Narrowing a range street by street

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• Remove hands from a range after each action: a call, a check, a bet.
• Ask on every street which hands would have raised, folded or bet instead.
• Reach the river with a short list of value hands and bluffs.
• Use the narrowed range to decide your river calls.

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

Start wide, cut on every street

A range is never fixed. It starts with the hands a player brings from that seat and loses some with every action. By the river, a player who opened, bet the flop and bet the turn holds a much shorter list than the one they started with.

Narrowing means following that process on purpose. It is most of what players mean by reading a hand, and it is what makes river decisions possible.

Three questions for every action

• What would have raised? Those hands leave when a player only calls or checks.
• What would have folded? Those leave when a player calls or bets.
• What would have taken the other action? A bet removes many of the hands that check; a check removes many of the hands that bet.

Answer them street by street and the range shrinks to something you can reason about. You do not need exact weights: sorting hands into "almost always here", "sometimes" and "almost never" is enough.

A worked walk

You defend the big blind against a button open. The board runs K♦7♣2♥, then 4♠, then 9♥. You check and call a small bet on the flop, both players check the turn, and on the river the button bets 5 bb into 10 bb.

• Preflop: you only called, so the button kept its whole opening range.
• Flop: a small bet on this board comes from a large part of that range, so little is removed yet.
• Turn: the button checked back. Most of its strong kings and sets would have bet again, so their weight drops; hands that want a cheap showdown, and hands that gave up, stay.
• River: the bet comes from what is left. A few strong hands that trapped or improved on the 9, and hands that gave up on the turn and now try to win the pot.

Say that leaves 9 combos of value and 6 of bluffs, 15 in all. To call you pay 5 bb to win a pot of 10 + 5 + 5 = 20 bb, so you need 5 / 20 = 25%.

Rail narrows ranges too

Rail's analysis walks both ranges through every hand you upload in the same way, street by street, with a model of which hands bet, check, call and raise. The river trainer starts from those narrowed ranges.

That narrowing is a heuristic model, not a solve: the ranges that reach the river are Rail's estimate of how players continue on earlier streets, and the analysis labels them that way. Treat a close grade as close.

A range-walk exercise is coming: you will guess a villain's range at each street of one of your own hands and compare it with the range Rail arrives at.

When opponents are not rational

Narrowing can feel hopeless against players who do odd things, and too slow at a live table. Three habits help:

• Narrow by player, not by chart: a passive player's river bet or raise is mostly value, whatever a balanced range would hold.
• Notice capped lines: a player who checked back a street rarely holds the very best hands, which makes your big bets and your bluff-catches easier.
• Do the work away from the table: replay your river decisions in Rail and narrow at leisure, so the patterns come quickly in game.

Rules of thumb

• For every action ask what would have raised, what would have folded, and what would have done the opposite.
• Sort hands into "almost always", "sometimes" and "almost never" instead of chasing exact weights.
• A check after a bet moves weight away from the strongest hands; it does not remove them.
• Count value and bluffs at the end, then compare the bluff share with the price.

When they break

• Against players who never bluff the river, the count is mostly value whatever the line looked like: fold more than the price suggests.
• Players who slowplay a lot keep strong hands in their checks, so a check narrows their range less than usual.