In chapter 3 of Play Optimal Poker 2, Andrew Brokos expands the framework of protection betting and semi-bluffing by showing how a player should systematically construct ranges on early streets. Using Opal’s difficult spot on the K♦ 8♦ 8♣ flop as a case study, he explains how to divide a range into calls, raises, and folds in a way that prepares for the complexity of future streets—where board textures change, equities shift, and leverage becomes real.
Why Opal’s Flop Situation Is So Difficult
Out-of-position + condensed range
Opal enters the flop disadvantaged:
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Her preflop calling range is weaker than the raiser’s.
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She lacks premium hands like AA, KK, AK, which she would have 3-bet preflop.
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Big stacks and multiple future betting rounds create leverage against her.
Although she occasionally flops trips with 8x, she does not do so often enough to compensate for her structural disadvantage.
A dynamic board
The K♦ 8♦ 8♣ flop is highly dynamic:
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Strong hands may weaken on later streets.
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Weak hands may spike into monsters.
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Ivan, in position, adapts more fluidly to changing textures.
Thus Opal cannot respond solely based on current hand strength—she must think about how her hands realize equity on different runouts.
The Range Construction Framework
Brokos gives a repeatable process for designing ranges during real play. The process mirrors solver logic but is simplified enough to execute at the table.
1. Envision Starting Ranges
Identify:
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Equity advantage: Who holds stronger cards overall?
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Nuts advantage: Who can make the strongest hands?
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Range shape (polarized, linear, condensed)
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Protection incentives: Which player benefits more from betting small?
On K♦ 8♦ 8♣:
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Ivan has equity advantage.
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Opal has some nuts (8x), but not enough to reverse positional or structural disadvantages.
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Ivan’s small bet forces Opal to defend widely.
2. Determine Needed Ranges
Given Ivan’s wide, linear, small c-bet:
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Opal needs:
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A large calling range
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A small, polarized raising range (~13%)
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A modest folding range, because pot odds are excellent
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As the out-of-position, condensed-range player, she challenges Ivan mainly by calling, not by raising.
3. Identify Pure Strategies
Pure strategies are hands that:
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Always fold
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Always call
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Always raise
For Opal:
Pure Calls
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All pairs 6x and better
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All flush draws
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Strong backdoor-draw Ace-highs occasionally fall into this bucket
Pure Folds
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Unpaired hands with low equity and no meaningful backdoor paths
Pure Raises
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Trips (8x)
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Some nut flush draws
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Occasional strong Kx depending on balance needs
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Strong combo draws
These pure strategies form the skeleton of the overall strategy.
4. Resolve Mixed Strategies
Mixed strategies fill in the middle of the range:
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Weak pairs → sometimes call, sometimes fold
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Big unpaired hands with backdoors → sometimes call, sometimes fold
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Some draws → mixed between calling and raising
Mixing ensures:
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Board coverage
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Unpredictability on future streets
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Balanced bluff/value ratios when raising
Opal mixes many hands because she must remain credible across 2162 possible turn–river combinations.
Key Concepts in Opal’s Construction
Equity vs Equity Realization
A hand like A♠Q♠ may have good raw equity but realizes it poorly if it cannot handle multiple barrels.
A hand like 66 may have less raw equity but:
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Can turn into a strong made hand
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Defends more effectively vs future bets
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Realizes equity more reliably
Thus 66 is a pure call while AQ mixes or folds depending on suits.
Why Opal Raises Trips Instead of Slowplaying
Slowplaying seems attractive, but:
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Ivan calls check-raises with many hands worse than trips
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Slowplaying risks losing the opportunity to build the pot
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Out of position, she loses control over whether bets go in on later streets
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Raising trips strengthens her polarized raising range, enabling value and bluff strategies later
Why Nut Flush Draws Often Raise
Nut flush draws:
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Dominate many future all-in situations
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Provide strong semi-bluff potential
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Block top-of-range flushes
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Need to appear in both calling and raising ranges for board coverage
But raising only A♦x♦ would create transparency, so Opal mixes in lower flush draws too.
Raising Non-obvious Hands (e.g., A♦T♣, 22)
These hands:
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Provide bluffing candidates on certain turns
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Help cover diamond turns or paired turns
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Prevent Opal’s raising range from being only value or only flush draws
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Allow her to threaten future barrels with the correct distribution
Adapting to Human Mistakes
Opal adjusts her strategy if Ivan deviates from equilibrium:
If Ivan overfolds to check-raises
→ Raise many more weak hands; give up on the turn.
If Ivan checks behind
→ Mostly check again on the turn; avoid overaggression.
If Ivan bets pot instead of small
→ Defend less often; raise nearly never.
If Ivan never overbets future streets
→ Call more bluff-catchers
→ Slowplay less often
→ Raise more strong hands on the flop
Planning Across Streets
Opal’s entire preflop calling range is designed to:
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Flop draw potential
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Hold backdoor equity
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Produce hands that can call or raise profitably under pressure
Her flop calling ranges reflect:
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Anticipated future board textures
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Necessary bluff-catchers
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Need for board coverage across different suits and ranks
This long-term planning is essential for avoiding capped ranges on dangerous turns and rivers.
Practical Heuristics for Humans
Brokos simplifies solver tendencies into actionable heuristics:
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Never fold a flush draw to a small bet.
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Rarely fold a pair to a small bet.
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Stubbornly call Ace-highs with backdoor potential.
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Raise trips mostly, not slowly.
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Mix flush draws between calling and raising.
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Choose bluffs that interact with the board in diverse ways.
When unsure, err toward:
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Calling vs small bets
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Not raising vs large bets
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Keeping your strategy balanced rather than polarized
Key Lessons from Chapter 3
♠ Prioritize playability over raw equity
Hands that handle future streets well are more valuable than hands slightly ahead right now.
♠ Maintain board coverage
Ensure both calling and raising ranges contain hands that can connect with a wide variety of turns and rivers.
♠ Small bets force wide defense
You must defend more hands vs small sizing to avoid giving opponents automatic profit.
♠ Deep stacks amplify leverage
The weaker your range and the deeper the stacks, the more important it is to plan for turn and river textures.
♠ You cannot control pot size out of position
Checking does not guarantee a cheap showdown; only the in-position player has that power.
♠ Adapt ranges to future requirements
Flop ranges must support credible value and bluffs on later streets across many runouts.