In chapter 7 of Play Optimal Poker 2, Andrew Brokos looks at how the big blind should defend on flops where she actually has the range advantage, using the 9♥ 7♦ 6♥ board as the main example. The chapter focuses on how Opal (BB) should mix calling, folding, and check-raising against Ivan’s continuation bets, and how to exploit opponents who c-bet too often without realizing they’re on a bad board for their range.
Big Picture: BB Has the Stronger Range Here
On the flop 9♥ 7♦ 6♥:
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The big blind:
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Has slightly more equity overall.
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Has more nutty hands (straights like T8s, more sets, strong two-pair, good draws).
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The UTG raiser:
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Still has strong hands (overpairs, top pair + overcards),
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But does not dominate the board the way he does on high, dry, or paired boards.
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Because of this:
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Ivan cannot safely c-bet his whole range.
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Opal’s job is to defend actively:
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Call a lot,
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Check-raise a meaningful chunk of hands,
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Fold very little vs small bets.
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Donk Betting: Theoretically OK, Practically Not Worth It
Brokos shows that:
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On this flop, the BB could justify a small donk-bet range (around ~15% of hands).
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That range would contain:
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Some very strong hands (sets/straights),
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Some vulnerable made hands,
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Some equity-driven semi-bluffs.
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But the EV increase is microscopic—basically a rounding error.
So for real-life purposes:
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Default: just check 100% and let the pre-flop raiser act.
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Only donk bet as an exploit if:
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You know villain misplays vs donk bets,
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Or you’re very confident in your construction and postflop skill.
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Facing a Small C-Bet ($4 into $13): Call a Lot, Raise Some, Rarely Fold
Against Ivan’s small c-bet:
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Opal’s response split (roughly):
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Call with ~60% of her range,
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Raise with ~16%,
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Fold the rest.
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The Folds: Mostly Weak Unpaired Overcards
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Pure folds:
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Unpaired overcards like AJo, KQo without a heart, etc.
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Important:
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She never folds underpairs (22–55) on this board vs the small bet.
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Even low pairs with a heart gain meaningful equity via backdoor flush potential.
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Because a small bet gives her 4:1 immediate odds, and Ivan can’t apply huge leverage on many turns (no big nuts advantage), she must defend extremely wide.
The Calls: Pairs, Decent Draws, Strong Overcards
Calling captures the bulk of her range:
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Any pair:
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Top, middle, bottom pairs.
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Pocket pairs below the board (22–55).
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Decent draws:
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Gutshots,
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Backdoor flush draws,
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Overcards with hearts or diamonds.
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Strong overcards like AK, especially with A♥, are almost always calls, never folds.
These hands don’t necessarily want to blow the pot up yet, but they realize equity well on this sort of board, especially since Ivan cannot barrel relentlessly.
The Raises: Strong Hands + Well-Chosen Bluffs
Her check-raising range is crucial, especially given her nut advantage.
High-frequency raises:
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Monsters:
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Top set (99),
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The nuts (T8s),
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Some strong made hands that stay ahead on many runouts.
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Strong draws:
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Good flush draws,
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Good open-ended straight draws.
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And then, for board coverage and future nuttiness, she mixes in:
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Some Tx combos (to make straights on 8 turns),
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Some diamond hands,
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Occasional bare A♥ or A♦:
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Those block villain’s strongest holdings,
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Set up profitable bluffs on heart or diamond turns.
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She very rarely check-raises 66 or 76s even though they’re strong, because:
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In a big pot vs a strong continuing range,
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Bottom set and bottom two-pair lose a lot of their equity,
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And they suffer badly on many turn cards.
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These hands prefer pot control and equity preservation: call now, navigate later.
Facing a Larger C-Bet ($9): Fold More, Raise a Bit More, Call Less
When Ivan bets bigger:
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Opal’s fold frequency jumps significantly (almost half her range vs $9).
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She still raises, and in fact:
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Check-raises slightly more often in percentage terms,
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But now with a more polarized range:
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Even more focused on nutty hands + strong bluffs.
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She calls less:
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The bigger the bet, the fewer marginal hands can justify continuing.
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This fits general principles:
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Larger bets:
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Force defender to fold more (worse price),
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Increase the value of polarized raising when you hold the nut advantage.
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Board Coverage: Why Her Check-Raises Aren’t Just “Obvious” Hands
Opal’s check-raising range is built to avoid being face-up on later streets. So:
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She doesn’t only raise:
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Sets, straights, flush draws, big OESDs.
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She also raises:
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Some diamond combos (so she can have flushes when diamonds come),
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Some Tx (so she can make straights on 8 turns),
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Some hands with key high cards (A♥, A♦) that serve as blockers and future bluff candidates.
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The idea: no matter what the turn/river are, her aggressive line can plausibly contain:
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Very strong hands,
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Well-chosen bluffs,
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And not just the “obvious” draw category.
Exploiting Over-Aggressive C-Betters
If Opal suspects Ivan is c-betting too often on this board:
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She stops caring about donk-betting theory
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Just check everything and let him mess up.
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She raises more and folds less:
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More raises with:
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Thin value (like 76s, 66, weaker made hands that were mostly calls at equilibrium),
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Additional bluff combos.
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Fewer folds with:
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Weak pairs,
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Marginal draws and overcards getting a good price.
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In short: when villain is over-betting his range, punish him with more check-raises and more stubborn defense.
Donk Bets on Other Boards
Brokos extends the logic to other textures:
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5♥ 4♦ 3♣:
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BB has a serious nut advantage (more sets, more straights).
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Solver wants a pretty large donk-bet frequency with a mixed, non-intuitive range.
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In practice: consider donking mainly:
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Strong made hands that don’t want to give free cards to overpairs/gutshots,
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Vulnerable overpairs and strong draws,
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A spread of bluffs (straight draws, backdoors, random overcards).
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J♦ 9♥ 7♦:
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Also dynamic, but position for the pre-flop raiser matters a lot.
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Here, the incentive to donk is much weaker; better to check range and build a robust check-raise strategy instead.
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Concrete Check-Raise Examples (from the Test Section)
On a flop like J♦ 9♥ 7♦, facing a small c-bet:
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Most likely raises:
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T♦ 8♦ (nut draw),
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J♣ J♥ (top set),
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Strong nut-draw bluffs like K♥ Q♥.
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Least likely raises:
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Hands like A♣ J♣, Q♣ J♣, 9♣ 7♣:
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Good but fragile top pair / two pair,
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Tough to play if the pot explodes on later streets.
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Small underpairs (33) never raise; they either call (with a diamond) or fold.
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Versus a bigger c-bet, raising becomes even more polarized:
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More JJ / T8 raises,
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Very little raising with “just strong” hands like AJ or 97.
Core Takeaways from Chapter 7
You can boil the chapter’s lessons down to these:
1. BB Can Donk Bet — But Usually Shouldn’t (Without an Exploit)
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When the big blind has a clear nuts advantage, a small donk-bet range makes theoretical sense.
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But in practice, the EV gain is tiny and the complexity cost is high.
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Default strategy: check 100% and play well vs c-bets.
2. Check-Raising Is a Key Weapon With Range Advantage
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On dynamic, coordinated boards where BB has strong combos:
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She must use check-raises aggressively.
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Her raising range should include:
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Strong made hands (sets, straights, strong two pair),
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Good draws (especially to the nuts),
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Some additional hands for future board coverage.
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3. BB Rarely Folds vs Small Bets
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Against small c-bets, especially when the raiser lacks nut advantage:
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BB should fold very few hands.
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Underpairs and lots of weak but live hands must be defended.
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Only truly hopeless unpaired overcards without backup are pure folds.
4. Adjust to Bet Size
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Bigger bets → BB:
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Folds more,
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Raises more polar, mostly very strong hands plus some bluffs,
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Calls less with marginal holdings.
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Smaller bets → BB:
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Calls wide,
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Raises a meaningful chunk,
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Folds very little.
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5. Exploit Over-C-Betting by Raising More, Folding Less
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If villain insists on “range-betting” boards where he doesn’t have the range/nuts advantage:
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Increase check-raises (both for value and as bluffs),
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Be more stubborn with marginal calls,
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Let him light money on fire trying to “own” a flop that actually belongs to you.
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