testing variance on random sampling method

main.nim

@@ -5,6 +5,10 @@ import combinators, game, fixedseq
 type
   ScoreSet* = array[Color, int]
 
+  ScoreSpread = object
+    lo: array[Color, float]
+    hi: array[Color, float]
+
   LegResults* = tuple[scores: ScoreSet, endStates: HashSet[Board]]
 
 
@@ -69,9 +73,24 @@ proc randomGames(b: Board, count: SomeInteger): ScoreSet =
   for i in 1 .. count:
     let winner = b.randomGame(r)
     inc result[winner]
-    if i mod 100_000 == 0 or i == count - 1:
-      stdout.write("simulated: " & $i & "\r")
-  echo ""
+  #   if i mod 100_000 == 0 or i == count - 1:
+  #     stdout.write("simulating " & count & "random games: " & $i & "\r")
+  # echo ""
+
+
+proc randomSpread(b: Board, nTests: SomeInteger, nSamples: SomeInteger): ScoreSpread =
+  for s in result.lo.mitems:
+    s = 1
+
+  for i in 0 ..< nTests:
+    let scores = b.randomGames(nSamples)
+    let total = scores.sum
+    for color, score in scores:
+      let pct = score / total
+      if pct < result.lo[color]:
+        result.lo[color] = pct
+      if pct > result.hi[color]:
+        result.hi[color] = pct
 
 
 var b: Board
@@ -85,6 +104,7 @@ for i, roll in randomFuture(b.diceRemaining, r):
   rolls[i] = (roll[0], roll[1] + 1)
 
 b.setState(rolls, @[])
+echo "Starting state:"
 b.display(1, 5)
 
 # block outer:
@@ -99,7 +119,16 @@ b.display(1, 5)
 # echo "winner: ", b.leader.get
 # b.display(min(b.camels) - 1, 16)
 
-let scores = b.randomGames(10_000_000)
-let total = scores.sum
-for i, c in scores:
-  echo Color(i), ": ", (100 * c / total).round(2), "% (", c, " / ", total, ")"
+# let scores = b.randomGames(10_000_000)
+# let total = scores.sum
+# for i, c in scores:
+#   echo Color(i), ": ", (100 * c / total).round(2), "% (", c, " / ", total, ")"
+
+for i in 0..3:
+  let samples = 10 ^ (i + 3)
+  echo "Simulating ", samples, " games 100 times"
+  let spread = b.randomSpread(100, samples)
+  for color, lo in spread.lo:
+    stdout.write($color & ": " & $lo.round(4) & "-" & $spread.hi[color].round(4) & ", ")
+    stdout.flushFile
+  echo "\n"