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<blockquote data-quote="RedShirtNo5" data-source="post: 2178379" data-attributes="member: 173">Final Result: 30.4633219726944Total Characters Accepted: 7790570Total Characters Rejected: 8986646&nbsp;Frequency of 3: 1260600Frequency of 4: 6470160Frequency of 5: 16175400Frequency of 6: 42342300Frequency of 7: 76619400Frequency of 8: 151608600Frequency of 9: 222522300Frequency of 10: 352479960Frequency of 11: 427598640Frequency of 12: 556140060Frequency of 13: 572790960Frequency of 14: 613664640Frequency of 15: 502437924Frequency of 16: 401485656Frequency of 17: 230640696Frequency of 18: 98128044&nbsp;[code][size=2]Private Sub Command1_Click()[/size]&nbsp;[size=2]Dim V As DoubleDim P As DoubleDim A As DoubleDim Value As DoubleDim Probability As DoubleDim S As IntegerDim D As IntegerDim Co As IntegerDim I As IntegerDim W As IntegerDim Ch As IntegerDim TotalAccepted As LongDim TotalRejected As LongDim T(18) As LongDim Result As String[/size]&nbsp;[size=2]V = 0#P = 0#[/size]&nbsp;[size=2]TotalAccepted = 0&amp;TotalRejected = 0&amp;[/size]&nbsp;[size=2]' We will cycle through each possible stat array that could be createdFor S = 3 To 18For D = 3 To 18For Co = 3 To 18For I = 3 To 18For W = 3 To 18For Ch = 3 To 18[/size]&nbsp;[size=2]' If the stat array is a &quot;worthless character&quot;, then skip itIf S &gt; 13 Or D &gt; 13 Or Co &gt; 13 Or I &gt; 13 Or W &gt; 13 Or Ch &gt; 13 Then&nbsp; &nbsp; If Int((S - 10) / 2) + Int((D - 10) / 2) + Int((Co - 10) / 2) + Int((I - 10) / 2) + Int((W - 10) / 2) + Int((Ch - 10) / 2) &gt; 0 Then[/size]&nbsp;[size=2]' If the stat array is not a worthless character, calculate the point buy value (PBV)' and the probability of that character occurring&nbsp; &nbsp; Value = PBV(S) + PBV(D) + PBV(Co) + PBV(I) + PBV(W) + PBV(Ch)&nbsp; &nbsp; Probability = prob(S) * prob(D) * prob(Co) * prob(I) * prob(W) * prob(Ch)[/size]&nbsp;[size=2]' Add the weighted point buy value to a running total&nbsp; &nbsp; V = V + Value * Probability&nbsp;' Track the total probability (P) of getting a &quot;non-worthless&quot; character for normalization below&nbsp; &nbsp; P = P + Probability[/size]&nbsp;[size=2]' Track the total number of accepted characters&nbsp; &nbsp; TotalAccepted = TotalAccepted + 1&amp;&nbsp;' Track chances of each number&nbsp; &nbsp; T(S) = T(S) + ways(S)&nbsp; &nbsp; T(D) = T(D) + ways(D)&nbsp; &nbsp; T(Co) = T(Co) + ways(Co)&nbsp; &nbsp; T(I) = T(I) + ways(I)&nbsp; &nbsp; T(W) = T(W) + ways(W)&nbsp; &nbsp; T(Ch) = T(Ch) + ways(Ch)&nbsp;&nbsp; &nbsp; Else&nbsp;&nbsp; &nbsp; TotalRejected = TotalRejected + 1&amp;&nbsp;&nbsp; &nbsp; End If[/size]&nbsp;[size=2]Else[/size]&nbsp;[size=2]&nbsp; &nbsp; TotalRejected = TotalRejected + 1&amp;&nbsp;End If[/size]&nbsp;[size=2]NextNextNextNextNextNext[/size]&nbsp;[size=2]' We know the probability (1-P) of rolling a worthless character, and we calculated the average point buy value (V) that results from a single roll of 4d6dl. Since you keep rolling until you get a non-worthless character, the percentage chance (1-P) of a worthless character gets distributed across the possible non-worthless characters. Thus, we simply need to normalize the result.A = V / P[/size]&nbsp;[size=2]' Display resultsResult = &quot;Final Result:&quot; + Str(A) + Chr(13)Result = Result + &quot;Total Accepted: &quot; + Str(TotalAccepted) + Chr(13)Result = Result + &quot;Total Rejected: &quot; + Str(TotalRejected) + Chr(13)For j = 3 To 18Result = Result + &quot;Frequency of &quot; + Str(j) + &quot;: &quot; + Str(T(j)) + Chr(13)Next[/size]&nbsp;[size=2]Text1.Text = Result[/size]&nbsp;[size=2]End SubFunction PBV(x)' This assumes that point buy for stats below 8 scales linearly&nbsp;If x = 3 Then PBV = -5#If x = 4 Then PBV = -4#If x = 5 Then PBV = -3#If x = 6 Then PBV = -2#If x = 7 Then PBV = -1#If x = 8 Then PBV = 0#If x = 9 Then PBV = 1#If x = 10 Then PBV = 2#If x = 11 Then PBV = 3#If x = 12 Then PBV = 4#If x = 13 Then PBV = 5#If x = 14 Then PBV = 6#If x = 15 Then PBV = 8#If x = 16 Then PBV = 10#If x = 17 Then PBV = 13#If x = 18 Then PBV = 16#End Function[/size]&nbsp;[size=2]Function prob(x)'These percentages taken from dcollins ([url=&quot;http://javascript&lt;b&gt;&lt;/b&gt;&lt;img%20src=&quot;http://www.enworld.org/images/smilies/redface.gif&quot;%20border=&quot;0&quot;%20alt=&quot;&quot;%20title=&quot;Embarrassment&quot;%20smilieid=&quot;3&quot;%20class=&quot;inlineimg&quot;%20/&gt;l('http://superdan.net.home.comcast.net/dndmisc/4d6curve.html');&quot;][color=#0000ff]http://superdan.net.home.comcast.net/dndmisc/4d6curve.html[/color][/url])If x = 3 Then prob = 1# / 1296#If x = 4 Then prob = 4# / 1296#If x = 5 Then prob = 10# / 1296#If x = 6 Then prob = 21# / 1296#If x = 7 Then prob = 38# / 1296#If x = 8 Then prob = 62# / 1296#If x = 9 Then prob = 91# / 1296#If x = 10 Then prob = 122# / 1296#If x = 11 Then prob = 148# / 1296#If x = 12 Then prob = 167# / 1296#If x = 13 Then prob = 172# / 1296#If x = 14 Then prob = 160# / 1296#If x = 15 Then prob = 131# / 1296#If x = 16 Then prob = 94# / 1296#If x = 17 Then prob = 54# / 1296#If x = 18 Then prob = 21# / 1296#End Function[/size]&nbsp;[size=2]Function ways(x)'These numbers taken from dcollins ([url=&quot;http://javascript&lt;b&gt;&lt;/b&gt;&lt;img%20src=&quot;http://www.enworld.org/images/smilies/redface.gif&quot;%20border=&quot;0&quot;%20alt=&quot;&quot;%20title=&quot;Embarrassment&quot;%20smilieid=&quot;3&quot;%20class=&quot;inlineimg&quot;%20/&gt;l('http://superdan.net.home.comcast.net/dndmisc/4d6curve.html');&quot;][color=#0000ff]http://superdan.net.home.comcast.net/dndmisc/4d6curve.html[/color][/url])If x = 3 Then ways = 1&amp;If x = 4 Then ways = 4&amp;If x = 5 Then ways = 10&amp;If x = 6 Then ways = 21&amp;If x = 7 Then ways = 38&amp;If x = 8 Then ways = 62&amp;If x = 9 Then ways = 91&amp;If x = 10 Then ways = 122&amp;If x = 11 Then ways = 148&amp;If x = 12 Then ways = 167&amp;If x = 13 Then ways = 172&amp;If x = 14 Then ways = 160&amp;If x = 15 Then ways = 131&amp;If x = 16 Then ways = 94&amp;If x = 17 Then ways = 54&amp;If x = 18 Then ways = 21&amp;[/code][/size]</blockquote>

[QUOTE="RedShirtNo5, post: 2178379, member: 173"] [size=2]Final Result: 30.4633219726944[/size] [size=2] Total Characters Accepted: 7790570 Total Characters Rejected: 8986646 Frequency of 3: 1260600 Frequency of 4: 6470160 Frequency of 5: 16175400 Frequency of 6: 42342300 Frequency of 7: 76619400 Frequency of 8: 151608600 Frequency of 9: 222522300 Frequency of 10: 352479960 Frequency of 11: 427598640 Frequency of 12: 556140060 Frequency of 13: 572790960 Frequency of 14: 613664640 Frequency of 15: 502437924 Frequency of 16: 401485656 Frequency of 17: 230640696 Frequency of 18: 98128044 [/size] [code] [size=2]Private Sub Command1_Click()[/size] [size=2]Dim V As Double Dim P As Double Dim A As Double Dim Value As Double Dim Probability As Double Dim S As Integer Dim D As Integer Dim Co As Integer Dim I As Integer Dim W As Integer Dim Ch As Integer Dim TotalAccepted As Long Dim TotalRejected As Long Dim T(18) As Long Dim Result As String[/size] [size=2]V = 0# P = 0#[/size] [size=2]TotalAccepted = 0& TotalRejected = 0&[/size] [size=2]' We will cycle through each possible stat array that could be created For S = 3 To 18 For D = 3 To 18 For Co = 3 To 18 For I = 3 To 18 For W = 3 To 18 For Ch = 3 To 18[/size] [size=2]' If the stat array is a "worthless character", then skip it If S > 13 Or D > 13 Or Co > 13 Or I > 13 Or W > 13 Or Ch > 13 Then If Int((S - 10) / 2) + Int((D - 10) / 2) + Int((Co - 10) / 2) + Int((I - 10) / 2) + Int((W - 10) / 2) + Int((Ch - 10) / 2) > 0 Then[/size] [size=2]' If the stat array is not a worthless character, calculate the point buy value (PBV) ' and the probability of that character occurring Value = PBV(S) + PBV(D) + PBV(Co) + PBV(I) + PBV(W) + PBV(Ch) Probability = prob(S) * prob(D) * prob(Co) * prob(I) * prob(W) * prob(Ch)[/size] [size=2]' Add the weighted point buy value to a running total V = V + Value * Probability ' Track the total probability (P) of getting a "non-worthless" character for normalization below P = P + Probability[/size] [size=2]' Track the total number of accepted characters TotalAccepted = TotalAccepted + 1& ' Track chances of each number T(S) = T(S) + ways(S) T(D) = T(D) + ways(D) T(Co) = T(Co) + ways(Co) T(I) = T(I) + ways(I) T(W) = T(W) + ways(W) T(Ch) = T(Ch) + ways(Ch) Else TotalRejected = TotalRejected + 1& End If[/size] [size=2]Else[/size] [size=2] TotalRejected = TotalRejected + 1& End If[/size] [size=2]Next Next Next Next Next Next[/size] [size=2]' We know the probability (1-P) of rolling a worthless character, and we calculated the average point buy value (V) that results from a single roll of 4d6dl. Since you keep rolling until you get a non-worthless character, the percentage chance (1-P) of a worthless character gets distributed across the possible non-worthless characters. Thus, we simply need to normalize the result. A = V / P[/size] [size=2]' Display results Result = "Final Result:" + Str(A) + Chr(13) Result = Result + "Total Accepted: " + Str(TotalAccepted) + Chr(13) Result = Result + "Total Rejected: " + Str(TotalRejected) + Chr(13) For j = 3 To 18 Result = Result + "Frequency of " + Str(j) + ": " + Str(T(j)) + Chr(13) Next[/size] [size=2]Text1.Text = Result[/size] [size=2]End Sub Function PBV(x) ' This assumes that point buy for stats below 8 scales linearly If x = 3 Then PBV = -5# If x = 4 Then PBV = -4# If x = 5 Then PBV = -3# If x = 6 Then PBV = -2# If x = 7 Then PBV = -1# If x = 8 Then PBV = 0# If x = 9 Then PBV = 1# If x = 10 Then PBV = 2# If x = 11 Then PBV = 3# If x = 12 Then PBV = 4# If x = 13 Then PBV = 5# If x = 14 Then PBV = 6# If x = 15 Then PBV = 8# If x = 16 Then PBV = 10# If x = 17 Then PBV = 13# If x = 18 Then PBV = 16# End Function[/size] [size=2] Function prob(x) 'These percentages taken from dcollins ([url="http://javascript<img%20src="http://www.enworld.org/images/smilies/redface.gif"%20border="0"%20alt=""%20title="Embarrassment"%20smilieid="3"%20class="inlineimg"%20/>l('http://superdan.net.home.comcast.net/dndmisc/4d6curve.html');"][color=#0000ff]http://superdan.net.home.comcast.net/dndmisc/4d6curve.html[/color][/url]) If x = 3 Then prob = 1# / 1296# If x = 4 Then prob = 4# / 1296# If x = 5 Then prob = 10# / 1296# If x = 6 Then prob = 21# / 1296# If x = 7 Then prob = 38# / 1296# If x = 8 Then prob = 62# / 1296# If x = 9 Then prob = 91# / 1296# If x = 10 Then prob = 122# / 1296# If x = 11 Then prob = 148# / 1296# If x = 12 Then prob = 167# / 1296# If x = 13 Then prob = 172# / 1296# If x = 14 Then prob = 160# / 1296# If x = 15 Then prob = 131# / 1296# If x = 16 Then prob = 94# / 1296# If x = 17 Then prob = 54# / 1296# If x = 18 Then prob = 21# / 1296# End Function[/size] [size=2]Function ways(x) 'These numbers taken from dcollins ([url="http://javascript<img%20src="http://www.enworld.org/images/smilies/redface.gif"%20border="0"%20alt=""%20title="Embarrassment"%20smilieid="3"%20class="inlineimg"%20/>l('http://superdan.net.home.comcast.net/dndmisc/4d6curve.html');"][color=#0000ff]http://superdan.net.home.comcast.net/dndmisc/4d6curve.html[/color][/url]) If x = 3 Then ways = 1& If x = 4 Then ways = 4& If x = 5 Then ways = 10& If x = 6 Then ways = 21& If x = 7 Then ways = 38& If x = 8 Then ways = 62& If x = 9 Then ways = 91& If x = 10 Then ways = 122& If x = 11 Then ways = 148& If x = 12 Then ways = 167& If x = 13 Then ways = 172& If x = 14 Then ways = 160& If x = 15 Then ways = 131& If x = 16 Then ways = 94& If x = 17 Then ways = 54& If x = 18 Then ways = 21& [/code] [/size] [/QUOTE]

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