Blocking Bets and The Mathematics Of Poker
Don't miss one article! Subscribe to the Full Feed RSS or get NPA in your inbox.
This week I’ve been reading The Mathematics of Poker by Bill Chen and Jerrod Ankenman. It’s quite a piece of work. The bulk of the book focuses on finding game theoretically optimal (GTO) solutions to simplified “toy” poker games. The purpose of these exercises is clearly twofold:
- To lay the groundwork for formulating GTO solutions to actual poker games
- To gain insight into what GTO solutions to actual poker games would look like without actually solving them
As I read about one of the simplest toy games in the book, it reminded me of how strong blocking bets can be in some situations.
The game is this. There are two players and each is “dealt” a real number between 0 and 1. At showdown, the lower number wins. But before showdown, there’s a betting round. In this toy game, no one is allowed to raise, and no one is allowed to fold. (The authors suggest that the no folding rule would be similar to a situation in a limit game where the pot is enormous.) So player X can bet or check. If player X bets, then player Y must call, and there’s a showdown. If player X checks, player Y may bet or check, with player X being forced to call a bet.
The remainder of this article is insider content available to premium members only. Log in to your account or become a premium member and get instant access.
Tags: bill-chen, blocking bets, game-theory, GTO, jerrod-ankenman, limit-holdem, no-limit-holdem, optimal solutions, poker, The Mathematics Of Poker, toy games

Now that’s a real engineer’s article.
And the book sounds like it was written by a real engineer too. It frequently happens that you want to create a computer simulation of a complicated system in order to try to understand it better. But building everything into the simulation would make it too large and unwieldy. So you pick out the most important aspects of the system and build a simulation of those. The simulator ends up being a lot simpler than the system, but if done correctly it can give you valuable insights into what the system does.
We do things like this all the time. It is very interesting to see someone applying this to poker.
I might have to buy this book.