LearnModule R1 · Betting the river
R1-L1
The river: value, bluffs and the middle
Why river betting ranges split into strong hands and bluffs, and how often a value bet must win when it gets called.
In this lesson
- Explain why a value bet must win more than half the time when called.
- Explain why river ranges split into strong hands and bluffs.
- Check the middle hands that neither win calls nor make better hands fold.
- Find river spots where betting beats checking.
A value bet must be called by worse
On the river no card is left to come. A bet can only win more than a check in two ways: a worse hand calls, or a better hand folds. Compare it with checking down. Say you bet 10 bb into 20 bb and are called. When you are ahead you win 10 bb more than a check would; when you are behind you lose 10 bb more.
If you are ahead 60% of the times you are called, each call earns 0.6 × 10 − 0.4 × 10 = 6 − 4 = 2 bb over checking. At 50% it earns nothing, and below 50% the bet loses. A value bet has to win more than half the time it is called — against the hands that call, not against the whole range.
- Gain over checking
- +1 bbBet
Why river ranges split
Put that together across a range and it splits in three. Strong hands bet: worse hands call them. Hands with no showdown value bet some of the time: checking never wins with them, so they are the bluffs. The middle — second pairs, weak pairs, ace-high — checks: a bet would be called only by better and fold out only worse.
Rail's river solves show exactly that shape. In position after a check, the strongest classes bet most of the time, middle and weak pairs check most often of all, ace-high checks far more than hands with no pair, and missed draws and no-pair hands bet a large share.
How many bluffs
A polarised range needs bluffs, or nobody calls its value. How many? Enough that a hand which beats only the bluffs breaks even calling. For a bet of the pot, 20 into 20, the caller risks 20 to win 40, so bluffs must be 20 / (20 + 40), about a third of the bets. For half the pot, 10 into 20, it is 10 / (20 + 20) = 25%.
Bigger bets carry more bluffs; smaller ones fewer. That is the bridge to sizing, lesson R1-L4.
- Indifferent at
- 33.3%
- EV of calling
- -0.2 bbFold
Rules of thumb
- Bet for value only when you win more than half the time you are called.
- Bet the strong, check the middle, bluff with hands that cannot win by checking.
- Ace-high and weak pairs check far more often than hands with no pair at all.
- Bigger bets need more bluffs: a pot-sized bet about one in three.
When they break
- Against a player who calls with any pair, the middle becomes thin value and bluffs shrink.
- Against one who folds too much, bluff more of the hands that cannot win by checking.
Example hands
Examples come from two places only: your own analysed hands in this lesson's spots, and a hand Rail deals and grades itself. Never a hand from outside Rail.
Sign in, with analysed hands, to see examples from your own play here.
Rail scripts this hand from the lesson's own practice, always the same one, and grades it with the analysis. Decide first, then read Rail's verdict.
Practice
The lesson is mastered when every exercise below that Rail can grade is passed. Missed items come back later as review cards.
Exercise 1
Pass: 3 of 3 rightThree rivers in position after a check: put each hand class into check, small, big or overbet, graded class by class.
Exercise 2
Pass: 1 of 2 rightTwo rivers in position after a check: paint the hands of your range that Rail's solve bets, graded hand by hand.
Exercise 3
Pass: 3 of 5 rightFive river decisions of any kind, graded by Rail's river solve.
Exercise 4
OptionalYour own first river decisions, the costliest first.
Sign in to practise on your own hands.