Picking river bluffs

In this lesson

• Choose bluffs that hold cards from the opponent's calling hands.
• Avoid bluffs that hold cards from the opponent's folding hands.
• Bluff first with hands that cannot win by checking.
• Decide which missed draws bet and which give up.
• Count combinations and card removal: a pair has 6 combos, a suited hand 4, an offsuit hand 12, and every card you hold removes the combos that need it.

Read first: The river: value, bluffs and the middle · Advice, not a lock: every lesson opens.

Concepts used: Blockers and unblockers, Bluff-catching, Ranges

Bluff with what cannot win by checking

The first question about a bluff is what the hand loses by not checking. Ace-high and small pairs sometimes win at showdown; a hand with no pair at all never does. So the hands with the least showdown value make the first bluffs, and the hands with some keep checking.

Rail's river solves say the same. In position after a check, and even more out of position, ace-high checks far more often than hands with no pair, which make up most of the bluffs.

Counting combinations

To choose among bluffs you need to count hands, and combinations and card removal are how. A pair has 6 combinations, a suited hand 4, an offsuit hand 12. Ace-king, suited and offsuit, is 4 × 4 = 16.

Every card you can see removes the combinations that need it. Hold one ace and only 3 × 4 = 12 ace-kings are left. On a king-high board three kings are left, and any two make a set: 3 × 2 / 2 = 3 combinations; hold a king yourself and only 2 × 1 / 2 = 1 is left.

Block the calls, leave the folds

A bluff works when the other player folds. So the best bluffs hold cards from the hands that would call — removing some of them — and none from the hands that would fold. A bluff holding a card of the top pair the opponent would call with makes that call less likely; a bluff holding a card of the missed draws that would fold makes the folds less likely.

Card removal is one effect among several, and the solve weighs them all at once: showdown value, what the hand blocks, and what the line says. Two hands that look alike can play differently for that reason; the drills deal you those hands.

River solves on demand: the charts' ranges narrowed on the flop and turn by Rail's heuristic model, with bets of 33%, 75% and 150% of the pot and all-in.

Rules of thumb

• Bluff first with hands that cannot win by checking.
• Count combinations: 6 for a pair, 4 suited, 12 offsuit; every visible card removes some.
• Prefer bluffs that hold cards of the hands that call.
• Avoid bluffs that hold cards of the hands that fold.

When they break

• Against a player who never folds a pair, stop bluffing whatever you hold.
• Against one who folds everything but the nuts, any hand with no showdown value will do.

Example hands

Practice

The lesson is mastered when every exercise below that Rail can grade is passed. Missed items come back later as review cards.