In our last episode we focused on flop construction, but if you were reading closely you came away with, or had reinforced, one of the most profound aspects of no-limit strategy, one which can buoy your play across any street of action:
Wagering and sizing choice have a direct correspondence to range versus range versus board considerations.
There’s a reason, in other words, all those cool poker sites are so equally cool with passing out all the charts and graphics a desperate regfish can get his hungry click on: they are of very little use as a stand-alone product in the multi-dimensional world of cash game poker strategy.
Because, of course, the eternal question that leads players stumped: What now?
(And by the way, as Mr. Deets has pointed out, why are those range matrices always backward? AA should be the right upper quadrant, one is demarcated by mathematicians as the first, just as we read nearly every form of media from the left to the right in the western world.)
More relevant for our analysis today, there’s a quantifiable reason for the out of position player to lead or check to potentially check-raise. In other words, the two are not merely the fraternal twins many lazy eyes and forum bums suppose. No chart – well, at least as far as I know – can tell you this.
So, never mind about where AA and friends should graphically repose – let’s get to work on the wagering/range correspondence.
Now, I originally suggested we’d close the Construction series with this specific hand, where Christian Soto of Solve for Why takes on the high-spirited Live at the Bike regular Eldar “Bear Jew” Adi. I’ve since changed my mind simply because I want to employ a turn action to more naturally connect to the previous article’s flop theme.
5/10/20, 5500 effective
EP Eldar opens AQcc to 100
BB Christian A9ss calls
Pot 225 4s9cJc
Pot 575 Turn Qs
Pot 3025 River 3h
Mid-stacked Pre-flop and Flop Considerations
Let’s start with a brief tour of how we arrived at the key decision point, not because anything unusual happened, but because all actions in a coherent strategy are connected and must be established for our audience with the turned Queen of Spades to be productive. With significant enough money to play for, although not the biggest stakes available to Soto, the Solve for Why partner will not be splashing as much as he might or has been rumored to do at smaller stakes. This is also a live stream game, giving him extra incentive to perform for business and personal reasons.
This is relevant because we’ll see over the course of this night and others that the mid-stacked, and certainly the deep-stacked, defense range of a serious player is not as wide as supposed, nor is the strategy of taking every price necessarily the only one once stacks are deep. While it is often conveniently posited that the BB should not only defend extremely speculatively or even take attractive odds in the classic EP – BU – BB formation while a severe underdog, this idea is mostly the hobgoblin of tournament and capped game cash players. The reason is, that when leverage and showdown are just a click or two away, hot and cold equity rules. When seeing a flop with Q5ss, no true disaster can happen at the self-created SPR, including making the large folding errors that greater reverse implied odds might otherwise induce. Depth, in other words, in big bet games is a kind of force that capped stacks can afford to be Newtonian about.
Without speculating too deeply about Soto’s particular strategy, it is publicly available information for the observant that he often chooses to delay leverage more often than other players – especially online cash and tournament players. He does not necessarily press the savvy if easy button of raise folding his entire linear range from the blinds. This is going to be more important than you might think, because it means Soto can arrive on the flop, and obviously the turn, with some strong hands more hysterical strategies will deny themselves in looking for immediate expected value and initiative. For instance, it wouldn’t be impossible, although I won’t list the most trapping range in his equity profile below, for him to have top set or an overpair on the flop.
So, while this is becoming a longer throat clearing than I’d hoped for, I think it helps us understand the primary reason why Soto has an interesting choice on the turn in this hand. I started by assigning Soto a condensed 18% range pre-flop, though I will use my editor’s modified 16% for some review of my conclusions, as I began to think I was too extreme in my initial ideas about Soto and may have some biases. But that is neither here nor there, ultimately, because what’s more important, whether the composition of my proposed range is right or wrong is that he observably doesn’t have the slutty 35%-plus range supposed by the price-takers, even if he is on record as encouraging this thinking.
Why? Because Soto historically has played for deep, live stacks, not micro edges over high iterations. If volume is impossible live, we compensate by playing bigger than we should and by playing bigger pots: the universe tends to correct itself. The same strategy, for instance, that defends [Qx][8x] from the BB to realize a tiny equity share in one dimension folds along the way too often in the deepstack dimension. It’s the live player’s oversimplification of the game, just as the capped game or online expert has sagely learned to bet range unilaterally in many spots in order to remove extraneous nuance at a marginal sacrifice of expected value. Conversely, no such shortcuts exist at the very scary top of the food chain.
Initial guess at Eldar’s equity profile…
… and Soto’s.
Soto’s original sample equity profile on the neutral flop of [4s][9c][Jc] using the first ranges I assigned the two, for instance, is reflective of a strategy designed to follow Eldar deep into the hand rather than letting him off the hook, mid-stacked or greater, for small pots.
Soto, starting with something like JJ-22,AQs-A5s,KTs+,QTs+,JTs,T9s,98s,87s,AJo,KTo+,QTo+,JTo, ends up on this flop with:
the same number of sets
more top pairs
better drawing quality
fewer ace highs
It shouldn’t take much demonstration to see why this equity profile might be of value with nearly 300 bigs to play for. Of course, Eldar as the pre-flop raiser naturally retains the overpairs as his primary advantage (still, remember my asterisk about Soto above). Once the greater depths of the Rubicon are crossed, Soto or the deep stack player can more effectively pour money into this pot, in exchange for surrendering some pre-flop steals, flop wins and other small pots. The mistaken view that the point of opening is to steal the blinds flies in the face of deepstack reality.
Looking to the IP player, I supposed Eldar, while a gem of a poker entertainer and fabulously loose when comfortable, to be slightly constrained. While I still don’t think he’ll resist certain parts of the deck, on this tougher table with scarier opponents than the usual LATB suspects, we’ll likely see him tighten up and make a real effort. A 19% range – 22+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,54s,43s,AJo+,KJo+,QJo – featuring all the suited aces and a few too many suited connectors was my starting point.
I would change my mind about these ranges as I investigated the hand.
The flop action goes a natural x/b/c. Given that the board is neutral, the PFR will fire large portions of his range, while Soto has flopped the middle. This equity can’t be folded and is not only unnecessary to raise, as I said, it’s my instinct that Soto will prefer to play turns even with some hands that could raise.
Choosing a Turn Wagering Construction
So, as the airline pilot bizarrely tells us, welcome to our destination. The turn is the [Qs], which gives Soto, in addition to new pairs, two pairs, and draws, a strong share of the nut range advantage. While Eldar still retains his over-pairs and has added three set combos, the distribution of the two straights is likely perceived to be skewed to the BB.
In other words, both the in position and out of position player share very strong hands. This matters, because now Soto faces a choice. With his perceived range and actual holding improved, Soto will not be folding the [As][9s] on [4s][9c][Jc][Qs]. (Not insignificantly, the condensed pre-flop BB strategy has yielded fruit – he is now a hot/cold range vs range favorite.)
So, what is Soto’s best action? Just as we did last time, we’ll use the nature of a bet to determine the most natural choice. Since Soto is inclined to have a leading range, I’ll assume his check-raises are limited, still leave him with the option to polarize through one, and focus on the initial, critical choice.
When the board combinatorially works in our favor, we have more bets – this is what the range vis-a-vis board establishes. It’s enough to say here that a bet is the sale of equity realization to the opponent. If the bettor has a combinatorial advantage, it is the logical maneuver to charge for his opponent’s realization rather than give him the opportunity to realize at a cost of zero.
The spectrum and sizing of bets, meanwhile, can be determined by how severe that advantage is. For instance, a tight PFR can offer the sale of realization with his entire range on [Ax][Kx][2x] but will be mistaken to offer the same price and rate on [Ax][Kx][10x]. With fewer bets and more dangerous resistance, the more limited distribution of prices now can conversely rise; just as [Ax][Kx][2x] allowed the PFR to sell cheaply for maximal expected value for his whole range. Such is the nature of wagering, which can be visualized as a spectrum with combinatorial advantage on each pole.
Ownership of this advantage is not going to be immediately clear on a board like this – we are not at the poles of the spectrum. Given the surface ambiguity, it is reasonable that Soto now makes the choice to sell realization to Eldar. After all, he’ll happily take a fold or a call – he’s got a strong draw and a perceived strong range, as we just went over.
However, the reason the hand is interesting is that not all hands or parts of one’s range are equivalent in a strategy that chooses between bets and checks and sizes. In other words, in an elaborate strategy that does not bet or check range at one size, Soto has other choices besides the natural sale of realization – polarization, for one.
The check-raise is the natural response to the claim of ownership of stronger value combos than the bettor has. It is more expensive and contorts the response to it. Hence the middle of that range tends to fall out when check-raising. Further, if range is being bet, the nature of wagering tells us that the price must be depressed – yet Soto does not depress the price, offering a hefty 75% of pot. He therefore must split the range he arrived on the turn with between checks and bets in order to continue profitably, as I pointed out above.
So we begin to see the issue with the turn lead more clearly. Where is A9ss in the construction of wagering? Poker is not a toy game: while our models are solid and reasonable, equities, or “hands” differ in quality, or as we say in poker, expected value. This is the question, because it is unlikely any one holding will respond to both the merged sale of value and the combinatorial narrowing known as polarization equally well. Yet this one is hard – we’d better look closely.
The showdown component of Soto’s hand is low linear value – the [9x] – and the robust equity of the hand, the nut draw. The low linear value, if we imagine it separated from its robust portion, is now offering sale to the PFR. However, what response will he have? When called, the linear value is behind, or it is charging the drawing portion of Eldar’s range. However, not only is the drawing portion of Eldar’s calling range likely to be robust, it is partially blocked by the robust portion of Soto’s holding.
Therefore this wager is becoming a protection bet against hands that it does not need much protection from: low pairs, a worse nine. Their equity has diminished significantly by the turn and by the spades covering them. Even sets, in other words, that do not raise, will sometimes lose to the nut flush. Selling realization to Eldar is thus a problem with such a hand.
And speaking of sets, a potential raise is an even worse problem for Soto. If his hand is raised by the in-position Eldar, Soto now finds himself in a spot. Yes, he can fight Eldar by repolarizing with a three-bet, but with the wrong blockers in his hand, he would be nakedly using his marginal perceived range advantage on a board where he shares nut equity advantage. Soto stacks off against two pair plus while behind and one card to come; surely this must be a low-frequency action. In other words, while a bet/3b line cannot ever be a complete disaster because of the raw equity of his hand, this turn action borders on a bad bet: the bettor forces his opponent to fold worse draws while he continues with high-equity hands.
So, by looking at the consequences of his action, we see Soto has a close but natural action with [As][9s] and the middle portions of the range: check. The narrowness of the range advantage means a lead can’t be poor, but with this hand and related ones facing the counteraction described above, checking to Eldar should be superior.
Consider the Counteraction
We can first look to Eldar’s range of actions for confirmation of our line’s tactical value. If Eldar calls a lead on this range card he will have allowed Soto to realize at no additional cost. If Soto checks, Eldar checking behind denies his own ability to bluff and achieve max value; conversely, all his SDV, which is slightly superior to Soto’s, simply realizes through the check or call.
In other words, Eldar does have an overall incentive to put in aggressive money against Soto when his own range is strengthened by the turn card: this is what should be on Soto’s mind when he decides to bet a weak showdown hand, nut draw or not. There is little Soto has gained from his lead with this portion of his range except denial against the weakest part of Eldar’s.
In fact, this is the traditional reason often players donk out, to cheaply deny equity… but what a waste of nut equity should he be raised without the intention to three-bet in response. (Yet he does not want to do that, either… conundrum.) Worse still, Eldar can still bluff catch effectively, leaving Soto in peril on the river and in danger of over-bluffing or folding the best hand when he checks, as he carries so many combos forward if betting range.
Now, what hands could lead, if any, becomes the question. The answer is any hand that wants to be able to 1) repolarize through a bet/3bet, 2) easily trap as a bet/call, or 3) can act as a threatening bet/fold. With absolute top-end range advantage but not range advantage itself, his value bets of [10c][8c] or [Kx][10x] can now obviously stand any action from IP and cage Eldar for finding that natural raise we just discussed – that is a pretty sweet parlay, choosing a range which works well against the natural action of your opponent! Since Eldar has fewer perceived straights, sets can become clear value bets. Hands that block the nuts and have equity themselves would be top bluffing or thin bet candidates. I hesitate, though, because this action does not protect his incentive to check, however, and therefore can’t ever be mandatory.
What size becomes natural? Well, if the correct hands are being bet, which is to say hands that can react with clarity to being raised, the bet could be substantial. However, this highlights the problem of wagering certain hands: by opening up the betting with the merged range out of position, Soto forces himself to pay the max to realize his equity when he can’t be folding, while simultaneously being less likely to be paid on the river.
In other words, if you are an online player or other sophisticated wagerer intent on simplifying a range bet to one size, sizing down becomes a viable answer in the abstract, because now continued turn and river play is more possible. Further, if you are splitting up bets of zero, x, and y, this bet is at its most efficient smaller and smaller, leaving the top and bottom hands in the larger, less frequently used of your several sizings.
In sum, a well-constructed lead on a favorable card must still abide by the basic philosophy of wagering. We find natural bets with combinatorial advantage but can stumble in a close spot by having too many or choosing unwise candidates.
Through the Solver
So with the conceptual work done, let’s look at the hand at some granularity and find out if our thinking is sound. As I mentioned above, we won’t use the slightly exaggerated, 18% leverage-delaying range I first suspected Soto to be using, but a similar 16% one which splits up the ace wheels to give a player a more polar three-betting range, as this will drive home the point of the this article in more general and usable terms.
I will also give Soto raises on the flop that most players will find more natural, whereas my first interpretation of Soto may give him too few – it won’t matter too much as we are focused on this check-call flop sequence.
The real change, upon reflection, is for Eldar: I first suspected Bear Jew to be taking liberties with hands like 43s or worse aces, but if anything, that contradicts his concern for a tough game. Eldar gets much tougher in this scenario, opening a more appropriate 12%. These sharper ranges were suggested by OOP editor and poker pro Greg Porter. While Soto’s range is changed a little, it’s really the new Eldar range that changes everything, forcing Soto to be a 53%-47% underdog preflop.
I’ll leave it to you to decide which Eldar shows up, and how that could change the responses.
For Eldar: AA-77,AKs-A8s,KQs-KJs,QJs,JTs,AKo-AJo,KQo,A7s-A2s,KTs,QTs[/25],66-44,T9s,98s,87s[/50]
For Soto: JJ-22,AJs-A6s,KQs-KTs,QJs-QTs,JTs-J9s,T9s-T8s,98s,87s,76s,65s,54s,AJo,KQo-KJo,QJo,A5s-A2s,K9s,Q9s,97s,86s,ATo,KTo,QTo,JTo[/35]
First off, it’s worth noting that the solver, which is going to construct beautifully if opaquely, is more than a little shocked by Eldar’s flop sizing, finding nearly no bets at this size when given alternatives. It will find more bets with AQcc and the rest of its range as the sizing depresses, running more and more barrels from 75% to 66% and 50% of the pot, but simply preferring a check at nearly 50% of the time rather than wagering to a more recreational player’s sizing. (I’m not going to explore a downbet, as compelling that sizing is for players, as I find it improbable Eldar the live reg would ever bet much less than half pot on this board.)
When it does bet, the solver’s sizings prefer the 66% sizing by a slight margin, rather than a more merged,smaller pricing construction, which would carry more combinations safely forward and allow Eldar many cbets to choose from. However, it simply is not likely to be the board for down sizing, nor does Eldar’s strong, contracted EP range want to surrender expected value. The paradigm of NL is that the EP player wants leverage on early streets, after all, and not be sucked into dangerous boards once behind.
In what is a telling detail, the naked flush draw of [Ac][8c] is bet by the solver much more often, as it benefits a little more from fold equity, and even will be reraised occasionally as a bluff should it be pressed. [Ac][Qc], its stronger counterpart and Eldar’s hand, is never reraised should Soto attack the flop continuation bet. While this is counterintuitive to simple equity pushing ideas, it’s not a stretch of the mind to see that on the spectrum of wagering, [Ac][Qc] trends merged, [Ac][8c] trends polar. Why? It’s the equity [Ac][Qc] retains without being nutted yet. Like [As][9s], it trends toward the showdown value [Ac][8c] does not have.
But let’s get to the point: what will the solver like on the turn should it be given the option to lead? If we find [Ax][9s] as one of its primary leads, my theory will need revision. We’ll have to look at sizings and reconsider Soto’s play. Of course, we are already doing that in one sense – GTO+, as I mentioned, declines Eldar’s sizing, and that has a big effect on the analysis.
Because of this, first look is a bit of false information, as we have to squint at Eldar’s action: in the event that Soto has called the more preferred half-pot bet on the flop which would include Eldar’s hand, A9ss is a clear but not universally preferred check on the turn. Given the option to bet large, as Soto does, the solver finds a bet 33% of the time with this hand, reflecting the split in combinatorial advantage we discussed. That’s twice as many checks, but I don’t feel good about it. It’s closer that I anticipated, even if overall my premise holds true. It has more leads with pure value, and blocker hands fortified by draws – worth thinking about.
However, what does that matter, if the solver rejects Eldar’s flop sizing? That can’t stand in for the situation except in the abstract – this isn’t what happened in-game. So instead, what if we force the solver to make Eldar’s big bet on the flop?
To do this, we’ll give him a typical reg’s betting range at this size, locking in 75% pot bets with overpairs, TPTK and big draws along with Eldar’s holding of [Ac][Qc]. Now we’re getting somewhere.
Well, remember back to our first part of this series and the effect the large bet has? This aggressive money induces action, and with about a quarter of his [As][9s], the forced bet at Eldar’s sizing does trigger the reraise on the flop. Efficiency becomes an issue again: the danger of repping too many combos and thus creating your own overfolds is the poker sin of aggressive dead money. To restate more simply, the forced, non-optimal bets put the bettor himself in peril. We could lock that action out, too, to see the effect and continue to explore, but in reality we don’t have to: one glance at the rest of his A9ss against the flop bet reveals a call, just as Soto did in-game.
So, then, the remainder of the [As][9s] left over for Soto on the turn, and our whole question today in a nutshell?
95% checks, 5% leads.
Whether it is through theory, examining the counter actions, or looking at the numbers, looks like we have a clear answer for our turn construction question.
No bets. Notice the offsuit K10 in the blue betting frequency. This situation is almost all an illusion though, because if you look closely, it and much of Soto’s range could not call the large flop bet, and so responded with raise or fold on the flop. A9ss was one of the few worth a call, at a 75% clip. So different is optimal play from your average game.
We’ll close the series with river play next. Sorry for the long delay.