100bb 6-max.
Hero is dealt 
Folds to SB/Villain, who opens to 3bb.
BB/Hero 3-bets to 9bb.
Villain calls.
Flop (18bb) 
SB checks.
BB checks.
Turn (18bb) 
SB bets 9bb.
BB calls.
River (36bb) 
SB checks.
BB 27bb. SB calls.
In this session, we shall dissect a hand between the Small-Blind and the Big-Blind in a 3-bet pot scenario. Our exploration today is underpinned by a sophisticated analysis using GTOplus, a solver that provides us with an equilibrium solution closely mirroring our hand history. We focus not just about this hand, but the broader strategies in 3-bet pots, particularly on Ace-high flops and runouts that complete flushes. We’ll delve into the art of extracting maximum value with the nuts and navigating these treacherous waters with precision.
Let’s delve into the minutiae of this hand history. The action commences with folds around to the Small-Blind, who opens with a raise to 3 big blinds. The plot thickens as the Big-Blind, holding the formidable Queen of Spades and Queen of Diamonds, escalates the stakes with a 3-bet to 9 big blinds.
The flop: Ace of Spades, Seven of Spades, Four of Diamonds. Brings a wealth of strategic possibilities! The Small-Blind, exercising caution, checks. The Big-Blind, perhaps sensing danger also checks. The turn reveals the Nine of Spades, completing three-to-a-flush. The Small-Blind, seizing the initiative, bets approximately half the pot. The Big-Blind, undeterred, parries with a call. The river presents the King of Spades, completing four-to-a-flush. The Small-Blind checks, passing the baton of aggression to the Big-Blind who bets about three-quarters of the pot, only to be met with a call from the Small-Blind.
Let’s turn our attention to the flop strategy on the Ace of Spades, Seven of Spades, Four of Diamonds board. The Small-Blind, in this situation, is likely to check an overwhelming majority of the time – a whopping 99%, to be precise. However, a sliver of aggression exists – about 1% – where some pocket pairs and weaker pairs might step out of the shadows to defend. This is because the Small-Blind’s range is highly polarized on this flop, boasting strong Ace-X hands and a plethora of unmade ones.
When the Small-Blind checks, the Big-Blind continues the clash with a betting frequency of about 47.5%. The size of these bets fluctuates between 20% and 50% of the pot. A 50% bet size is often the weapon of choice when wielding Ace-King or Ace-Queen for value, including some 2-pair combinations like Ace-Seven and Ace-Four. However, it’s important to note that sets are conspicuously absent from this betting range, preferring to bet smaller. The bluffing arsenal in this scenario might include backdoor flush draws or straight draws – think King of Spades, Six of Diamonds, or Ten of Clubs, Nine of Clubs. Our Big-Blind’s Queens of Spades and Diamonds, however, are unlikely to tread this path.
On the other hand, a 20% or 35% bet size welcomes weaker Ace-X hands, such as Ace-Two, into the fray, as well as sets like Sevens or even Aces. This range is less polarized, featuring more middle-of-the-road hands like Eights through Kings, which aim to check back the turn and attempt to showdown. The bluff selection for these bet sizes remains similar.
The checking range for the Big-Blind on the flop brims with top-pair hands, however it’s less populated with Ace-King or Ace-Queen, as these often take the aggressive route on the flop. These premium hands might check back on the flop only to unleash a larger bet on the turn if the opportunity arises, or perhaps even raise against a bet. Pocket pairs, often adopt a passive stance on the flop, but face a dilemma when bet into on the turn, oscillating between calling and folding. And let’s not forget the plethora of unmade hands – those that missed the flop entirely but linger in the hand – often check hoping to materialize into something more substantial, perhaps a modest one-pair or even a backdoor straight or flush.
Continuing our journey through this intricate hand, we now shift our focus to the turn, where the combat intensifies with the emergence of the Nine of Spades. This card adds layers of complexity and tests the mettle of our players, with the completion of the spade flush.
In this critical juncture, the Small-Blind wields two potent weapons in terms of bet sizes: the full pot bet, and a more moderate 50% pot bet. Each size carries with it a distinct strategic purpose and a narrative of its own.
Let us first consider the full pot bet, a move as polarizing as it is audacious. This bet boldly announces hands of great strength or ambitious bluffs. Here, the Small-Blind could be wielding two-pair, sets, or even completed flushes, challenging the Big-Blind to a continue the duel. The bluffing range here is a motley crew of straight draws and hands that artfully block Ace-King or Ace-Queen, such as the Queen of Hearts and Eight of Hearts, which obstruct the Big-Blind’s Ace-Queen holding. Even weak pairs, like the Seven of Clubs and Six of Clubs, join this bluffing brigade, hoping to evolve into stronger hands like two-pair or trips, while simultaneously blocking potential Ace-Seven combinations of the Big-Blind.
Facing a full pot bet, the Big-Blind’s Queens of Spades and Diamonds are compelled to call, with strong equity flowing from the flush-draw. This situation also delineates a clear stratagem for other hands: pairs with a flush draw are beckoned to call, while pairs deprived of flush potential often find themselves reluctantly folding. A hand like Ace of Diamonds and Two of Diamonds finds itself torn between calling and folding.
Now, let us turn our gaze to the more temperate 50% pot bet, a less polarized approach yet full of strategic nuance. This bet size is often employed with top-pair hands seeking value, while simultaneously using weaker pairs as deceptive bluffs. The objective here is to extract value from hands that fall short of top-pair, such as eager flush-draws that are likely to call. Given that top-pair hands form the cornerstone of this value range, all top-pair combinations, most Nine-X hands, and virtually all flush draws are inclined to call this bet. However, unmade hands and pairs without a flush draw often find themselves folding. A hand like Queen of Diamonds and Queen of Hearts, devoid of flush potential, finds no solace here and folds, while our Big-Blind’s Queens of Spades and Diamonds, with their flush draw, are equity-bound to call.
Thus, our hand unfolds with a 50% pot bet by the Small-Blind, met with a call by the Big-Blind. As our hand reaches its crescendo with the River, the King of Spades makes its appearance, completing a panoply of flush possibilities. This new card changes the entire complexion of the hand.
The Small-Blind, cognizant of the flush-heavy board and the Big-Blind’s range advantage in flush draws, is likely to adopt a more cautious stance. Indeed, the Small-Blind checks with a frequency of about 84.3%, a nod to the shifted dynamics of the hand. The betting range, when it does materialize, often consists of weak flushes betting a modest 25% of the pot. This is a nuanced move, a combination of a value bet and a blocking bet, designed to extract value from top-pair hands while simultaneously guarding against stronger hands.
The Small-Blind’s checking range, interestingly, shelters most of their flushes, a tactic to protect the middle of their range, which now includes top-pair hands. When the Small-Blind checks, the Big-Blind, holding the initiative, bets with 50.2% of their range. The value component of this range is predominantly two-pair (with Ace-King being somewhat ambivalent between betting and checking) or stronger, employing a variety of bet sizes ranging from 50% of the pot to the thematic all-in, representing a 228% bet of the pot.
The 50% pot bet is densely populated with weaker flushes seeking value, aiming to entice calls from the Small-Blind’s top-pair hands. As the bet sizes swell, the Big-Blind’s range becomes increasingly polarized. A pot-sized bet is a clarion call of at least a fourth-flush or stronger for value. A bet of 150% of the pot signals a third-flush or stronger, and an all-in bet is a beacon for a second-flush or the nut flush.
In our hand, the Big-Blind’s Queens of Spades and Diamonds, now transformed into the nut flush, find themselves in the enviable position of holding the strongest hand. The most common play here would be the all-in bet, leveraging the full power of this mighty hand. However, there’s a subtlety here; the Big-Blind can opt for smaller bet sizes. This stratagem isn’t just about maximizing value; it’s about strategic balance, protecting the weaker flushes in their range from facing an all-in bet. It’s a move that allows the Big-Blind to potentially extract value from the Small-Blind’s bluffs, inducing them to shove along-side the weaker flushes.
In conclusion, the Big-Blind’s play with the Queens of Spades and Diamonds was a masterclass in poker strategy. From the preflop 3-bet to the river’s nuanced decision-making, each move was calibrated to the evolving dynamics of the hand. The final act, the decision to bet big or not on the river, showcases a strong understanding of range dynamics, opponent tendencies, and the subtle art of value extraction.