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Part 4 · Lesson 22 of 25 · Pro

Poker finance: swaps and backing

Course by Hernan Alejandro Gajardo Morales

Swap half your results with an equally good player and you keep every bb of your win rate, while your swings shrink to 71% and the bankroll you need halves. Swapping a share of your results with another player, or selling action to a backer, changes your risk without changing your expectation.

The hand

You and the Regular both win 5 bb per 100 hands with a standard deviation of 100, and your results are independent. You agree to swap 50%: each of you pays the other half of his results.

Predict first

After the swap, what is your win rate?

  1. Still 5 bb per 100
  2. Half as much: 2.5 bb per 100
  3. Twice as much: two players' wins

Formula

SD after swapping share x with an equal, independent player = σ × √((1 − x)² + x²)

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 25 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.