fix mask selection

README.md

@@ -0,0 +1,22 @@
+# `cup` - CamelUp probability calculator
+
+This tool calculates probable outcomes for the board game CamelUp.
+It can calculate all possible outcomes for a single game leg in about 5ms, so effectively instantaneously.
+Full-game calculations take a little bit longer and are not exact (since it isn't practical to simulate all possible full game states.)
+However it can easily simulate a million random games in about 80ms in the worst case, which should provide estimates accurate to within about 0.2%.
+(Numbers from running on a Ryzen 3700X.)
+
+```
+Usage: 
+  cup [-i] SPACE:STACK [...SPACE:STACK] [DICE]
+
+SPACE refers to a numbered board space (1-16).
+STACK refers to a stack of camel colors from bottom to top, e.g. 
+      YBR (Yellow, Blue, Red, with Red on top).
+DICE refers to the set of dice that have already been rolled,
+     e.g. GPR (Green, Purple, Red)
+
+Options:
+  -i      Interactive mode (currently unimplemented)
+  -h      Show this message and exit
+```

combinators.nim

@@ -1,5 +1,5 @@
 import algorithm, random, sugar
-import fixedseq, game
+import faststack, fixedseq, game
 
 
 proc nextPermutation(x: var FixedSeq): bool =

config.nims

@@ -0,0 +1,5 @@
+# --threads: on
+# --d: release
+# --opt: speed
+# --passC: -flto
+# --passL: -flto

cup.nim

@@ -0,0 +1,17 @@
+import game, simulation, ui
+
+
+when isMainModule:
+  let config = parseArgs()
+  var b: Board
+  b.init
+  b.setState(config.state, [])
+  b.diceRolled = config.diceRolled
+  echo b.showSpaces(1, 16)
+  let legScores = b.getLegScores
+  echo "\nCurrent leg probabilities:"
+  echo legScores.showPercents()
+  
+  let gameScores = b.randomGames(1_000_000)
+  echo "\nFull game probabilities (1M simulations):"
+  echo gameScores.showPercents()

faststack.nim

@@ -0,0 +1,204 @@
+import bitops, strutils, random
+
+
+proc show(i: SomeInteger, bitlength = 16) =
+  echo BiggestInt(i).toBin(bitlength)
+
+
+type
+  Color* = enum
+    cRed, cGreen, cBlue, cYellow, cPurple
+
+  ColorStack* = object
+    data: uint16
+    len*: uint8
+
+
+const
+  masks = [
+    0'u16, # dummy value just to get the indices right
+    0b0_000_000_000_000_111,
+    0b0_000_000_000_111_111,
+    0b0_000_000_111_111_111,
+    0b0_000_111_111_111_111,
+    0b0_111_111_111_111_111,
+  ]
+  allColors* = ColorStack(len: 5, data: 0b0_000_001_010_011_100)
+
+
+template offset(s: ColorStack, idx: Natural): uint8 =
+  # Compute the bit offset for a given index. 
+  # Dependent on the stack's length.
+  (s.len - 1 - idx.uint8) * 3
+  # items are stored from left to right but right-aligned, so we
+  # need to shift right to access anything other than the last
+
+
+template offset(s: ColorStack, idx: BackwardsIndex): uint8 =
+  # for backwards index, we are still shifting right but
+  # the lower the index the less we have to shift
+  (idx.uint8 - 1) * 3
+
+
+proc add*(s: var ColorStack, c: Color) =
+  # e.g. if stack is 0b0000000000000100:
+  # and color is 0b00000011
+  # shift: 0b0000000000100000
+  # bitor: 0b0000000000100000 and 0b00000011
+  # results in 0b0000000000100011
+  s.data = (s.data shl 3).bitor(cast[uint8](c))
+  inc s.len
+
+
+proc high*(s: ColorStack): uint8 = s.len - 1
+
+proc low*(s: ColorStack): uint8 = 0 # just... always 0, I guess
+
+
+proc `[]`*(s: ColorStack, i: uint8 | BackwardsIndex): Color =
+  # shift, then mask everything but the three rightmost bits
+  result = Color(
+    (s.data shr s.offset(i)) and masks[1]
+  )
+
+
+proc `[]=`*(s: var ColorStack, i: uint8 | BackwardsIndex, c: Color) =
+  let offset = s.offset(i)
+  s.data = (s.data and bitnot(masks[1] shl offset)) or (c.uint16 shl offset)
+
+
+iterator items*(s: ColorStack): Color =
+  # s.len is unsigned so it will wrap around if we do s.len - 1 in that case
+  if s.len != 0:
+    for i in countdown(s.len - 1, 0'u8):
+      yield Color((s.data shr (i * 3)) and masks[1])
+
+
+iterator pairs*(s: ColorStack): (uint8, Color) =
+  var count = 0'u8
+  for color in s:
+    yield (count, color)
+    inc count
+
+
+proc find*(s: ColorStack, needle: Color): int8 =
+  for i in 0'u8 .. s.high:
+    if s[i] == needle:
+      return i.int8
+  return -1
+
+
+proc moveSubstack*(src, dst: var ColorStack, startIdx: uint8) =
+  if startIdx >= src.len:
+    raise newException(IndexDefect, "index " & $startIdx & " is out of bounds.")
+  # Moves a sub-stack from the top of src to the top of dst
+  # shift the dst stack by the length of the substack to make room
+  let nToMove = src.len - startIdx
+  let shift = nToMove * 3
+  dst.data = dst.data shl shift
+  # then we mask the source data to present only the items 
+  # being moved, and OR that with the shifted dst data
+  dst.data = dst.data or (src.data and masks[nToMove])
+  dst.len += nToMove
+  # then we shift the source to get rid of the moved items
+  src.data = src.data shr shift
+  src.len -= nToMove
+
+
+proc moveSubstackPre*(src, dst: var ColorStack, startIdx: uint8) =
+  if startIdx >= src.len:
+    raise newException(IndexDefect, "index " & $startIdx & " is out of bounds.")
+  # Moves a sub-stack from the top of src to the bottom of dst
+  let nToMove = src.len - startIdx
+  # shift src to position the substack above its destination,
+  # get rid of everything to the left of the substack,
+  # and OR that with the existing dst data
+  let newLen = dst.len + nToMove
+  dst.data = dst.data or ( (src.data shl (dst.len * 3)) and masks[newLen] )
+  dst.len = newLen
+  # get rid of the substack we just moved
+  src.data = src.data shr (nToMove * 3)
+  src.len -= nToMove
+
+
+proc swap*(s: var ColorStack, i1, i2: uint8) =
+  # Swap the values at two indices in the stack
+  if i1 == i2: return
+
+  # i1 and i2 are unsigned, so we have to watch out for underflows
+  let diff = if i1 > i2:
+    (i1 - i2) * 3
+  else:
+    (i2 - i1) * 3
+
+  # take masks[1] from above (rightmost position) and shift to position of i1.
+  # then do the same for i2, and OR them together.
+  let mask = (masks[1] shl s.offset(i1)) or (masks[1] shl s.offset(i2))
+  # get rid of everything but the two values we're swapping
+  let masked = s.data and mask
+  # shift by the distance between values in both directions, combine, then mask
+  let swapped = ((masked shl diff) or (masked shr diff)) and mask
+  # finally, AND with the inverse of mask so that only the values being 
+  # swapped are erased, and combine that with the swapped values
+  s.data = (s.data and mask.bitnot) or swapped
+
+
+proc shuffle*(r: var Rand, s: var ColorStack) =
+  # Fisher-Yates shuffle
+  for i in countdown(s.high, 1'u8):
+    let j = r.rand(i).uint8
+    if j != i:
+      s.swap(i, j)
+
+
+proc reverse*(s: var ColorStack, first, last: uint8) =
+  var x = first
+  var y = last
+  while x < y:
+    s.swap(x, y)
+    inc x
+    dec y
+
+
+iterator asInt*(s: ColorStack): int8 =
+  for i in 0'u8 .. s.high:
+    yield int8(s[i]) # now we do have to convert
+
+
+proc `$`*(s: ColorStack): string =
+  result = "St@["
+  for c in s:
+    if result[^1] != '[':
+      result.add(", ")
+    result.add($c)
+  result.add("]")
+
+
+proc check(s: ColorStack) =
+  # ensure length is accurate
+  var d = s.data
+  for i in 0'u8 .. 4'u8:
+    if (d and masks[1]) > 4:
+      raise newException(RangeDefect, "Value out of range.")
+    if d > 0 and i >= s.len:
+      raise newException(RangeDefect, "Invalid length.")
+    else:
+      d = d shr 3
+
+
+when isMainModule:
+  var one: ColorStack
+  one.add(cRed)
+  one.add(cGreen)
+  one.add(cBlue)
+  one.add(cYellow)
+  one.add(cPurple)
+
+  var two: ColorStack
+
+  one.moveSubstack(two, 2)
+
+
+  echo one, " ", one.len
+  echo two, " ", two.len
+  echo two.find(cRed)

game.nim

@@ -1,32 +1,39 @@
 import hashes, options
-import fixedseq
+import fixedseq, faststack
+
+export faststack.Color, faststack.ColorStack, faststack.allColors
 
 
-type
+# type
-  Color* = enum
+#   Color* = enum
-    cRed, cGreen, cBlue, cYellow, cPurple
+#     cRed, cGreen, cBlue, cYellow, cPurple
 
-  ColorStack* = FixedSeq[5, Color, int8]
+#   ColorStack* = FixedSeq[5, Color, int8]
 
 
-proc initColorStack*: ColorStack =
+# proc initColorStack*: ColorStack =
-  result.initFixedSeq
+#   result.initFixedSeq
 
 
-proc getAllColors: ColorStack = 
+# proc getAllColors: ColorStack = 
-  var i = 0
+#   var i = 0'u8
-  for c in Color.low .. Color.high:
+#   for c in Color.low .. Color.high:
-    result[i] = c
+#     result[i] = c
 
-const allColors* = getAllColors()
+const
-const colorNames: array[Color, string] =
+  colorNames: array[Color, string] =
     ["Red", "Green", "Blue", "Yellow", "Purple"]
+  colorAbbrevs: array[Color, char] = ['R', 'G', 'B', 'Y', 'P']
 
 
 proc `$`*(c: Color): string =
   result = colorNames[c]
 
 
+proc abbrev*(c: Color): char =
+  result = colorAbbrevs[c]
+
+
 proc `$`*(s: ColorStack): string =
   result.add("St@[")
   for i, color in s:
@@ -44,8 +51,8 @@ type
     tForward = 1
 
   Square* = object
-    camels: ColorStack
+    camels*: ColorStack
-    tile: Option[Tile]
+    tile*: Option[Tile]
 
   Board* = object
     squares*: array[1..16, Square]
@@ -76,8 +83,8 @@ proc hash*(b: Board): Hash =
 
 
 proc init*(b: var Board) =
-  for sq in b.squares.mitems:
+  # for sq in b.squares.mitems:
-    sq.camels.initFixedSeq
+  #   sq.camels.initFixedSeq
   b.initialized = true
 
 
@@ -86,9 +93,9 @@ proc display*(b: Board, start, stop: int) =
     let sq = b.squares[i]
     let lead = $i & ": "
     if sq.tile.isSome:
-      echo lead, sq.tile.get
+      stdout.writeLine($lead & $sq.tile.get)
     else:
-      echo lead, sq.camels
+      stdout.writeLine($lead & $sq.camels)
   echo ""
 
 
@@ -106,7 +113,7 @@ proc setState*(b: var Board;
   b.leader = some(leadCamel)
 
 
-proc diceRemaining*(b: Board): ColorStack =
+proc diceRemaining*(b: Board): FixedSeq[5, Color, int8] =
   result.initFixedSeq
   for color, isRolled in b.diceRolled:
     if not isRolled: result.add(color)
@@ -134,11 +141,11 @@ proc advance*(b: var Board, die: Die) =
     endPos += int(t)
     if t == tBackward: prepend = true
 
-  let stackStart = b[startPos].camels.find(color)
+  let stackStart = b[startPos].camels.find(color).uint8
   if prepend:
     b[startPos].camels.moveSubstackPre(b[endPos].camels, stackStart)
     let stackLen = b[startPos].camels.len - stackStart
-    for i in 0 ..< stackLen:
+    for i in 0'u8 ..< stackLen:
       # we know how many camels we added to the bottom, so set the position for each of those
       b.camels[b[endPos].camels[i]] = endPos
   else:

main.nim

@@ -1,110 +0,0 @@
-import math, options, sequtils, random, sets
-import combinators, game, fixedseq, ui
-
-
-type
-  ScoreSet* = array[Color, int]
-
-  ScoreSpread = object
-    lo: array[Color, float]
-    hi: array[Color, float]
-
-  LegResults* = tuple[scores: ScoreSet, endStates: HashSet[Board]]
-
-
-proc update*(scores: var ScoreSet, toAdd: ScoreSet) =
-  for i, s in toAdd:
-    scores[i] += s
-
-
-proc display*(scores: ScoreSet) =
-  let total = scores.sum
-  for color, score in scores:
-    echo color, ": ", round(100 * scores[color] / total, 2), '%'
-
-
-proc projectLeg*(b: Board): LegResults =
-  var scores: ScoreSet
-  var endStates: HashSet[Board]
-
-  var diceRemaining: ColorStack
-  diceRemaining.initFixedSeq
-  for i, c in b.diceRolled:
-    if not c: diceRemaining.add(i)
-
-  for future in possibleFutures(diceRemaining):
-    var prediction = b # make a copy
-    for dieRoll in future:
-      prediction.advance(dieRoll)
-    inc scores[prediction.leader.get]
-    # deduplicate results
-    endStates.incl(prediction)
-
-  result = (scores, endStates)
-
-
-proc projectOutcomes(b: Board, maxDepth = 1): ScoreSet =
-  var outcomeStack = @[ [b].toHashSet ]
-  for depth in 1..maxDepth:
-    echo "simulating ", outcomeStack[^1].len, " possible legs."
-    var endStates: HashSet[Board]
-
-    for o in outcomeStack[^1]:
-      var o = o # make it mutable
-      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])
-      endStates.incl(projection[1])
-      stdout.write("simulated: " & $result.sum & "\r")
-
-    outcomeStack.add(endStates)
-  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 1 .. count:
-    let winner = b.randomGame(r)
-    inc result[winner]
-  #   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
-
-
-when isMainModule:
-  let config = parseArgs()
-  var b: Board
-  b.init
-  b.setState(config.state, [])
-  b.diceRolled = config.diceRolled
-  b.display(1, 5)
-  let scores = b.projectLeg()[0]
-  scores.display

simulation.nim

@@ -0,0 +1,171 @@
+import cpuinfo, math, options, random, tables
+import combinators, game, faststack, fixedseq
+
+
+type
+  ScoreSet* = array[Color, int]
+  WinPercents* = array[Color, float]
+
+  ScoreSpread = object
+    lo*: array[Color, float]
+    hi*: array[Color, float]
+
+  LegResults* = tuple[scores: ScoreSet, endStates: CountTable[Board]]
+
+
+proc update*(scores: var ScoreSet, toAdd: ScoreSet) =
+  for i, s in toAdd:
+    scores[i] += s
+
+
+proc display*(scores: ScoreSet) =
+  let total = scores.sum
+  for color, score in scores:
+    let line = $color & ": " & $round(100 * scores[color] / total, 2) & '%'
+    stdout.writeLine(line)
+    stdout.flushFile()
+    # echo color, ": ", round(100 * scores[color] / total, 2), '%'
+
+
+proc percents*(scores: ScoreSet): WinPercents =
+  let total = scores.sum
+  for c, score in scores:
+    result[c] = score / total
+
+
+# ======================
+# Single-leg simulations
+# ======================
+
+iterator legEndStates(b: Board): Board =
+  var diceRemaining: FixedSeq[5, Color, int8]
+  diceRemaining.initFixedSeq
+  for i, c in b.diceRolled:
+    if not c: diceRemaining.add(i)
+
+  for future in possibleFutures(diceRemaining):
+    var prediction = b # make a copy so we can mutate
+    for dieRoll in future:
+      prediction.advance(dieRoll)
+    yield prediction
+
+
+proc getLegScores*(b: Board): ScoreSet =
+  for prediction in b.legEndStates:
+    inc result[prediction.leader.get]
+
+
+# =====================
+# Full-game simulations
+# =====================
+
+# get rid of this later
+import strutils
+proc showSpaces*(b: Board; start, stop: Natural): string =
+  let numSpaces = stop - start + 1
+  let width = 4 * numSpaces - 1
+  var lines: array[7, string]
+  # start by building up an empty board
+  for i in 0 .. 6: # gotta initialize the strings
+    lines[i] = newString(width)
+    for c in lines[i].mitems:
+      c = ' '
+  # fill in the dividers
+  lines[5] = repeat("=== ", numSpaces - 1)
+  lines[5].add("===")
+
+  # now populate the board
+  for sp in 0 ..< numSpaces:
+    # fill in the square numbers
+    let squareNum = sp + start
+    let cellMid = 4 * sp + 1
+    for i, chr in $squareNum:
+      lines[6][cellMid + i] = chr
+
+    # fill in the camel stacks
+    for i, color in b.squares[squareNum].camels:
+      let lineNum = 4 - i # lines go to 6, but bottom 2 are reserved
+      let repr = '|' & color.abbrev & '|'
+      for j, chr in repr:
+        lines[lineNum][cellMid - 1 + j] = chr
+
+  result = lines.join("\n")
+# get rid of this later
+
+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 randomGamesWorker(b: Board, count: Natural, r: var Rand): ScoreSet =
+  for i in 1 .. count:
+    let winner = b.randomGame(r)
+    inc result[winner]
+
+
+# =======================
+# Multithreading nonsense
+# =======================
+
+type WorkerArgs = object
+  board: Board
+  count: Natural
+  seed: int64
+
+
+# have to do this at the module level so it can be shared
+var gamesChannel: Channel[ScoreSet]
+gamesChannel.open()
+
+
+proc randomGamesThread(args: WorkerArgs) =
+  var r = initRand(args.seed)
+  let scores = randomGamesWorker(args.board, args.count, r)
+  gamesChannel.send(scores)
+
+
+proc randomGames*(b: Board, count: Natural, parallel = true, numThreads = 0): ScoreSet =
+  randomize()
+
+  if not parallel:
+    var r = initRand(rand(int64))
+    return randomGamesWorker(b, count, r)
+
+  let numThreads =
+    if numThreads == 0:
+      countProcessors()
+    else:
+      numThreads
+
+  var workers = newSeq[Thread[WorkerArgs]](numThreads)
+  for i, w in workers.mpairs:
+    var numGames = int(floor(count / numThreads))
+    if i < (count mod numThreads):
+      numGames += 1
+    let args = WorkerArgs(board: b, count: numGames, seed: rand(int64))
+
+    createThread(w, randomGamesThread, args)
+
+  for i in 1 .. numThreads:
+    let scores = gamesChannel.recv()
+    result.update(scores)
+
+
+proc randomSpread*(b: Board; nTests, nSamples: Natural): 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

test.nim

@@ -0,0 +1,97 @@
+import math, random, strformat, times, std/monotimes
+import fixedseq, game, simulation, ui
+
+
+type
+  TestResults = object
+    ops: int
+    time: Duration
+
+
+proc summarize(tr: TestResults) =
+  let secs = tr.time.inMilliseconds.float / 1000
+  stdout.write("Test completed:\n")
+  stdout.write("  " & $tr.ops, " operations in " & $round(secs, 2) & " seconds\n")
+  stdout.write("  " & $round(tr.ops.float / secs, 2) & " operations per second")
+  stdout.flushFile()
+
+
+template executionTime(body: untyped): Duration =
+  let start = getMonoTime()
+  body
+  getMonoTime() - start
+
+
+proc getRand(): Rand =
+  randomize()
+  result = initRand(rand(int64))
+
+
+proc randomDice(r: var Rand): seq[tuple[c: Color, p: int]] = 
+  for c in Color:
+    let v = r.rand(1..3)
+    result.add((c, v))
+  result.shuffle
+
+
+proc newRandomGame(r: var Rand): Board =
+  var dice: array[5, tuple[c: Color, p: int]]
+  for i in 0 .. 4:
+    dice[i] = (Color(i), r.rand(1..3))
+
+  result.init
+  result.setState(dice, [])
+
+
+proc games(nTests, nSamples: SomeInteger, parallel = true): TestResults =
+  var r = getRand()
+  var scores: ScoreSet
+  for i in 1 .. nTests:
+    let b = newRandomGame(r)
+    let dur = executionTime:
+        let s = b.randomGames(nSamples, parallel = parallel)
+    result.ops += s.sum()
+    result.time += dur
+
+
+proc testLegs(n: Natural = 100): auto =
+  var boards: seq[Board]
+  var r = initRand(rand(int64))
+  for i in 1 .. n:
+    var b: Board
+    b.init
+    let dice = randomDice(r)
+    b.setState(dice, [])
+    boards.add(b)
+    stdout.write("Constructed: " & $i & "\r")
+  echo ""
+  
+  echo "Running..."
+  let start = cpuTime()
+  for b in boards:
+    discard b.getLegScores
+  result = cpuTime() - start
+
+
+proc testSpread(nTests, nSamples: Natural) =
+  var b: Board
+  b.init
+  var r = initRand(rand(int64))
+  let dice = randomDice(r)
+  b.setState(dice, [])
+  b.display(1, 5)
+  let spread = randomSpread(b, nTests, nSamples)
+
+  stdout.writeLine("Variance:")
+  for c in Color:
+    let variance = 100 * (spread.hi[c] - spread.lo[c])
+    stdout.writeLine(fmt"{c}: {round(variance, 2):.2f}%")
+  
+  let diff = 100 * (max(spread.hi) - min(spread.lo))
+  stdout.writeLine(fmt"Win percentage differential: {round(diff, 2):.2f}%")
+
+  stdout.flushFile()
+
+
+when isMainModule:
+  games(10, 10_000_000).summarize()

ui.nim

@@ -1,5 +1,5 @@
-import os, strutils
+import os, math, strutils, strformat
-import game
+import faststack, fixedseq, game, simulation
 
 
 const help = 
@@ -19,6 +19,11 @@ Options:
   -h      Show this message and exit
 """
 
+
+# =============================
+# User input parsing/validation
+# =============================
+
 type
   CmdConfig* = object
     state*: seq[tuple[c: Color, p: int]]
@@ -63,3 +68,53 @@ proc parseArgs*(): CmdConfig =
       for c in p:
         let color = parseColor(c)
         result.diceRolled[color] = true
+
+
+# ==========================
+# Game state representations
+# ==========================
+
+proc showSpaces*(b: Board; start, stop: Natural): string =
+  let numSpaces = stop - start + 1
+  let width = 4 * numSpaces - 1
+  var lines: array[7, string]
+  # start by building up an empty board
+  for i in 0 .. 6: # gotta initialize the strings
+    lines[i] = newString(width)
+    for c in lines[i].mitems:
+      c = ' '
+  # fill in the dividers
+  lines[5] = repeat("=== ", numSpaces - 1)
+  lines[5].add("===")
+
+  # now populate the board
+  for sp in 0 ..< numSpaces:
+    # fill in the square numbers
+    let squareNum = sp + start
+    let cellMid = 4 * sp + 1
+    for i, chr in $squareNum:
+      lines[6][cellMid + i] = chr
+
+    # fill in the camel stacks
+    for i, color in b.squares[squareNum].camels:
+      let lineNum = 4 - i # lines go to 6, but bottom 2 are reserved
+      let repr = '|' & color.abbrev & '|'
+      for j, chr in repr:
+        lines[lineNum][cellMid - 1 + j] = chr
+
+  result = lines.join("\n")
+
+
+proc showPercents*(scores: ScoreSet): string =
+  var lines: array[5, string]
+  for color, pct in scores.percents:
+    let label = align($color, 7) # e.g. " Green"
+    var bar = repeat(" ", 20)
+    let percentage = round(pct * 100, 2)
+    # populate the progress bar
+    let barFill = int(round(pct * 100 / 20))
+    for i in 0 ..< barFill:
+      bar[i] = '='
+
+    lines[int(color)] = fmt"{label}: [{bar}] {percentage}%"
+    result = lines.join("\n")