Updated rust dependencies

We need GameState::rewards_for_players implemented, the library
currently doesn't need to specify for a singular player.

Cargo.lock

@@ -3,27 +3,113 @@
 version = 4
 
 [[package]]
-name = "cfg-if"
+name = "anstyle"
-version = "1.0.1"
+version = "1.0.14"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9555578bc9e57714c812a1f84e4fc5b4d21fcb063490c624de019f7464c91268"
+checksum = "940b3a0ca603d1eade50a4846a2afffd5ef57a9feac2c0e2ec2e14f9ead76000"
+
+[[package]]
+name = "bitflags"
+version = "2.13.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b4388bee8683e3d04af747c73422af53102d2bd24d9eadb6cbc100baef4b43f8"
+
+[[package]]
+name = "cfg-if"
+version = "1.0.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9330f8b2ff13f34540b44e946ef35111825727b38d33286ef986142615121801"
+
+[[package]]
+name = "clap"
+version = "4.6.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1ddb117e43bbf7dacf0a4190fef4d345b9bad68dfc649cb349e7d17d28428e51"
+dependencies = [
+ "clap_builder",
+]
+
+[[package]]
+name = "clap_builder"
+version = "4.6.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "714a53001bf66416adb0e2ef5ac857140e7dc3a0c48fb28b2f10762fc4b5069f"
+dependencies = [
+ "anstyle",
+ "clap_lex",
+ "terminal_size",
+]
+
+[[package]]
+name = "clap_lex"
+version = "1.1.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c8d4a3bb8b1e0c1050499d1815f5ab16d04f0959b233085fb31653fbfc9d98f9"
+
+[[package]]
+name = "condtype"
+version = "1.3.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "baf0a07a401f374238ab8e2f11a104d2851bf9ce711ec69804834de8af45c7af"
+
+[[package]]
+name = "divan"
+version = "0.1.21"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a405457ec78b8fe08b0e32b4a3570ab5dff6dd16eb9e76a5ee0a9d9cbd898933"
+dependencies = [
+ "cfg-if",
+ "clap",
+ "condtype",
+ "divan-macros",
+ "libc",
+ "regex-lite",
+]
+
+[[package]]
+name = "divan-macros"
+version = "0.1.21"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9556bc800956545d6420a640173e5ba7dfa82f38d3ea5a167eb555bc69ac3323"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "errno"
+version = "0.3.14"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "39cab71617ae0d63f51a36d69f866391735b51691dbda63cf6f96d042b63efeb"
+dependencies = [
+ "libc",
+ "windows-sys",
+]
 
 [[package]]
 name = "getrandom"
-version = "0.2.16"
+version = "0.3.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "335ff9f135e4384c8150d6f27c6daed433577f86b4750418338c01a1a2528592"
+checksum = "899def5c37c4fd7b2664648c28120ecec138e4d395b459e5ca34f9cce2dd77fd"
 dependencies = [
  "cfg-if",
  "libc",
- "wasi",
+ "r-efi",
+ "wasip2",
 ]
 
 [[package]]
 name = "libc"
-version = "0.2.174"
+version = "0.2.186"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1171693293099992e19cddea4e8b849964e9846f4acee11b3948bcc337be8776"
+checksum = "68ab91017fe16c622486840e4c83c9a37afeff978bd239b5293d61ece587de66"
+
+[[package]]
+name = "linux-raw-sys"
+version = "0.12.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "32a66949e030da00e8c7d4434b251670a91556f4144941d37452769c25d58a53"
 
 [[package]]
 name = "ppv-lite86"
@@ -36,38 +122,43 @@ dependencies = [
 
 [[package]]
 name = "proc-macro2"
-version = "1.0.95"
+version = "1.0.106"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "02b3e5e68a3a1a02aad3ec490a98007cbc13c37cbe84a3cd7b8e406d76e7f778"
+checksum = "8fd00f0bb2e90d81d1044c2b32617f68fcb9fa3bb7640c23e9c748e53fb30934"
 dependencies = [
  "unicode-ident",
 ]
 
 [[package]]
 name = "quote"
-version = "1.0.40"
+version = "1.0.46"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1885c039570dc00dcb4ff087a89e185fd56bae234ddc7f056a945bf36467248d"
+checksum = "dfbc457d0c7a0759a614551b11a6409e5951f6c7537be1f1b7682b9ae9230368"
 dependencies = [
  "proc-macro2",
 ]
 
 [[package]]
-name = "rand"
+name = "r-efi"
-version = "0.8.5"
+version = "5.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
+checksum = "69cdb34c158ceb288df11e18b4bd39de994f6657d83847bdffdbd7f346754b0f"
+
+[[package]]
+name = "rand"
+version = "0.9.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "44c5af06bb1b7d3216d91932aed5265164bf384dc89cd6ba05cf59a35f5f76ea"
 dependencies = [
- "libc",
  "rand_chacha",
  "rand_core",
 ]
 
 [[package]]
 name = "rand_chacha"
-version = "0.3.1"
+version = "0.9.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
+checksum = "d3022b5f1df60f26e1ffddd6c66e8aa15de382ae63b3a0c1bfc0e4d3e3f325cb"
 dependencies = [
  "ppv-lite86",
  "rand_core",
@@ -75,26 +166,46 @@ dependencies = [
 
 [[package]]
 name = "rand_core"
-version = "0.6.4"
+version = "0.9.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
+checksum = "76afc826de14238e6e8c374ddcc1fa19e374fd8dd986b0d2af0d02377261d83c"
 dependencies = [
  "getrandom",
 ]
 
+[[package]]
+name = "regex-lite"
+version = "0.1.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "cab834c73d247e67f4fae452806d17d3c7501756d98c8808d7c9c7aa7d18f973"
+
 [[package]]
 name = "rustic_mcts"
 version = "0.1.0"
 dependencies = [
+ "divan",
  "rand",
  "thiserror",
 ]
 
 [[package]]
-name = "syn"
+name = "rustix"
-version = "2.0.103"
+version = "1.1.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e4307e30089d6fd6aff212f2da3a1f9e32f3223b1f010fb09b7c95f90f3ca1e8"
+checksum = "b6fe4565b9518b83ef4f91bb47ce29620ca828bd32cb7e408f0062e9930ba190"
+dependencies = [
+ "bitflags",
+ "errno",
+ "libc",
+ "linux-raw-sys",
+ "windows-sys",
+]
+
+[[package]]
+name = "syn"
+version = "2.0.118"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1b9ae57f904213ebb649ce6895b8a66c66f0203b9319718f69a5612a065b1422"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -102,19 +213,29 @@ dependencies = [
 ]
 
 [[package]]
-name = "thiserror"
+name = "terminal_size"
-version = "2.0.12"
+version = "0.4.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "567b8a2dae586314f7be2a752ec7474332959c6460e02bde30d702a66d488708"
+checksum = "230a1b821ccbd75b185820a1f1ff7b14d21da1e442e22c0863ea5f08771a8874"
+dependencies = [
+ "rustix",
+ "windows-sys",
+]
+
+[[package]]
+name = "thiserror"
+version = "2.0.18"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "4288b5bcbc7920c07a1149a35cf9590a2aa808e0bc1eafaade0b80947865fbc4"
 dependencies = [
  "thiserror-impl",
 ]
 
 [[package]]
 name = "thiserror-impl"
-version = "2.0.12"
+version = "2.0.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7f7cf42b4507d8ea322120659672cf1b9dbb93f8f2d4ecfd6e51350ff5b17a1d"
+checksum = "ebc4ee7f67670e9b64d05fa4253e753e016c6c95ff35b89b7941d6b856dec1d5"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -123,30 +244,54 @@ dependencies = [
 
 [[package]]
 name = "unicode-ident"
-version = "1.0.18"
+version = "1.0.24"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5a5f39404a5da50712a4c1eecf25e90dd62b613502b7e925fd4e4d19b5c96512"
+checksum = "e6e4313cd5fcd3dad5cafa179702e2b244f760991f45397d14d4ebf38247da75"
 
 [[package]]
-name = "wasi"
+name = "wasip2"
-version = "0.11.1+wasi-snapshot-preview1"
+version = "1.0.4+wasi-0.2.12"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ccf3ec651a847eb01de73ccad15eb7d99f80485de043efb2f370cd654f4ea44b"
+checksum = "b67efb37e106e55ce722a510d6b5f9c17f083e5fc79afc2badeb12cc313d9487"
+dependencies = [
+ "wit-bindgen",
+]
+
+[[package]]
+name = "windows-link"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f0805222e57f7521d6a62e36fa9163bc891acd422f971defe97d64e70d0a4fe5"
+
+[[package]]
+name = "windows-sys"
+version = "0.61.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ae137229bcbd6cdf0f7b80a31df61766145077ddf49416a728b02cb3921ff3fc"
+dependencies = [
+ "windows-link",
+]
+
+[[package]]
+name = "wit-bindgen"
+version = "0.57.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1ebf944e87a7c253233ad6766e082e3cd714b5d03812acc24c318f549614536e"
 
 [[package]]
 name = "zerocopy"
-version = "0.8.26"
+version = "0.8.53"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1039dd0d3c310cf05de012d8a39ff557cb0d23087fd44cad61df08fc31907a2f"
+checksum = "75726053136156d419e285b9b7eddaaea9e3fea6ce32eed44a89901f0bd98de1"
 dependencies = [
  "zerocopy-derive",
 ]
 
 [[package]]
 name = "zerocopy-derive"
-version = "0.8.26"
+version = "0.8.53"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9ecf5b4cc5364572d7f4c329661bcc82724222973f2cab6f050a4e5c22f75181"
+checksum = "4714fd92cf900833d49538023a9b3915155210801d1c1169eba513b2addefd71"
 dependencies = [
  "proc-macro2",
  "quote",

Cargo.toml

@@ -12,5 +12,12 @@ categories = ["algorithms", "data-structures"]
 
 
 [dependencies]
-rand = "~0.8"
+rand = "~0.9"
 thiserror = "~2.0"
+
+[dev-dependencies]
+divan = "~0.1"
+
+[[bench]]
+name = "e2e"
+harness = false

benches/e2e.rs

@@ -0,0 +1,187 @@
+use std::collections::HashMap;
+
+use rustic_mcts::policy::backprop::BackpropagationPolicy;
+use rustic_mcts::policy::decision::DecisionPolicy;
+use rustic_mcts::policy::selection::SelectionPolicy;
+use rustic_mcts::policy::simulation::SimulationPolicy;
+use rustic_mcts::{Action, GameState, MCTSConfig, RewardVal, MCTS};
+
+fn main() {
+    // Run registered benchmarks.
+    divan::main();
+}
+
+#[divan::bench]
+fn tic_tac_toe() {
+    // Set up a new game
+    let mut game = TicTacToe::new();
+
+    // Create MCTS configuration
+    let config = MCTSConfig {
+        max_iterations: 10_000,
+        max_time: None,
+        tree_size_allocation: 10_000,
+        selection_policy: SelectionPolicy::UCB1Tuned(1.414),
+        simulation_policy: SimulationPolicy::Random,
+        backprop_policy: BackpropagationPolicy::Standard,
+        decision_policy: DecisionPolicy::MostVisits,
+    };
+
+    // Main game loop
+    while !game.is_terminal() {
+        // Create a new MCTS search
+        let mut mcts = MCTS::new(game.clone(), &config);
+
+        // Find the best move
+        match mcts.search() {
+            Ok(action) => {
+                // Apply the AI's move
+                game = game.state_after_action(&action);
+            }
+            Err(_) => {
+                break;
+            }
+        }
+    }
+}
+
+/// Players in Tic-Tac-Toe
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+enum Player {
+    X,
+    O,
+}
+
+impl rustic_mcts::Player for Player {}
+
+/// Tic-Tac-Toe move
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+struct Move {
+    /// Board position index (0-8)
+    index: usize,
+}
+
+impl Action for Move {}
+
+/// Tic-Tac-Toe game state
+#[derive(Debug, Clone)]
+struct TicTacToe {
+    /// Board representation (None = empty, Some(Player) = occupied)
+    board: [Option<Player>; 9],
+
+    /// Current player's turn
+    current_player: Player,
+
+    /// Number of moves played so far
+    moves_played: usize,
+}
+
+impl TicTacToe {
+    /// Creates a new empty Tic-Tac-Toe board
+    fn new() -> Self {
+        TicTacToe {
+            board: [None; 9],
+            current_player: Player::X,
+            moves_played: 0,
+        }
+    }
+
+    /// Returns the winner of the game, if any
+    fn get_winner(&self) -> Option<Player> {
+        // Check rows
+        for row in 0..3 {
+            let i = row * 3;
+            if self.board[i].is_some()
+                && self.board[i] == self.board[i + 1]
+                && self.board[i] == self.board[i + 2]
+            {
+                return self.board[i];
+            }
+        }
+
+        // Check columns
+        for col in 0..3 {
+            if self.board[col].is_some()
+                && self.board[col] == self.board[col + 3]
+                && self.board[col] == self.board[col + 6]
+            {
+                return self.board[col];
+            }
+        }
+
+        // Check diagonals
+        if self.board[0].is_some()
+            && self.board[0] == self.board[4]
+            && self.board[0] == self.board[8]
+        {
+            return self.board[0];
+        }
+        if self.board[2].is_some()
+            && self.board[2] == self.board[4]
+            && self.board[2] == self.board[6]
+        {
+            return self.board[2];
+        }
+
+        None
+    }
+
+    fn reward_for_player(&self, player: &Player) -> RewardVal {
+        if let Some(winner) = self.get_winner() {
+            if winner == *player {
+                return 1.0; // Win
+            } else {
+                return 0.0; // Loss
+            }
+        }
+
+        // Draw
+        0.5
+    }
+}
+
+impl GameState for TicTacToe {
+    type Action = Move;
+    type Player = Player;
+
+    fn get_legal_actions(&self) -> Vec<Self::Action> {
+        let mut actions = Vec::new();
+        for i in 0..9 {
+            if self.board[i].is_none() {
+                actions.push(Move { index: i });
+            }
+        }
+        actions
+    }
+
+    fn state_after_action(&self, action: &Self::Action) -> Self {
+        let mut new_state = self.clone();
+
+        // Make the move
+        new_state.board[action.index] = Some(self.current_player);
+        new_state.moves_played = self.moves_played + 1;
+
+        // Switch player
+        new_state.current_player = match self.current_player {
+            Player::X => Player::O,
+            Player::O => Player::X,
+        };
+
+        new_state
+    }
+
+    fn is_terminal(&self) -> bool {
+        self.get_winner().is_some() || self.moves_played == 9
+    }
+
+    fn rewards_for_players(&self) -> HashMap<Self::Player, RewardVal> {
+        HashMap::from_iter(vec![
+            (Player::X, self.reward_for_player(&Player::X)),
+            (Player::O, self.reward_for_player(&Player::O)),
+        ])
+    }
+
+    fn get_current_player(&self) -> &Self::Player {
+        &self.current_player
+    }
+}

examples/auto_tic_tac_toe.rs

@@ -84,11 +84,7 @@ struct Move {
     index: usize,
 }
 
-impl Action for Move {
+impl Action for Move {}
-    fn id(&self) -> usize {
-        self.index
-    }
-}
 
 /// Tic-Tac-Toe game state
 #[derive(Clone)]
@@ -152,6 +148,19 @@ impl TicTacToe {
 
         None
     }
+
+    fn reward_for_player(&self, player: &Player) -> RewardVal {
+        if let Some(winner) = self.get_winner() {
+            if winner == *player {
+                return 1.0; // Win
+            } else {
+                return 0.0; // Loss
+            }
+        }
+
+        // Draw
+        0.5
+    }
 }
 
 impl GameState for TicTacToe {
@@ -188,19 +197,6 @@ impl GameState for TicTacToe {
         self.get_winner().is_some() || self.moves_played == 9
     }
 
-    fn reward_for_player(&self, player: &Self::Player) -> RewardVal {
-        if let Some(winner) = self.get_winner() {
-            if winner == *player {
-                return 1.0; // Win
-            } else {
-                return 0.0; // Loss
-            }
-        }
-
-        // Draw
-        0.5
-    }
-
     fn rewards_for_players(&self) -> HashMap<Self::Player, RewardVal> {
         HashMap::from_iter(vec![
             (Player::X, self.reward_for_player(&Player::X)),

examples/tic_tac_toe.rs

@@ -119,11 +119,7 @@ struct Move {
     index: usize,
 }
 
-impl Action for Move {
+impl Action for Move {}
-    fn id(&self) -> usize {
-        self.index
-    }
-}
 
 /// Tic-Tac-Toe game state
 #[derive(Clone)]
@@ -195,6 +191,19 @@ impl TicTacToe {
 
         None
     }
+
+    fn reward_for_player(&self, player: &Player) -> RewardVal {
+        if let Some(winner) = self.get_winner() {
+            if winner == *player {
+                return 1.0; // Win
+            } else {
+                return 0.0; // Loss
+            }
+        }
+
+        // Draw
+        0.5
+    }
 }
 
 impl GameState for TicTacToe {
@@ -231,19 +240,6 @@ impl GameState for TicTacToe {
         self.get_winner().is_some() || self.moves_played == 9
     }
 
-    fn reward_for_player(&self, player: &Self::Player) -> RewardVal {
-        if let Some(winner) = self.get_winner() {
-            if winner == *player {
-                return 1.0; // Win
-            } else {
-                return 0.0; // Loss
-            }
-        }
-
-        // Draw
-        0.5
-    }
-
     fn rewards_for_players(&self) -> HashMap<Self::Player, RewardVal> {
         HashMap::from_iter(vec![
             (Player::X, self.reward_for_player(&Player::X)),

src/mcts.rs

@@ -6,7 +6,8 @@ use crate::policy::simulation::simulate_reward;
 use crate::state::GameState;
 use crate::tree::arena::Arena;
 use crate::tree::node::{Node, RewardVal};
-use rand::prelude::SliceRandom;
+use crate::tree::print_tree;
+use rand::prelude::IndexedRandom;
 use std::collections::HashMap;
 use std::time::Instant;
 
@@ -74,8 +75,15 @@ impl<'conf, S: GameState + std::fmt::Debug> MCTS<'conf, S> {
         if !selected_node.state.is_terminal() {
             self.expand(selected_id);
             let children: &Vec<usize> = &self.arena.get_node(selected_id).children;
-            let random_child: usize = *children.choose(&mut rand::thread_rng()).unwrap();
+            match children.choose(&mut rand::rng()) {
-            selected_id = random_child;
+                Some(&random_child) => {
+                    selected_id = random_child;
+                }
+                None => {
+                    // We ran out of nodes
+                    return Err(MCTSError::NonTerminalGame);
+                }
+            }
         }
         let rewards = self.simulate(selected_id);
         self.backprop(selected_id, &rewards);
@@ -130,6 +138,10 @@ impl<'conf, S: GameState + std::fmt::Debug> MCTS<'conf, S> {
             None => Err(MCTSError::NoBestAction),
         }
     }
+
+    pub fn print_tree(&self) {
+        print_tree(self.root_id, &self.arena)
+    }
 }
 
 /// Errors returned by the MCTS algorithm

src/policy/backprop/mod.rs

@@ -69,18 +69,14 @@ fn standard_backprop<S: GameState>(
     let mut current_id: usize = node_id;
     loop {
         let node = arena.get_node_mut(current_id);
-        let player = node.state.get_current_player().clone();
+        node.increment_visits();
-        match rewards.get(&player) {
+        for (player, reward) in rewards.iter() {
-            Some(reward) => {
+            node.record_player_reward(player.clone(), *reward);
-                node.increment_visits();
+        }
-                node.record_player_reward(player, *reward);
+        if let Some(parent_id) = node.parent {
-                if let Some(parent_id) = node.parent {
+            current_id = parent_id;
-                    current_id = parent_id;
+        } else {
-                } else {
+            break;
-                    break;
-                }
-            }
-            None => (),
         }
     }
 }
@@ -94,19 +90,14 @@ fn weighted_backprop<S: GameState>(
     let mut current_id: usize = node_id;
     loop {
         let node = arena.get_node_mut(current_id);
-        let player = node.state.get_current_player().clone();
         let weight = weight_for_depth(depth_factor, node.depth);
-        match rewards.get(&player) {
+        for (player, reward) in rewards.iter() {
-            Some(reward) => {
+            node.record_player_reward(player.clone(), (*reward) * weight);
-                node.increment_visits();
+        }
-                node.record_player_reward(player, (*reward) * weight);
+        if let Some(parent_id) = node.parent {
-                if let Some(parent_id) = node.parent {
+            current_id = parent_id;
-                    current_id = parent_id;
+        } else {
-                } else {
+            break;
-                    break;
-                }
-            }
-            None => (),
         }
     }
 }

src/policy/selection/ucb1_tuned.rs

@@ -36,15 +36,15 @@ pub fn select_best_child<S: GameState>(
                 exploration_constant,
                 parent_visits,
                 node_a.visits,
-                node_a.rewards(player),
                 node_a.reward_average(player),
+                node_a.reward_variance(player),
             );
             let ucb_b = ucb1_tuned_value(
                 exploration_constant,
                 parent_visits,
                 node_b.visits,
-                node_b.rewards(player),
                 node_b.reward_average(player),
+                node_b.reward_variance(player),
             );
             ucb_a.partial_cmp(&ucb_b).unwrap()
         })
@@ -57,41 +57,31 @@ pub fn ucb1_tuned_value(
     exploration_constant: f64,
     parent_visits: u64,
     child_visits: u64,
-    child_rewards: Option<&Vec<RewardVal>>,
     reward_avg: RewardVal,
+    reward_variance: f64,
 ) -> RewardVal {
-    match child_rewards {
+    if child_visits == 0 {
-        None => {
+        RewardVal::INFINITY // Always explore nodes that have never been visited
-            RewardVal::INFINITY // Always explore nodes that have never been visited
+    } else {
-        }
+        let parent_visits: RewardVal = parent_visits as RewardVal;
-        Some(child_rewards) => {
+        let child_visits: RewardVal = child_visits as RewardVal;
-            if child_visits == 0 {
-                RewardVal::INFINITY // Always explore nodes that have never been visited
-            } else {
-                let parent_visits: RewardVal = parent_visits as RewardVal;
-                let child_visits: RewardVal = child_visits as RewardVal;
 
-                // N: number of visits to the parent node
+        // N: number of visits to the parent node
-                // n: number of visits to the child node
+        // n: number of visits to the child node
-                // x_i: reward of the ith visit to the child node
+        // x_i: reward of the ith visit to the child node
-                // X: average reward of the child
+        // X: average reward of the child
-                // C: exploration constant
+        // C: exploration constant
-                //
+        //
-                // UCB1-Tuned = X + C * sqrt(Ln(parent_visits) / child_visits * min(1/4, V_n)
+        // UCB1-Tuned = X + C * sqrt(Ln(parent_visits) / child_visits * min(1/4, V_n)
-                //   V(n) = sum(x_i^2)/n - X^2 + sqrt(2*ln(N)/n)
+        //   V(n) = sum(x_i^2)/n - X^2 + sqrt(2*ln(N)/n)
-                let exploitation = reward_avg;
+        let exploitation = reward_avg;
-                let mut variance = (child_rewards.iter().map(|&x| x * x).sum::<RewardVal>()
+        let mut variance = reward_variance + (2.0 * parent_visits.ln() / child_visits).sqrt();
-                    / child_visits)
+        if variance > 0.25 {
-                    - (reward_avg * reward_avg)
+            variance = 0.25;
-                    + (2.0 * parent_visits.ln() / child_visits).sqrt();
-                if variance > 0.25 {
-                    variance = 0.25;
-                }
-                let exploration =
-                    exploration_constant * (parent_visits.ln() / child_visits * variance).sqrt();
-
-                exploitation + exploration
-            }
         }
+        let exploration =
+            exploration_constant * (parent_visits.ln() / child_visits * variance).sqrt();
+
+        exploitation + exploration
     }
 }

src/policy/simulation/random.rs

@@ -4,14 +4,14 @@
 
 use crate::state::GameState;
 use crate::tree::node::{Node, RewardVal};
-use rand::prelude::SliceRandom;
+use rand::prelude::IndexedRandom;
 use std::collections::HashMap;
 
 pub fn simulate<S: GameState>(node: &Node<S>) -> HashMap<S::Player, RewardVal> {
     let mut state: S = node.state.clone();
     while !state.is_terminal() {
         let legal_actions = state.get_legal_actions();
-        let action = legal_actions.choose(&mut rand::thread_rng()).unwrap();
+        let action = legal_actions.choose(&mut rand::rng()).unwrap();
         state = state.state_after_action(&action);
     }
     state.rewards_for_players()

src/state.rs

@@ -7,7 +7,7 @@ use std::hash::Hash;
 ///
 /// When leveraging MCTS for your game, you must implement this trait to provide
 /// the specifics for your game.
-pub trait GameState: Clone {
+pub trait GameState: Clone + Debug {
     /// The type of actions that can be taken in the game
     type Action: Action;
 
@@ -40,11 +40,11 @@ pub trait GameState: Clone {
     /// instead should modify a copy of the state and return that.
     fn state_after_action(&self, action: &Self::Action) -> Self;
 
-    /// Returns the reward from the perspective of the given player for the game state
+    /// Returns the rewards for all players from their perspective for the game state
     ///
-    /// This evaluates the current state from the perspective of the given player, and
+    /// This evaluates the current state from the perspective of each player, and
-    /// returns the reward indicating how good of a result the given state is for the
+    /// returns a HashMap mapping each player to the result of this evaluation, which
-    /// player.
+    /// we call the reward.
     ///
     /// This is used in the MCTS backpropagation and simulation phases to evaluate
     /// the value of a given node in the search tree.
@@ -55,9 +55,6 @@ pub trait GameState: Clone {
     /// - 0.0 => a loss for the player
     ///
     /// Other values can be used for relative wins or losses
-    fn reward_for_player(&self, player: &Self::Player) -> RewardVal;
-
-    /// Returns the rewards for all players at the current state
     fn rewards_for_players(&self) -> HashMap<Self::Player, RewardVal>;
 
     /// Returns the player whose turn it is for the game state
@@ -72,10 +69,7 @@ pub trait GameState: Clone {
 ///
 /// An action is dependent upon the specific game being defined, and includes
 /// things like moves, attacks, and other decisions.
-pub trait Action: Clone + Debug {
+pub trait Action: Clone + Debug {}
-    /// Returns a uniqie identifier for this action
-    fn id(&self) -> usize;
-}
 
 /// Trait used for players participating in a game
 pub trait Player: Clone + Debug + PartialEq + Eq + Hash {}

src/tree/mod.rs

@@ -1,2 +1,27 @@
 pub mod arena;
 pub mod node;
+
+use crate::state::GameState;
+use crate::tree::arena::Arena;
+use crate::tree::node::Node;
+
+pub fn print_tree<S: GameState>(node_id: usize, arena: &Arena<S>) {
+    let mut to_print: Vec<usize> = Vec::new();
+    to_print.push(node_id);
+    while let Some(node_id) = to_print.pop() {
+        let node: &Node<S> = arena.get_node(node_id);
+        if node.depth > 0 {
+            for _ in 0..node.depth - 1 {
+                print!("|  ")
+            }
+            print!("|- ");
+        }
+        println!(
+            "{:?} a:{:?} v:{}  {:?}",
+            node_id, node.action, node.visits, node.player_view
+        );
+        for child_id in node.children.iter().rev() {
+            to_print.push(*child_id);
+        }
+    }
+}

src/tree/node.rs

@@ -1,5 +1,4 @@
 use std::collections::HashMap;
-use std::fmt::Debug;
 
 use crate::state::GameState;
 
@@ -15,7 +14,7 @@ pub type RewardVal = f64;
 ///
 /// This class is not thread safe, as the library does not provide for parallel
 /// search.
-#[derive(Debug)]
+#[derive(std::fmt::Debug)]
 pub struct Node<S: GameState> {
     /// The game state at the given node, after `action`
     pub state: S,
@@ -30,7 +29,7 @@ pub struct Node<S: GameState> {
     pub visits: u64,
 
     /// The player's evaluation of the node
-    pub player_view: HashMap<S::Player, PlayerNodeView>,
+    pub player_view: HashMap<S::Player, PlayerRewardView>,
 
     /// The depth of the node in the tree, this is 0 for the root node
     pub depth: usize,
@@ -70,10 +69,10 @@ impl<S: GameState> Node<S> {
         }
     }
 
-    pub fn rewards(&self, player: &S::Player) -> Option<&Vec<RewardVal>> {
+    pub fn reward_variance(&self, player: &S::Player) -> f64 {
         match self.player_view.get(player) {
-            Some(pv) => Some(&pv.rewards),
+            Some(pv) => pv.weighted_variance / self.visits as f64,
-            None => None,
+            None => 0.0,
         }
     }
 
@@ -82,37 +81,44 @@ impl<S: GameState> Node<S> {
     }
 
     pub fn record_player_reward(&mut self, player: S::Player, reward: RewardVal) {
-        let pv = self
+        let pv = self.player_view.entry(player).or_default();
-            .player_view
+        let prev_reward_average = pv.reward_average;
-            .entry(player)
-            .or_insert(PlayerNodeView::default());
-        pv.rewards.push(reward);
         pv.reward_sum += reward;
-        pv.reward_average = pv.reward_sum / pv.rewards.len() as f64;
+        pv.reward_average = pv.reward_sum / self.visits as f64;
+        pv.weighted_variance += (reward - prev_reward_average) * (reward - pv.reward_average);
     }
 }
 
 /// A player's specific perspective of a node's value
 ///
 /// Each player has their own idea of the value of a node.
-#[derive(Debug)]
+pub struct PlayerRewardView {
-pub struct PlayerNodeView {
     /// The total reward from simulations through this node
     pub reward_sum: RewardVal,
 
     /// The average reward from simulations through this node, often called the node value
     pub reward_average: RewardVal,
 
-    /// The rewards we have gotten so far for simulations through this node
+    /// The weighted variance from simulations through this node
-    pub rewards: Vec<RewardVal>,
+    ///
+    /// This is used to calculate online sample variance.
+    /// See Donald E. Knuth. Seminumerical Algorithms, volume 2 of The Art of Computer Programming, chapter 4.2.2, page 232
+    pub weighted_variance: f64,
 }
 
-impl Default for PlayerNodeView {
+impl Default for PlayerRewardView {
     fn default() -> Self {
-        PlayerNodeView {
+        PlayerRewardView {
             reward_sum: 0.0,
             reward_average: 0.0,
-            rewards: Vec::new(),
+            weighted_variance: 0.0,
         }
     }
 }
+
+impl std::fmt::Debug for PlayerRewardView {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(f, "{{sum={} avg={}}}", self.reward_sum, self.reward_average)?;
+        Ok(())
+    }
+}