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Part 3 · Lesson 16 of 25 · Pro

The [0,1] game: continuous hands

Course by Hernan Alejandro Gajardo Morales

Number every hand from 0, the best, to 1, the worst. With a pot of one bet, the best strategy has three bands: value-bet the best 22%, bluff the worst 11% and check everything in between. The [0,1] games replace cards with a random number and solve how a whole range should play.

The hand

Each player gets a number between 0 and 1, every number equally likely, and the lower number wins. The pot is 1 bet. You may bet 1; the Regular may call or fold.

Predict first

Which of your hands should bluff?

  1. The worst ones
  2. The ones just below your value bets
  3. None: bluffs do not pay at equilibrium

Formula

α = 1 ÷ (P + 1). Caller calls with the best c = 2(1 − α) ÷ ((1 + α)(2 − α)); bettor value-bets the best c ÷ 2 and bluffs the worst α × c ÷ 2

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 chapters 16–18 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.