Microsoft Small Basic

Program Listing:

' Probability of Poker - Challenge 4 (April 2012)
' Copyright (c) 2012 Nonki Takahashi
' Published as WDR858-0

defaultColor = TextWindow.ForegroundColor
resultColor = "White"
TextWindow.WriteLine("PROBABILITY OF GETTING 4 OF A KIND AND A FULL HOUSE")
TextWindow.WriteLine("")

N_KINDS = 13
N_SUITS = 4

TextWindow.WriteLine("BY CALCULATION:")

' combination of 5 cards : nTry = (13*4)C5
n = N_KINDS * N_SUITS
r = 5
Combination()
nTry = ans
TextWindow.WriteLine("5 cards combination = " + nTry)

' combination of getting 4 of a kind : n4 = 13C1 * (12*4)C1
n4 = N_KINDS * ((N_KINDS - 1) * N_SUITS)
TextWindow.WriteLine("4 of a kind combination = " + n4)

' combination of getting a full house : nFH = (13 C1 * 4C3) * (12C1 * 4C2)
n = N_SUITS
r = 3
Combination()
nFH = N_KINDS * ans
n = N_SUITS
r = 2
Combination()
nFH = nFH * (N_KINDS - 1) * ans
TextWindow.WriteLine("full house combination = " + nFH)

PrintResults()

TextWindow.WriteLine("")
TextWindow.WriteLine("BY SIMULATION:")

suits[1]="S"                  ' Space
suits[2]="D"                  ' Diamond
suits[3]="H"                  ' Heart
suits[4]="C"                  ' Clober
nTry = Math.Round(nTry / 100) ' # try
n4 = 0                        ' # 4 of a kind
nFH = 0                       ' # full house
TextWindow.WriteLine("try count = " + 0)
TextWindow.WriteLine("4 of a kind count = " + n4)
TextWindow.WriteLine("full house count = " + nFH)
For i = 1 To nTry
  Pick5()
  Sort()
  Are4ofaKind()
  If ans Then
    n4 = n4 + 1
    TextWindow.CursorLeft = 12
    TextWindow.CursorTop = 10
    TextWindow.WriteLine(i)
    TextWindow.CursorLeft = 20
    TextWindow.CursorTop = 11
    TextWindow.WriteLine(n4)
  EndIf
  AreFullHouse()
  If ans Then
    nFH = nFH + 1
    TextWindow.CursorLeft = 12
    TextWindow.CursorTop = 10
    TextWindow.WriteLine(i)
    TextWindow.CursorLeft = 19
    TextWindow.CursorTop = 12
    TextWindow.WriteLine(nFH)
  EndIf
EndFor
TextWindow.CursorLeft = 0
TextWindow.CursorTop = 10
TextWindow.WriteLine("try count = " + nTry)
TextWindow.WriteLine("4 of a kind count = " + n4)
TextWindow.WriteLine("full house count = " + nFH)
PrintResults()

TextWindow.WriteLine("")
' (end of program)

' Print Results
' param nTry
' param n4
' param nFH
Sub PrintResults
  TextWindow.ForegroundColor = resultColor
  TextWindow.Write("4 of a kind probability = 1 / ")
  TextWindow.Write((Math.Round(nTry / n4 * 100) / 100) + " = ")
  TextWindow.WriteLine(Math.Round(n4 / nTry * 100000) / 100000)
  TextWindow.Write("full house probability = 1 / ")
  TextWindow.Write((Math.Round(nTry / nFH * 100) / 100) + " = ")
  TextWindow.WriteLine(Math.Round(nFH / nTry * 100000) / 100000)
  TextWindow.ForegroundColor = defaultColor
EndSub

' Print Cards (for debug)
' param cards[5]
' param n - # kinds
' param nKinds[n] - # of ith kind
' param kinds[n] - ith kind
Sub PrintCards
  Stack.PushValue("param", i)
  For i = 1 To 5
    TextWindow.Write(cards[i] + " ")
  EndFor
  TextWindow.Write(": ")
  For i = 1 To n
    If nKinds[i] > 1 Then
      TextWindow.Write(Text.Append(kinds[i], "*") + nKinds[i] + " ")
    Else
      TextWindow.Write(kinds[i] + " ")
    EndIf
  EndFor
  TextWindow.WriteLine("")
  i = Stack.PopValue("param")
EndSub
' Random Card
' return card
Sub RandomCard
  suit = Math.GetRandomNumber(N_SUITS)
  kind = Math.GetRandomNumber(N_KINDS)
  card = suits[suit] + kind
EndSub

' Sort
' param cards[5]
' return n - # kinds
' return nKinds[n] - # of ith kind
' return kinds[n] - ith kind
Sub Sort
  Stack.PushValue("param", i)
  Stack.PushValue("param", j)
  n = 0
  For i = 1 To 5
    card = cards[i]
    kind = Text.GetSubTextToEnd(card, 2)
    same = "false"
    For j = 1 To n
      If kinds[j] = kind Then
        same = "true"
        nKinds[j] = nKinds[j] + 1
        Goto breakS
      EndIf
    EndFor
breakS:
    If same = "false" Then
      n = n + 1
      kinds[n] = kind
      nKinds[n] = 1
    EndIf
  EndFor
  j = Stack.PopValue("param")
  i = Stack.PopValue("param")
EndSub

' Are 4 of a Kind
' param n - # kinds
' param nKinds[n] - # of ith kind
' param kinds[n] - ith kind
' return ans = "true" if cards[5] are 4 of a kind
Sub Are4ofaKind
  If n <> 2 Then
    ans = "false"
  ElseIf nKinds[1] <> 4 And nKinds[2] <> 4 Then
    ans = "false"
  Else
    ans = "true"
  EndIf
EndSub

' Are Full House
' param n - # kinds
' param nKinds[n] - # of ith kind
' param kinds[n] - ith kind
' return ans = "true" if cards[5] are full house
Sub AreFullHouse
  If n <> 2 Then
    ans = "false"
  ElseIf nKinds[1] <> 3 And nKinds[2] <> 3 Then
    ans = "false"
  Else
    ans = "true"
  EndIf
EndSub

' Pick 5 Cards
' return cards[5]
Sub Pick5
  Stack.PushValue("param", i)
  For i = 1 To 5
    same = "true"
    While same
      RandomCard()
      cards[i] = card
      same = "false"
      For j = 1 To i - 1
        If cards[j] = card Then
          same = "true"
          Goto break
        EndIf
      EndFor
break:
    EndWhile
  EndFor
  i = Stack.PopValue("param")
EndSub

' Combination nCr
' param n
' param r
' return ans = nCr
Sub Combination
  Stack.PushValue("param", i)
  If (n - r) < r Then
    r = n - r
  EndIf
  ans = 1
  For i = 0 To r - 1
    ans = ans * (n - i)
  EndFor
  For i = 2 To r
    ans = ans / i
  EndFor
  i = Stack.PopValue("param")
EndSub