Calling down with a bluff-catcher

In this lesson

• Count the opponent's value hands and bluffs for the line they took.
• Check how your own cards change those counts.
• Use minimum defence as a starting point, not a rule.
• Fold more against big river bets from players who rarely bluff.
• Apply the same method in single-raised, 3-bet and limped pots.

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

Concepts used: Bluff-catching, Blockers and unblockers, MDF and alpha

The price of a call

A bluff-catcher beats every bluff and loses to every value bet. Whether it calls is a question about the betting range, and the price tells you how many bluffs it must hold. Facing 15 bb into 20 bb, you call 15 to win 35: you need to win 15 / (35 + 15) = 30% of the time.

Bigger bets ask more: 30 bb into 20 bb asks for 30 / 80, 37.5%. Smaller ones less: a third of the pot, 6.6 bb into 20 bb, about 19.9%.

Count value and bluffs

Then count the line. Say the hands that bet the river this way are 10 combinations of value and 5 of bluffs: a third bluffs, more than the 30% the price asks. Calling 15 into 20 wins 35 a third of the time and loses 15 two thirds: about +1.67 bb a call.

Your own cards change the count. Holding a card of the opponent's value hands removes some of them and makes the call better; holding a card of the missed draws they bluff with removes bluffs and makes it worse. Minimum defence, here 20 / 35, about 57%, says how much of your whole range must continue; it does not say which hands.

Bigger bets, more folds

Rail's river solves fold more of the middle as the bet grows. Against a third of the pot most middle pairs call; against three quarters most of them fold; against one and a half pots more still, and the strong hands carry most of the defence.

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. The paint asks for the hands that call or raise.

Rules of thumb

• Price first: the call divided by the pot after it.
• Count the line's value and bluffs, then adjust for the cards you hold.
• Minimum defence is how much of the range continues, not which hands.
• The bigger the bet, the more of your middle folds.

When they break

• Against a player who never bluffs the river, fold every bluff-catcher.
• Against one who bluffs every missed draw, call more of the middle.

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.