Chapter 5: River — With all the information in, make the biggest decision

The River Has Only Three Options

There are no draws and no equity. All you have is the hand you hold now

Value

You beat your opponent’s calling range. Think only about whether you can get calls from hands you beat.

Bluff

Zero chance of winning. Choose only hands that have no way to win other than making your opponent fold.

Check

In-between hands that are neither value nor a bluff. Betting here is the action that loses the most EV.

What to decide first on the river

Is your hand “winning” or “losing”? There is no in-between
If it is losing, bluff or fold. Calling is an option only when your opponent bets

The Standard for Thin Value

Get only this decision about betting thin wrong, and you lose a lot

Conditions for betting

You beat at least half of your opponent’s calling range
Your opponent has a reason to call with those hands
You can fold when raised

Conditions for not betting

Your opponent’s calling range is only hands stronger than yours
Your opponent is the type who bluffs (checking is better)

If you cannot name three or more specific hands in your opponent’s calling range, you are not yet in a position to decide.

The order of the decision

① Name the specific hands your opponent calls with
② Work out the share of them you beat
③ Bet if it is over half; check if it is under

A common mistake

“Bet because it is one pair” = not looking at the calling range

How to Choose River Bluffs

Which hands you bluff with decides most of the success

Conditions to meet

Zero showdown value (no chance of winning)
Blocks your opponent’s strong hands
Does not block the hands your opponent folds

Hands that suit it

Missed flush draws (ones that include an A)
Missed straight draws
A-x that blocks your opponent’s nuts

Hands that do not suit it

Weak one pair (it can win if you check)
Hands that block your opponent’s bluffs
Even missed draws, if they remove the hands your opponent folds

The ratio to value

With a 50% bet, bluffs are 25.0% of the whole
With a 100% bet, 33.3%
With a 150% bet, 37.5%

The ratio is settled by calculation. For a bet s, it is s ÷ (1 + 2s). The bigger you bet, the more bluffs you can add, because you are asking your opponent for more folds.

The Bluff Catcher Framework

Against your opponent’s bet, break it down in six steps

① From the pot odds, calculate the equity you need
② Count your opponent’s value combos (with specific hands)
③ Count your opponent’s bluff candidate combos
④ Does bluffs ÷ (value + bluffs) exceed the equity you need?
⑤ Correct those counts with the blockers in your hand
⑥ Make the final adjustment with population tendencies and this opponent’s own tendencies

Once you reach ④, the decision becomes a number. Calling on feel happens because you skip ② and ③.

An Example: Counting Combos on the River

A♠7♦2♣ → K♥ → 3♠, and your opponent makes a pot-sized bet

The situation

You: called from the BB. A♥J♦ (top pair)
Opponent: opened from the BTN and bet all three streets
A pot-sized (100%) bet on the river
The equity you need = 33.3%

Your opponent’s value candidates (before counting your own hand)

AK (uses both the A and the K): the board removes one card of each, so 9 combos
AA: one A is on the board, so 3 combos
KK: one K is on the board, so 3 combos
33: one 3 is on the board, so 3 combos → 18 in total

Your opponent’s bluff candidates

Missed spade draws: a few combos
Missed broadway hands such as QJ and JT
Realistically, about 6 – 10 combos

Conclusion

Bluff rate = 8 ÷ 26 ≒ 31%. Just under 33.3% (before counting your own hand)

Correcting the Same Example with Blockers

Just one card you hold changes the calculation itself

When you hold A♥J♦

You hold one A → your opponent’s AA and AK go down
So the value combos go down, and the bluff rate goes up
Counting your A♥, AK is 2 × 3 = 6 and AA is 1, so value is 13 in total (KK 3 and 33 3 do not change)
With bluffs still at 8, it is 8 ÷ 21 ≒ 38%. This does not count the bluffs (QJ, JT and so on) that your J♦ removes; if they go down, this share goes down

Blockers work in both directions (the A reduces value and pushes you toward a call; the J reduces bluffs and pushes you toward a fold). With 7 bluffs it is 35% (lean toward calling), and with 6 or fewer it falls below 33.3% and leans toward folding, so this is a borderline hand: whether to call or fold turns on how many bluff combos your J♦ removes.

Blockers that work against you

Holding one spade reduces your opponent’s missed flush draws (= bluffs)
The bluff rate goes down, so calling becomes harder

So the conclusion is this

A bluff catcher that holds an A and no spade = lean toward calling
A bluff catcher that holds a spade = lean toward folding
Even with the same “one pair,” the decision is reversed

The final adjustment (the population)

Many players bluff too little on the river
The bigger the size, the more they underbluff
When in doubt, leaning toward folding is safe in real play

This is what blockers really are. Not “holding it feels strong,” but a calculation of concretely how many combos it removes from your opponent’s combo table.

Population Tendencies and the River

Deviations from theory are biggest on the river


Underbluffing the river	Most players do not bluff enough
Even more marked with overbets	150% or more leans almost entirely to value
Check-raises are almost all value	River check-raise bluffs are extremely rare
Small bets include bluffs	33% or less may be a bet with the whole range
They want to get to showdown	They tend to call even with weak pairs = you can value bet thin

Adjustments you can derive from this

Against big river bets, you can fold more than theory says (but only when it is based on observation)
You can go for thin value more than theory says (because the population calls easily)

What you will learn in this chapter