In chapter 8 of Play Optimal Poker 2, Andrew Brokos digs into how the pre-flop raiser should continue betting the turn after his flop c-bet is called, especially on the coordinated 9♥ 7♦ 6♥ board where he didn’t start with a big flop range advantage. The core theme is how Ivan learns to use his emerging nuts advantage on many turns to barrel profitably with the right mix of value, bluffs, and protection hands.
How Opal’s Flop Call Sets Up Ivan’s Turn Advantage
On the flop 9♥ 7♦ 6♥:
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Ivan bets small.
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Opal in the big blind:
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Folds her worst junk,
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Check-raises many of her strongest made hands and best draws,
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Calls mostly with middling hands.
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Result: her calling range is quite condensed—a lot of medium-strength hands, fewer true monsters than she had preflop, and not much total trash.
So on the turn:
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Ivan, who bet many of his own strong hands on the flop,
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Now often has a nuts advantage vs a BB who:
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Raised her top tier,
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Called with the middle,
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Folded the bottom.
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But how big that nuts edge is depends heavily on the particular turn card. That’s the heart of the chapter.
Comparing Four Turn Cards: 7♥, A♣, 8♠, 2♦
Ivan raised UTG, c-bet 9♥ 7♦ 6♥ small, got called, and now faces four possible turns: 7♥, A♣, 8♠, 2♦. He can bet 75% pot ($16) or overbet 200% pot ($42).
1. Equity & EV Across the Four Turns
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Best equity & EV: A♣
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Ivan has many more Ax combinations than Opal.
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The Ace helps him a lot but doesn’t magically unlock new nut hands for her.
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He enjoys both an equity edge and nuts advantage.
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Worst equity: 2♦ and 8♠
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2♦ mostly does nothing for his unpaired hands except sometimes add a backdoor flush; Opal can turn similar draws.
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8♠ is even more dangerous strategically:
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Opal has tons of straights and two-pair combos.
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Ivan’s overpairs and top pairs are much less “big-pot worthy”.
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Interesting twist:
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Ivan’s equity is slightly lower on 2♦ than 8♠,
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But his EV is slightly better on the 2♦:
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On 2♦, Opal’s range stays more condensed (a lot of medium-strength stuff).
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Ivan can treat overpairs as near “effective nuts” and leverage them.
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On 8♠, her range includes way more true monsters; his value hands lose power.
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7♥:
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Equity is roughly split,
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But Ivan has more flushes, boats, and quads than Opal because she raised many of her best draws on the flop.
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That gives him a solid nuts advantage and strong EV.
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2. Betting Frequencies on Different Turns
Brokos summarizes solver output with a big chart, but the pattern is the important bit:
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Highest betting frequencies:
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On turns like 7♥ and other cards that complete major draws.
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Ivan had more strong draws in his flop betting range than Opal had in her calling range, so he connects more often.
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Lowest betting frequencies:
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On very bad cards for him, like the 2♦ and especially the 8♠.
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Also surprisingly low betting frequency on A♣:
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Even though it’s great for his equity/EV,
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It gives him many strong but not invincible hands (pocket pairs, top pair) that:
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Don’t need huge fold equity,
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Don’t love facing check-raises,
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Prefer pot control from in position.
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When he does bet, he usually uses a polarized or semi-polarized range and checks a lot of his medium-strength stuff.
3. When Does Ivan Overbet?
He only has substantial overbet ranges on:
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Non-heart Aces and Kings, and
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8♥.
On these turns, his overbets are very polarized:
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Strong value:
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Sets,
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Top full houses,
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Some nuttish top pairs (on A/K turns),
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Strong flushes (especially on 8♥).
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Bluffs:
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Misses with good blockers,
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Strong draws (flush draws, pair+draw),
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Air that benefits strongly from fold equity.
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On A♣, for example, he overbets with:
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AA (which Opal doesn’t have),
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Strong sets,
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Flush draws,
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Combos like 98 (pair + draw),
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Some unpaired no-draw hands that rely entirely on fold equity.
On 8♥, his overbets target:
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Opal’s many straights,
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With a range heavy in:
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Flushes,
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Sets,
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Overcards with one big heart (draw + blocker).
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Scenario 1: Barreling the 7♥ Turn
Board runs: 9♥ 7♦ 6♥ – 7♥.
Static vs Dynamic
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This turn makes the board more static:
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Nut flushes, full houses, and quads will mostly remain the best hands on most rivers.
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There aren’t many future cards that flip the ranking dramatically among the very top of the range.
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This structure favors:
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The player with the nuts advantage (Ivan),
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Using a polarized betting range:
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Nuts and near-nuts,
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Plus clean bluffs,
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While checking a condensed, medium-strength chunk.
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Ivan’s Pure Value Bets
Ivan always bets his absolute monsters here:
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Quads,
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Full houses,
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Nut flushes.
Why?
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He can’t rely on Opal to do the pot-building for him:
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Many of her stronger hands will just call or check-call, not jam.
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If he doesn’t bet, he risks missing value from her:
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Straights,
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Flushes,
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Overpairs,
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Strong one-pair hands.
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He also bets some overpairs like QQ and KK frequently:
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They gain from:
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Fold equity vs weak pair/draw combos,
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Decent equity when called.
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Nuts advantage + limited check-raising from Opal (she raises very rarely here) means:
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These medium-strong hands can be included in a depoloarized betting range safely.
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Ivan’s Bluffing Candidates
He doesn’t have pure, “always-bet” bluffs here, but he frequently uses:
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Overcard + flush draw hands (like A♥ Kx):
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Reasonable showdown value,
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Great equity if called,
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Good blockers.
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Total air with no future (e.g., Q♦ J♦ with no real draw):
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Nothing to gain by checking,
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Strong benefit from fold equity,
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Works well as a pure bluff given his nuts advantage.
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Pure Checks: Equity Preservation
His pure checks:
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Medium strength that have some showdown value versus the weak portion of Opal’s range,
but would get owned if they start building a big pot:-
88,
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AK without a heart,
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T9, 98,
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And A♥ K♥, which is a special case:
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It’s the nut flush but blocks the second-nut flush and many strong calling hands.
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So it gets less value from a big bet compared to other flushes.
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That makes it a great slowplay candidate here.
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By checking these, he preserves their equity and avoids bloating the pot when he’s often only marginally ahead.
Scenario 2: Barreling the 2♦ Turn
Board: 9♥ 7♦ 6♥ – 2♦.
Opal checks again; Ivan is considering betting 75% pot or checking (overbets exist but are a small slice).
This Turn Is More Dynamic
The 2♦:
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Adds a second flush draw,
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Leaves many overcards still available on the river (T, J, Q, K, A),
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Ensures that almost every river changes things significantly.
This makes the board more dynamic:
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Both ranges will shift a lot in strength depending on the river.
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Board coverage becomes crucial:
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Ivan wants strong hands and bluff candidates across many possible rivers,
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In both his betting and checking branches.
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Always Betting His Nut Hands
Ivan always bets his nuttiest holdings:
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99 and 77 (top sets).
Why no slowplay?
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On dynamic textures, slowplaying is expensive:
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Your full house/near-nuts now may just be “good but not incredible” later.
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You can still make nut hands on rivers by:
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Checking some draws on the turn,
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Which is cheaper than checking sets now and hoping to still be safe later.
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Being capped on some rivers is tolerable:
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On the river, there’s no leverage behind a bet.
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He can just call at the right frequencies to keep Opal indifferent to bluffing.
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Why Overpairs with a Heart (or Diamond) Bet More Often
Hands like:
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Q♥ Q♦, K♥ K♦, and similar:
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Are always bets or high-frequency bets,
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While Q♠ Q♣ or K♠ K♣ are lower-frequency bets or pure checks.
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Reason:
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A heart (or relevant suit) gives them better future value on flush rivers:
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When a heart comes and Ivan bets for value,
holding a heart means:-
Fewer strong flushes in Opal’s range,
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More profitable thin value bets.
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Blockers aren’t just for bluffs:
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They also make value bets more effective by reducing the chance of being coolered.
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So anticipating that extra river value nudges these combos toward betting now on the turn.
How Draws Are Split Between Checks and Bets
Ivan keeps straight draws, heart draws, and diamond draws in both ranges for coverage. He chooses which to bet based mainly on:
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How much they gain from folds,
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And how much showdown value they have if he checks.
Examples of patterns:
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AK (even with a flush draw):
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Rarely bets as a bluff,
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Strong enough to win unimproved often enough,
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Doesn’t gain as much from folds.
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AQ / AJ (especially with suits):
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More interested in fold equity:
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They sometimes fold out better high-card hands,
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With a flush draw, they also have good equity.
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With suited versions, they can be indifferent between betting/checking.
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AT suited with gutshot + flush draw (A♦ T♦, A♥ T♥):
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Bet almost always:
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Strong draw,
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Valuable fold equity,
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Extra equity from the gutshot.
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Lower flush draws:
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Often high-frequency bets:
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Less showdown value,
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More dependent on fold equity and hitting big.
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OESDs:
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Only 88 and 98 qualify here.
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88 always checks (too much showdown value and already a pair),
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98, especially 9♦ 8♦, often bets:
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Can value bet against worse pairs,
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Has strong draw equity,
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Blocks 88 and 87 in Opal’s continuing range.
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Practical Heuristics from the “Test Yourself” Spots
Brokos reinforces the concepts with other boards, like 9♦ 6♠ 5♠ → A♦ turn, or → 8♣ turn, and shows how:
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Overbets fit best when:
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Your range is nut-heavy,
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Villain has many bluff-catchers or draws,
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You have clear value and clear bluff candidates with good blockers.
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Some hands that “look like obvious bets” are actually better checks:
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AQ on an A-turn where you’ll face check-raises and can’t value bet two streets,
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A♠Q♠ type nut-draw/top-pair combos that:
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Have tons of showdown value,
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Want to keep some flush draws in your checking range.
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Small pairs or weak made hands can be excellent bluff candidates when:
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They block key nutted holdings,
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Have poor showdown value on the current texture,
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Fit naturally into a polarized overbet range.
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Core Lessons from Chapter 8
Brokos closes with a set of conceptual points about turn play:
1. Flop Aggressor Often Drifts Into a Nuts Advantage by the Turn
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Even when the flop didn’t belong to Ivan,
his flop bet + Opal’s call dynamic means:-
He retains many strong hands,
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She has raised out her very best,
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Her call range is compressed around medium-strength.
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That gives Ivan many turn spots where he can pressure her with leveraged betting.
2. Static vs Dynamic Turns Demand Different Turn Strategies
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Static turns (like paired + flush-completing ones on this board):
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The same top hands stay best on most rivers.
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Ideal for polarized betting:
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Top value + low-equity bluffs.
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Dynamic turns (like low cards adding more draws, second flush draws, or big overcards with many changing rivers ahead):
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Lots of future cards reshuffle hand values.
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Call for depolarized ranges:
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Semi-bluffs,
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Protection bets,
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Thin value bets,
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And careful board coverage.
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3. Playing Out of Position Is Worst on Dynamic Boards
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Out of position, with a condensed range on a dynamic board,
you have to:-
Split ranges into bet/check,
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Keep board coverage across many possible rivers,
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While your opponent controls bet sizing.
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That juggling act is difficult and EV-costly, which is why Ivan’s positional advantage matters more on dynamic turns.