Probability in Char. Gen.

[frisbeet]

Nobody know when to bump a good thread.

 

[Thanee]

Actually, the choice of that particular approximation has less of an effect than it would seem at first, since characters with large numbers of low stats also tend to eb hopeless

It's a good half point if you ignore Rerolling (see my post on the first page).

Rerolling then adds about 2 points to the tally, more than I had guessed.

Bye
Thanee

 

[drothgery]

My VB.NET Monte Carlo attempt is coming with around 30.9, a little higher than most of you got, though I'm playing with the VS.NET 2005 Beta 2 compilers, and this code uses some new features, so I'm wondering if I'm making any mistakes...

[sblock]

Private Sub GoBtn_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles GoBtn.Click
        Dim iterationsCount As Integer
        Dim totalPoints As Long = 0
        Dim avgPoints As Double

        If Integer.TryParse(Me.NumTb.Text, iterationsCount) Then
            Dim rnd As New System.Random

            For i As Integer = 0 To iterationsCount
                totalPoints += RollCharacter(rnd)
            Next

            avgPoints = totalPoints / iterationsCount
            RsltsLbl.Text = avgPoints.ToString
        End If
    End Sub

    Private Function RollCharacter(ByVal rnd As Random) As Integer
        Dim charPoints As Integer = 0
        Dim diceRslts As New List(Of Integer)
        Dim rollValue As Integer
        Dim maxVal As Integer = 0
        Dim totalMod As Integer = 0
        Dim maxStat As Integer = 0

        For i As Integer = 1 To 6
            'roll 4d6, drop the lowest
            rollValue = 0
            diceRslts.Clear()

            For d As Integer = 0 To 3
                diceRslts.Add(rnd.Next(1, 7))
            Next

            diceRslts.Sort()

            For d As Integer = 1 To 3
                rollValue += diceRslts(d)
            Next

            'get point value, adjust total modifier
            Select Case rollValue
                Case 3
                    totalMod += -4
                    charPoints += 0
                Case 4
                    totalMod += -3
                    charPoints += 0
                Case 5
                    totalMod += -3
                    charPoints += 0
                Case 6
                    totalMod += -2
                    charPoints += 0
                Case 7
                    totalMod += -2
                    charPoints += 0
                Case 8
                    totalMod += -1
                    charPoints += 0
                Case 9
                    totalMod += -1
                    charPoints += 1
                Case 10
                    totalMod += 0
                    charPoints += 2
                Case 11
                    totalMod += 0
                    charPoints += 3
                Case 12
                    totalMod += 1
                    charPoints += 4
                Case 13
                    totalMod += 1
                    charPoints += 5
                Case 14
                    charPoints += 6
                    totalMod += 2
                Case 15
                    charPoints += 8
                    totalMod += 2
                Case 16
                    charPoints += 10
                    totalMod += 3
                Case 17
                    charPoints += 13
                    totalMod += 3
                Case 18
                    charPoints += 16
                    totalMod += 4
            End Select

            maxStat = Math.Max(maxStat, rollValue)
        Next

        If totalMod > 0 AndAlso maxStat > 13 Then
            Return charPoints
        Else
            Return RollCharacter(rnd)
        End If

    End Function

[/sblock]

 

[Qwyxzl]

My take on this problem is a bit different and thus I cam out with a different result. What we are looking for is not an average but the point buy value that is the most likely to occur out of all of the possible combinations of valid characters. In order to do this I created a program that generates every possible combination (16777216 sets of scores). As it generates them it determines if a given set is acceptable (7816299 sets) or not (8960917 sets). If a set is acceptable then it determines the point value of the set (using values less than 9 = 0). Then I add to an array containing all possible point buy values (0-96) the probability of generating that score. The point buy value that has the highest total is 28. I wrote it in c if anyone is interested in looking at it.

Qwyxzl

 

[Olgar Shiverstone]

How do you take into account the relative value of odd vs. even scores with regard to ability modifiers? Point buy gives you a certain advantage in allowing optimization against even scores at character creation, while odd scores generated by rolling are often "wasted" (example: fighter with Cha 10 is better than Cha 11, since in PB I can use the point from Cha elsewhere).

I find that this makes a relative point buy number actually of greater value than it would first appear, as it is easier to optimize your stat set to a character type.

 

[Rystil Arden]

My take on this problem is a bit different and thus I cam out with a different result. What we are looking for is not an average but the point buy value that is the most likely to occur out of all of the possible combinations of valid characters. In order to do this I created a program that generates every possible combination (16777216 sets of scores). As it generates them it determines if a given set is acceptable (7816299 sets) or not (8960917 sets). If a set is acceptable then it determines the point value of the set (using values less than 9 = 0). Then I add to an array containing all possible point buy values (0-96) the probability of generating that score. The point buy value that has the highest total is 28. I wrote it in c if anyone is interested in looking at it.

Qwyxzl

Umm...you found the mode instead of the mean. Its not really a fair average unless the distribution is Gaussian, which it is not.

 

[Qwyxzl]

Umm...you found the mode instead of the mean. Its not really a fair average unless the distribution is Gaussian, which it is not.

The original question was not to find the average but to find the point buy value that best represented the 4d4dl generation method.

I am curious about researching the expected DMG point value of a "Standard" "4d6, drop the lowest"(4d6dl) D&D character.

Therefore I think the best representation is the mode.

Qwyxzl

 

[Rystil Arden]

The original question was not to find the average but to find the point buy value that best represented the 4d4dl generation method.



Therefore I think the best representation is the mode.

Qwyxzl

Nope. Expected Value has a very specific definition in probability. And its not the mode. It is written as the function E[]