Blockers and combinatorics: counting your way to better bluffs

Every hand starts as 1,326 possible two-card combinations. Knowing how that number shrinks is the entire skill.

Four quick rules you must have memorized:

• Any unpaired hand (e.g. AK): 16 combos — drops to 12 if one card is on the board/in your hand, 9 if two relevant cards are accounted for.
• Any specific suited hand (e.g. A♠K♠): 4 combos.
• Any pocket pair (e.g. QQ): 6 combos — drops to 3 if one of that rank is visible, 1 if two are.
• Trips/sets math: if the board shows a Q and you hold no Q, villain has 3 combos of QQ left and 3 of any AQ-type top pair per kicker (AQ = 3 combos once a Q is on board).

Why this matters: bluffing is just asking *"how many value combos can villain actually have, and how many did I just remove?"* If you can't count the second number, you're guessing. A blocker is any card in your hand that subtracts combos from villain's calling range. The best bluffs hold cards that gut his strong hands and his other bluff-catchers.

The classic beginner error: holding the ace as a 'blocker' when villain was never calling with worse aces anyway. You want to block the hands that CALL, and unblock the hands that FOLD.

Use this checklist before you fire a big river bluff:

• Do I block his nutted value? Holding one card of the nut combo (e.g. the A on an A-high flush board when bluffing the flush) removes his strongest calls.
• Do I block his bluff-catchers? On a board where second pair is the call, holding a card that pairs you with second pair is *bad* — you're blocking the very hands you want him to call with.
• Do I UNBLOCK his folds? If villain folds busted straight draws, you want a hand that does NOT contain those draw cards, so a maximum number of his range is the fold-region.

Concrete example. Board A♠ 9♦ 4♣ 2♦ 7♥, you're triple-barreling as the preflop raiser. Villain's calling range is mostly Ax. - A♥x is a *mediocre* bluff card: you block his AJ/AQ/AK that fold to a third barrel, and you DON'T block the 99/44/A9 two-pair-plus that snap. Net: you removed folds, kept calls. - K♥Q♥ (busted backdoor) is a *better* triple-barrel: it blocks KK/QQ bluff-catchers, blocks his own KQ that might bluff-catch light, and contains zero of his Ax value. You unblock everything that calls and nick a few hands that might have hero-called.

You raise to 2.2bb from the CO, BB calls. Effective stack 40bb. Pot on the river is ~12bb.

Board: K♦ Q♦ 7♠ 3♦ 8♣. The flush came and missed nobody's obvious line; you've barreled flop and turn. You want to overbet-jam ~16bb into 12bb to deny the bluff-catch.

Villain's continuing range is roughly: KQ (value), Kx flush-blocker calls, sets (77/33 = 3 combos each), and A♦x / J♦x missed flushes that pay off. Count what beats a jam:

• Sets: 77 = 3 combos, 33 = 3 combos. He often raises these earlier, so call it ~3 total here.
• KQ: with a K and Q on board, KQ = 2 suited + minus-blocked offsuit ≈ 6 combos in his flatting range.
• Made flushes: any two diamonds he flatted = a handful.

Now pick your bluff. A♦5♦ vs J♥10♥: - A♦5♦ holds the nut-flush blocker — you remove his strongest made flush combos AND you hold the case A diamond he fears, so he can't have the nuts. This is the textbook jam. - J♥10♥ is a busted straight draw with no diamond — it blocks his KJ/QJ/JT bluff-catchers a little but does nothing to his flushes. Weaker bluff; check-give-up is fine.

Rule of thumb: on a completed flush board, the single ace of the flush suit is worth more than any pair of pips. Fire it; fold the no-blocker busted draws.

Blockers tell you *which* hand to bluff. Minimum defense frequency (MDF) and bluff-to-value ratios tell you *how often.*

The pot-odds shortcut for your bluff size:

• Bet ½ pot → villain needs to fold 25% for it to print as a pure bluff (you risk 0.5 to win 1.0 + 0.5 = 1.5; 0.5/2.0 = 25%).
• Bet ¾ pot → needs ~30% folds.
• Bet full pot → needs 33% folds.
• Overbet 1.5x pot → needs ~40% folds.

Then size your bluffing region to your value. On the river, a polarized bettor wants a bluff:value ratio matched to size:

• ½ pot: bluff ~2 value : 1 bluff region (33% of bets are bluffs).
• ¾ pot: roughly 1 : 1 (40% bluffs).
• Pot: ~1 : 1 leaning to 2 bluffs : 3 value (40%).
• 2x pot overbet: up to ~45% bluffs — overbets *earn* more bluffs.

Practical loop: count your value combos on this exact runout, multiply by the ratio for your size, and that's your bluff budget. Fill the budget with the best-blocker hands first and discard the worst-blocker bluffs into check/give-up. If you have 6 value combos and you're betting pot, you get ~4 bluff combos — so pick the 4 hands that block the most calls, not the 9 busted draws you happen to hold.

Blockers aren't just a river toy. They quietly swing your biggest pots earlier.

3-bet bluff selection (preflop). When you 3-bet light, the best bluffs hold one blocker to the nut hands you fear:

• A5s–A2s are premium 3-bet bluffs: the ace blocks AA, AK, and AQ, so villain has fewer premium 4-bet/call combos. The 5–2 gives you a backup wheel draw.
• KQs / KJs block KK and QQ and AK/AQ — strong 3-bet bluffs vs a tight opener.
• Avoid bluff-3-betting hands like 76s that block *nothing* of his range; they're flat-or-fold, not 3-bet bluffs.

Turn barrels. Before you fire the second bullet, ask which turn cards add blockers to his river-calling range:

• Barreling a flush-completing or straight-completing turn while holding the blocker to that nut draw lets you rep it AND removes his made version. Example: board J♠ 8♠ 4♥, turn 2♠ — barreling with the A♠ in hand is gold: you block the nut flush, so he can't have it, and you keep the threat alive.
• Conversely, a turn that gives villain a ton of new bluff-catchers with no blocker on your side is a check-back spot, even with a 'standard' barreling hand.

ICM overlay (final-table awareness). Near a pay jump, villains fold more, so fold equity rises — your blocker bluffs get cheaper and more profitable. But size down: jamming the nut-flush blocker for 16bb at a 40bb stack is fine in a cash-equivalent spot; near a money bubble, a smaller ¾-pot bluff with the same blocker captures most of the fold equity at a fraction of the risk.