straight draws, like QJ, QT and JT?
  • Check fold hands: everything else

I wonder if I should play some of my check and defend hands as a check raise, or if I don’t want to have a check raising range here?

I’ll also have to come back to this and see how my combos of value compared to my combos of bluffs…

Yes, that is a useful system and similar to what I use intuitively, not having read any books about this.

Tournament play really is so different from deep stack cash games, that it is hardly the same game at all.

In deep stack cash games there is this inherent belief that players will not open unless they have hands that are within the approved range for their position or call likewise. However in tournament play most pots are not heads-up, and because of the cage-fight element is is necessary to take a stab at many pots to keep opponents on their toes. If you don’t open mediocre hands from early position some of the time, you become too easy to read.

Hence I will sometimes open big with something like T8s, specifically looking for a flop with a certain texture, like I want a flop that has an MM in it, or a flush draw, or I am giving it up pretty quickly. If I am in late position and playing vs the blinds and the flop is checked back to me, I may let it ride to see what comes on the turn and then bet if I like the turn card. The assumption is always that opponent’s most likely hands are Ax, AH, or small pocket pair. On RP layers with pocket pairs will call bets all the way to the river looking for a set, and a pocket pair is often among the suspects when a player in the blinds donk bets down to the river. He wants to see if you are chasing a draw, or have a made hand.

So a flop like T 9 3 is pretty useful if there is just one Spade, as any spade will give flush draw for river, and any J or 7 will give an open ended straight draw, and any 9 or 8 will give 2 pairs and any T trips, so there are 20 cards that might improve my hand on the turn, giving a lot of potential to win a big pot on the river against an opponent who may think that I made one pair on the turn or was just making a hopeful stab.

The other advantage here is that opponent will find it very hard to put me on a hand.

Such moves may be EV- in ring game play, but in tournament play you are looking much more to make hands that will double you up and being the opener is a huge advantage, though there are some players who will call with utter trash when on the button (but their flop bluffs can sometimes be reraised when you have nothing either).

The knack is in very quickly calculating which hands in your range could have been hit by the flop, how to represent this to your opponent, and whether your opponent is capable of understanding what you are representing. Most opponents on RP are not. Also doing all this in about 3 seconds before you are folded out is a big ask.

Tournament or cash game, I think speculative hands like this start dropping to -EV as stacks and SPR get lower and position gets worse, and improve with deeper stacks and better position. But even deep stacked and with good position, I find the board coverage they provide more valuable than the direct winnings from the hand.

Level 57: Flop Range Construction, continued

OK, need to count our combos. Have to probably just guess when playing live, but it is nice to periodically check how close we’re getting as we decide what parts of our range to make various plays with…

Board: Kh9d4h
Range: AA-22, AK-AT, A9s-A3s, KQ, KJs-K8s, QJs-Q9s, SC–>43s, 1G–>86s
Value Hands: AK (12), KhQh, A9s (3), A4s (3), 99 (3), 44 (3) for 25 combos
Bluff hands: QJs (4), QhTh, Qh9h, JhTh, 8h7h, 7h6h, 6h5h, 5h4h, 4h3h, Th8h, 9h7h, 8h6h, JdTd, Td8d, 8d7d for 18 combos

So we fell massively short of the 2 bluffs to 1 value bet target, even failing to have as many bluffs as value (despite the value range looking so compact, and the bluff range defined looking so extensive). And I’m not even sure a hand like QhJh is even still a bluff it has so much equity against a normal button flatting range.

So what could we add?

  • some of the weaker Ax of hears, with less showdown value
  • bottom pair with other draws
  • some weaker combo draws
  • various gut shot straight draws
  • more back door flushes

So even with what feels like a very narrow betting range, it can be difficult to find enough bluffs to hit a high bluffing target. Even our biggest category above, the back door flushes, has only 13 additional unclaimed combos: AdQd, AdJd, AdTd, Ad8d, Ad7d, Ad6d, Ad5d, Ad3d, QdTd, 7d6d, 6d5d, 5d4d, 4d3d.

In part this is probably because we’ve chosen a poor board to polarize on. A wetter board would provide more draws, and while Kh9d4h is a two tone board, it isn’t particularly connected, which greatly reduces the number of straight draws. So in retrospect, it might have been better to just fire a smaller continuation bet with a substantially wider portion of our range, and begin polarizing on most turns.

Still, I think polarizing on the flop here is probably not bad, either, but you’ll have to dip down to some very low equity hands to keep from being relatively value heavy (you’ll see solvers do this quite often, though).

Level 58: Protecting the Checking Range

Looking at older literature, I see far less emphasis on protecting the checking range, and so I suspect the play of Pluribus, Pokersnowie, solvers, and other programs that generally play at a superhuman level has had a strong influence here.

It’s interesting that at the same time that these programs are teaching us that optimal bluff rates are actually much higher than most ever imagined, they are also playing a much more defensive game, reserving a larger portion of their range for bluff catching.

I’m just getting started in trying to digest this trend. Hopefully it will help, since I’ve just started playing at the highest high stakes table, 20k/40k. I think there are still a lot of boards where the player with the range advantage will bet small (20% to 40% of pot) with a very high percentage of their range, and in this case there is probably less need to protect any kind of checking range.

But on boards where the flop is more neutral to both ranges, or where it favors the opponents range, polarization will begin earlier, and so in addition to picking out some hands that can derive 3 streets of value, and then even more hands that will at least fire 1 bluff, there is a fairly wide range of very strong checking hands that will even often include many top pair combinations.

More classical play certainly included some of this. With a hand that didn’t need much protection, if you felt it was probably not good for 3 streets of value, well then some of the time you would pick the flop as the street to check back. There were also certain monster hands that you would slow play, thinking that there weren’t many hands left in the opponent’s range that could call a bet with say, top set or a flopped full house. But I get the sense that there is now a difference in frequency for this kind of move, where the size of the range of strong hands you are checking back on the flop has increased considerably.

I’m still curious as to what the fundamental reasons for this are. If it is because of the higher frequency of bluffs in stronger play, then is it really necessary to do this against fishier types who’s bets are almost value, and who call at fairly high frequencies? I suspect not… so I think I’ll mostly use this type of flop range construction when I go post flop with stronger, more aggressive players, and just fire away with more of my value range against fish.

Level 59: Donk Betting

Well, well… everything I read when I was starting seemed to almost always say I shouldn’t be donk betting. It is interesting to see this also getting overturned in modern theory. I guess it kind of makes sense… who cares who raised the prior street? It’s all a question of… well, what is it a question of???

  • who has the range advantage on the existing board
  • who has the nut advantage
  • who has the polarization advantage

The range advantage is typically going to go to the pre-flop raiser, especially in a raise vs big blind situation, or like a high jack limp and call to a cutoff raise. It’s closer with a call behind in position, but still the pre-flop raiser will normally have a slight range advantage on most flops. Low card boards are the most balanced, but as almost every board misses the bulk of any range, the player that starts out with the stronger range typically has a small equity edge on almost any board.

The nut advantage can often go to the defender, especially on low card flops where they will often have far more combinations of straights, sets, and two pair type hands.

The polarization advantage can go both ways. On a flop where the defender has the nut advantage, they’ll usually be more polarized, but as the defender in general will be more capped, with fewer AA-JJ and AK type hands, that means the pre-flop raiser will have a polarization advantage on a majority of boards.

Any of these advantages can provide a basis for betting on the flop, and so just because you will have fewer flops as the defender that will give you these advantages does not mean that you will not have flops that favor your range. So I think it might be time for Donkey Fever…

Good points. Donk betting can be extremely valuable in the late stage or final tables of MTTs. Let’s say you have 3 players in a raised pot with blinds of 500/1000. Stacks are around 20BB.

On the bubble, there is a raise to 2000, a call on the button, SB folds, BB calls, so pot is now 6500 chips. If BB leads out with a donk bet of 3250 chips, what do the other players need to call or raise, bearing in mind that they are all getting perilously close to stack commitment, and that if they lose this hand, they become much more vulnerable? In many cases the donk bet will take down the pot by default as calling with a draw or 2 overcards is too expensive to continue and may be fatal.

The donk bet, if coming from a small stack, may actually be a shove, but if the small stack is large enough to severely damage the stack of the early raiser, it may be enough to scare off a call, and if you are on the bubble, you really don’t want to allow the small stack the chance to double up and get back into the contest.

Level 60: Nash Equilibrium

Yikes. That sounds fancy. What’s going on here?

Hmmm… ok. So this is from the branch of mathematics developed in the 1950’s called Game Theory (the original formulation was by Jon von Neuman in 1944). It sounds like it mostly applies in a heads up situation between 2 players, where, assuming both players perfectly understand each other’s strategy, they have no incentive to modify what they are doing, as there are no alterations to their play that would further improve their EV. They have reached a stable state: equilibrium.

The simple game with one player always getting an A or Q, and the other player a K, reaches equilibrium where the first player always bets with the ace, and bets 50% of the time with the Q. At that point, if the player with K calls 50% of the time, the first player has no incentive to increase or decrease the rate of bluffing when holding a queen. Essentially, this very simple game has been solved (perfect play for both players is understood), and that solution is a Nash equilibrium state, where neither player can make improvements, even if they understand exactly what the other player is doing.

  1. (in economics and game theory) a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged.

Many of the earlier AI programs that first beat humans in heads up play operated by attempting to calculate Nash equilibrium strategies that resulted in both players breaking even when the equilibrium was maintained, but that resulted in a loss for the player breaking equilibrium (deviating from the perfect counter strategy).

Should work well as long as the computers do not go on tilt.

You would think that in the recent Polk vs Negreanu and Hellmuth vs Negreanu series that both players would be using optimum, or very close to optimum strategies, but I suspect a bit of tilt crept in on the part of DNegs.

I think it is important to realize that normal sized computers (with less than millions of cores) have not actually solved even heads up poker, and that there is no solution yet at all for multi-player variants. So there is no clearly defined Nash Equilibrium solution for poker yet, and so even the play of computers is still likely to see considerable improvement over the coming years. Human play today will probably never really approach true equilibrium.