wheelgame3.frink

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// Simulator for the big-wheel-spinnin' game on The Price Is Right
// This produces the probabilties (and best plays) for each player.

players = eval[input["Enter number of players: "]]
beat = eval[input["Enter score to beat: [0] ", 0]]

pe1 = pe[beat, 1, players]

println["Projected earnings for player 1 are $pe1"]

// Find projected earnings for player, given a score to beat, the player
// number, and the number of players.
pe[beat, player, players] :=
{
   if player == players
      return spinToBeat[beat]
   
   sum = 0
   for s = 5 to 100 step 5
   {
      p = makeProjections[s, beat, player, players]
      sum = sum + p
   }
   return sum / 20
}


// Make projections for a player, given their total is already sum,
// Value to beat is beat, their player number is player, and
// players is the total number of players.
makeProjections[sum, beat, player, players] :=
{
   spin = projSpin[sum, beat, player, players]
   stay = projStay[sum, beat, player, players]

   if player == 1
   {
      println["$sum"]
      println["  Stay: " + stay]
      println["  Spin: " + spin]
   }
   
   if spin > stay
      return spin
   else
      return stay
}


// Gets projected value for spinning the wheel.
projSpin[num, beat, player, players] :=
{
   pe = 0
   
   for s = 5 to 100 step 5
   {
      sum = s + num
      if player == 1
      {
         if sum >= beat
            if sum <= 100
               pe = pe + (1-pe[sum, player+1, players])
      } else
      {
         // Not first player
         if sum > beat
            if sum <= 100
               pe = pe + 1  // Beat first player.
            else            // Too high, defer to next player
               pe = pe + pe[beat, player+1, players]
         else
            if sum == beat
               pe = pe + (1 - 1/2 * (1 - pe[beat, player+1, players]))
            else
               pe = pe + pe[beat, player+1, players]
       }
   }

   return pe/20      
}

// Gets projected value from staying.
projStay[num, beat, player, players] :=
{
   if player == 1
      if num < beat
         return 0
      else
         return (1 - pe[num, player+1, players])
   else
      if num > beat
         return 1
      else  // This player can't win, return pe of next player(s)
         if num == beat
            return 1 - (1/2 * (1 - pe[num, player+1, players]))
         else
            return pe[beat, player+1, players]
}


// Return probability that you'll beat the value
// given by beat.  This should only be called for the last player.
spinToBeat[beat, val=0, spinNum=1] :=
{
   if beat > 100
      return 1    // Other guy busted, you win
   
   if val > beat
      return 1    // Don't spin... you've won.

   if spinNum > 2  // You have no more spins
      if val == beat
         return 1/2  // Tie
      else
         return 0    // Lost

   pe = 0
   
   for n = 5 to 100 step 5
   {
      sum = n + val
      if sum <= 100
         if sum > beat   
            pe = pe + 1      // You've beat it
         else
            pe = pe + spinToBeat[beat, sum, spinNum+1] // Spin again
   }

   return pe/20      
}

max[a,b] := a > b ? a : b


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This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.

Alan Eliasen was born 19970 days, 17 hours, 11 minutes ago.