#regret #incomplete #information #game #counterfactual

bin+lib cfr

Counterfactual regret minimization solver for two-player zero-sum incomplete-information games

10 releases

0.4.2 Nov 20, 2023
0.4.1 Jul 26, 2023
0.4.0 Jan 15, 2023
0.3.1 Oct 22, 2022
0.0.1 Jul 3, 2022

#16 in Games

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MIT license


Counterfactual Regret (CFR)

crates.io docs license build

Counterfactual regret minimization solver for two-player zero-sum incomplete-information games in rust. This is a rust library and binary for computing approximate nash-equilibria of two-player zero-sum incomplete-information games.



To use the library part of this crate, add the following to your Cargo.toml.

cfr = { version = "0.1.0", default-features = false }

Then implement IntoGameNode, for a type that represents a node in your game tree (or alternatively can generate new nodes).

Finally execute:

use cfr::{Game, IntoGameNode};
struct MyData { ... }
impl IntoGameNode for MyData { ... }
let game = Game::from_root(...)?;
let strategies = game.solve_external();
let info = strategies.get_info();
let regret = info.regret();
let [player_one, player_two] = strategies.as_named();


This package can also be used as a binary with a few different input formats. install it with

$ cargo install cfr

Solving a game will produce the expected utility to player one, as well as the regrets and the strategy found in json format.

$ cfr -i game_file
  "expected_one_utility": 0.05555555727916178,
  "player_one_regret": 1.186075528125663e-06,
  "player_two_regret": 8.061797025377127e-05,
  "regret": 8.061797025377127e-05,
  "player_one_strategy": { ... },
  "player_two_regret": { ... }

The command line tool can interpret a custom json dsl, and gambit .efg files.

JSON Format

The DSL is defined by:

node     ::= terminal || chance || player
terminal ::= { "terminal": <number> }
chance   ::= {
               "chance": {
                 "infoset"?: <string>,
                 "outcomes": {
                   "<named outcome>": { "prob": <number>, "state": node },
player   ::= {
               "player": {
                 "player_one": <bool>,
                 "infoset": <string>,
                 "actions": { "<named action>": node, ... }

A minimal example highlighting all types of nodes, but of an uninteresting game is:

  "chance": {
    "outcomes": {
      "single": {
        "prob": 1.0,
        "state": {
          "player": {
            "player_one": true,
            "infoset": "none",
            "actions": {
              "only": {
                "terminal": 0.0

In this game there's a 100% chance of the "single" outcome, followed by a move by player one where they have information "none" and only have one action: "only". After selecting that action, they get payoff 0.

Gambit Format

The gambit format follows the standard gambit extensive form game format, with some mild restrictions.

  • Gambit specifies that actions are optional, but this requires every player and chance node specifies thier actions.
  • Actions must be unique, and there are some very mild restrictions on non-conflicting information set names (See duplicate infosets).
  • The gambit format allows for arbitrary player, non-constant-sum extensive form games, but this only allows two-player constant-sum perfect recall games.
  • For efficiency this uses double precision floats, because equilibria are approximate, thus in extreme circumstances payoffs might not be representable.


If implementing IntoGameNode is confusing for your game, here are more complicated examples of games that don't quite fit in the documentation:

  • Kuhn Poker - this can also be run using cargo run --example kuhn_poker --.
  • Liar's Dice - this is implemented as a benchmark to allow using nightly apis.


This section has more details on errors the command line might return.

Json Error

This error occurs when the json doesn't match the expected format for reading. See JSON Format for details on the specification, and make sure that the json you're providing matches that specification.

Gambit Error

This error occurs when the gambit file can't be parsed. There should be more info about exactly where the error occured. See gambit format for more details on the format.

Auto Error

The game file couldn't be parsed by any known game format. In order to get more detailed errors regarding the parsing failure, try rerunning again with --input-format <format> to get more precise errors

Duplicate Infosets

Gambit .efg files don't require naming infosets, but cfr requires string names for every infoset. It will default to useing the string version of the infoset number, but this will fail if that infoset name is already taken. For example:

p 1 1 "2" { ... } 0
p 1 2 { ... } 0

will throw this error as long as a name for infoset 2 isn't defined elsewhere.

Constant Sum

Counterfactual regret minimization only works on constant sum games. Since gambit files define payoffs independently, this verifies that the range of the sum of every profile is less than 0.1% of the range of the of the payoffs for a single player. If you encounter this error, cfr will not for this game.

Game Error

This error occurs if there were problems with the game specification that made creating a compact game impossible. See the documentation of GameError for more details.

Solve Error

The error occured if there were problems solving it. This should only happen if you requested too many threads, or the threads couldn't be spawned. See the documentation of SolveError for more details.

To Do

  • With the implementation of discounted CFR, the incremental regret updates hold even less frequrntly. We should instead check the true regret after a certain number of iterations. This takes some restructuing, as well as some benchmarking to make sure that time isn't wasted on regret calculation.
  • We currently set the number of threads arbitrarily high, but we have the full game tree before we decide how many threads to spawn, so we could be smarter about both setting a maximum, and setting the load factor based on the tree size.
  • This currently requires that infosets and actions be hashable and, depending on the usecase, cloneable. Most of the functions could be rewritten to take combinations of Hash, Ord, or Clone and use the most performant option given the trait bounds. This doesn't seem particularly useful and would be a lot of work, so it's omitted for now.


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