From f05ab2cfa2a3a6978925a5be7039273cc1351621 Mon Sep 17 00:00:00 2001
From: Joseph Montanaro <jfmontanaro@modg.org>
Date: Wed, 24 Mar 2021 10:54:50 -0700
Subject: [PATCH] stochastic modeling for full games

---
 combinators.nim | 13 ++++++++++---
 fixedseq.nim    | 10 ++++++++--
 game.nim        | 21 ++++++++++++++++++---
 main.nim        | 30 ++++++++++++++++++++++++++----
 4 files changed, 62 insertions(+), 12 deletions(-)

diff --git a/combinators.nim b/combinators.nim
index 74b3814..3fc5a6e 100644
--- a/combinators.nim
+++ b/combinators.nim
@@ -1,4 +1,4 @@
-import sequtils
+import random, sugar
 import fixedseq, game
 
 
@@ -15,7 +15,7 @@ iterator allPermutations*(x: FixedSeq): FixedSeq =
 
 iterator allDigits*(lo, hi, size: Natural): auto =
   if size > 0: # otherwise we get an infinite loop
-    var digits: FixedSeq[5, int8, int8]
+    var digits: FixedSeq[5, int, int8]
     digits.initFixedSeq
     for i in 0 ..< size:
       digits.add(lo)
@@ -41,4 +41,11 @@ iterator possibleFutures*(dice: FixedSeq): auto =
       var f = initFixedSeq(5, Die, int8)
       for i in 0 .. dice.high:
         f.add((perm[i], digits[i]))
-      yield f
\ No newline at end of file
+      yield f
+
+
+proc randomFuture*(dice: FixedSeq, r: var Rand): FixedSeq[5, Die, int8] =
+  result.initFixedSeq
+  let order = dice.dup(shuffle(r))
+  for i, color in order:
+    result.add((color, r.rand(1..3)))
diff --git a/fixedseq.nim b/fixedseq.nim
index 468f0c5..d99bf01 100644
--- a/fixedseq.nim
+++ b/fixedseq.nim
@@ -1,4 +1,4 @@
-import algorithm
+import algorithm, random
 
 
 type
@@ -16,6 +16,11 @@ proc initFixedSeq*(s: var FixedSeq) =
   s.last = -1
 
 
+proc `[]`*(s: FixedSeq, i: Natural): FixedSeq.Contents =
+  if i > s.last:
+    raise newException(IndexDefect, "index " & $i & " is out of bounds.")
+  s.data[i]
+
 proc `[]`*(s: var FixedSeq, i: Natural): var FixedSeq.Contents =
   if i > s.last:
     raise newException(IndexDefect, "index " & $i & " is out of bounds.")
@@ -98,7 +103,8 @@ proc nextPermutation*(s: var FixedSeq): bool = s.data.nextPermutation
 
 proc prevPermutation*(s: var FixedSeq): bool = s.data.prevPermutation
 
-proc maxSize*(s: FixedSeq): FixedSeq.Pointer = s.data.len
+proc shuffle*(s: var FixedSeq, r: var Rand) =
+  r.shuffle(s.data)
 
 
 proc moveSubstack*(src, dst: var FixedSeq; start: Natural) =
diff --git a/game.nim b/game.nim
index 3efa469..693d796 100644
--- a/game.nim
+++ b/game.nim
@@ -9,6 +9,18 @@ type
   ColorStack* = FixedSeq[5, Color, int8]
 
 
+proc initColorStack: ColorStack =
+  result.initFixedSeq
+
+
+proc getAllColors: ColorStack = 
+  var i = 0
+  for c in Color.low .. Color.high:
+    result[i] = c
+
+const allColors = getAllColors() # compile-time evaluation
+
+
 proc `$`*(s: ColorStack): string =
   result.add("St@[")
   for i, color in s:
@@ -38,9 +50,6 @@ type
     initialized: bool
 
 
-const allDice = @[cRed, cGreen, cBlue, cYellow, cPurple]
-
-
 proc `[]`*[T](b: var Board, idx: T): var Square =
   b.squares[idx]
 
@@ -90,6 +99,12 @@ proc setState*(b: var Board;
   b.leader = some(leadCamel)
 
 
+proc diceRemaining*(b: Board): ColorStack =
+  result.initFixedSeq
+  for color, isRolled in b.diceRolled:
+    if not isRolled: result.add(color)
+
+
 proc resetDice*(b: var Board) =
   var d: array[Color, bool]
   b.diceRolled = d
diff --git a/main.nim b/main.nim
index c727d16..4d45357 100644
--- a/main.nim
+++ b/main.nim
@@ -1,4 +1,4 @@
-import math, options, sequtils, sets, sugar
+import math, options, sequtils, random, sets
 import combinators, game, fixedseq
 
 
@@ -41,7 +41,8 @@ proc projectOutcomes(b: Board, maxDepth = 1): ScoreSet =
 
     for o in outcomeStack[^1]:
       var o = o # make it mutable
-      o.resetDice # o was describina an end-of-leg state, so dice were exhausted
+      if outcomeStack.len > 1:
+        o.resetDice # o was describina an end-of-leg state, so dice were exhausted
 
       let projection = o.projectLeg
       result.update(projection[0])
@@ -52,11 +53,32 @@ proc projectOutcomes(b: Board, maxDepth = 1): ScoreSet =
   echo "\nDistinct end states: ", outcomeStack.mapIt(it.len).sum
 
 
+proc randomGame(b: Board, r: var Rand): Color =
+  var projection = b
+  while true:
+    for roll in randomFuture(projection.diceRemaining, r):
+      projection.advance(roll)
+      if projection.gameOver:
+        return projection.leader.get
+    projection.resetDice
+
+
+proc randomGames(b: Board, count: SomeInteger): ScoreSet =
+  randomize()
+  var r = initRand(rand(int64))
+  for i in 0 ..< count:
+    let winner = b.randomGame(r)
+    inc result[winner]
+    if i mod 100_000 == 0:
+      stdout.write("simulated: " & $i & "\r")
+  echo ""
+
+
 var b: Board
 b.init
 b.display(1, 5)
 
-b.setState({cGreen: 4, cYellow: 3, cPurple: 4, cBlue: 3, cRed: 4}, @[])
+b.setState({cGreen: 4, cYellow: 3, cPurple: 4, cBlue: 3, cRed: 5}, @[])
 b.display(1, 5)
 
 # b.advance((cRed, 1))
@@ -70,7 +92,7 @@ b.display(1, 5)
 # echo s
 # echo s[2]
 
-let r = b.projectOutcomes(2)
+let r = b.randomGames(10_000_000)
 let total = r.sum
 for i, c in r:
   echo Color(i), ": ", (100 * c / total).round(2), "% (", c, " / ", total, ")"