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Part 3 · Lesson 11 of 25 · Pro

Half-street games and the bluffing ratio

Holding 12 flushes on the river, bet the pot with exactly 6 bluffs; bet half the pot and the right number is 4. One formula sets both, and it also tells the caller how often he must call.

The hand

A half-street game: you may bet, the Tight-aggressive player may only call or fold. You know whether you hold the best hand or nothing at all: the clairvoyance game. Your range has 12 flushes and plenty of missed draws, and the pot is 10 bb.

Predict first

You bet the pot with your 12 flushes. How many missed draws should bet with them?

  1. 4
  2. 6
  3. 12

Formula

α = s ÷ (1 + s). Bluffs per value bet = α; share of the betting range that is bluffs = α ÷ (1 + α); minimum defense = 1 − α = 1 ÷ (1 + s)

This lesson is part of Pro. Above are its opening, its question and the idea it leads to; the worked numbers, the common mistake, the interactive tool and the check are in the app.

The app adds an interactive tool for this lesson, a hand replay, narration and practice questions with new numbers every time.

Open this lesson in the app

This lesson builds on ideas from chapter 11 of The Mathematics of Poker by Bill Chen and Jerrod Ankenman (ConJelCo, 2006), explained in our own words; nothing is copied from the book. Poker Math Coach is not affiliated with or endorsed by the authors or publisher.