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<blockquote data-quote="frisbeet" data-source="post: 762650" data-attributes="member: 10287">This is a great question!&nbsp; I've wondered too about an analytical formula for determining the probability of achieving one outcome from throwing some set of dice.&nbsp; I couldn't figure it out.&nbsp; The issue to which I wanted to apply this idea was D&amp;D weapon damage calculations.&nbsp; Determining the average weapon damage in combat is not as simple as averaging the damage roll when you fight creatures with damage reduction--you actually need the discreet probability distribution of the damage roll (and critical hit damage roll).&nbsp; Since&nbsp; there are only a small number of combinations of rolls you need to make for all D&amp;D weapons: 1d4, 2d4, 3d4, 4d4, 6d4, 8d4, 1d6, 2d6, etc., I went ahead and counted all the ways of rolling outcomes for each dice combo, using a little help from Excel and recognizing patterns.&nbsp; It was still a pain in the ass.Here's an example, for 4d6.oc___#ways___probability4_____1______0.0007716049382716055_____4______0.003086419753086426_____10_____0.007716049382716057_____20_____0.01543209876543218_____35_____0.02700617283950629_____56_____0.043209876543209910____80_____0.061728395061728411____104____0.080246913580246912____125____0.096450617283950613____140____0.10802469135802514____146____0.11265432098765415____140____0.10802469135802516____125____0.096450617283950617____104____0.080246913580246918____80_____0.061728395061728419____56_____0.043209876543209920____35_____0.027006172839506221____20_____0.015432098765432122____10_____0.0077160493827160523____4______0.0030864197530864224____1______0.000771604938271605The rest of the roll combo distributions can be found at<a href="http://www.geocities.com/frisbeet/DandDandFightin.html" target="_blank">http://www.geocities.com/frisbeet/DandDandFightin.html</a>Select the &quot;Weapon Comparison&quot; Excel file.&nbsp; Unhide the &quot;rolls&quot; worksheet.&nbsp; Hopefully this helps a little.</blockquote>

[QUOTE="frisbeet, post: 762650, member: 10287"] This is a great question! I've wondered too about an analytical formula for determining the probability of achieving one outcome from throwing some set of dice. I couldn't figure it out. The issue to which I wanted to apply this idea was D&D weapon damage calculations. Determining the average weapon damage in combat is not as simple as averaging the damage roll when you fight creatures with damage reduction--you actually need the discreet probability distribution of the damage roll (and critical hit damage roll). Since there are only a small number of combinations of rolls you need to make for all D&D weapons: 1d4, 2d4, 3d4, 4d4, 6d4, 8d4, 1d6, 2d6, etc., I went ahead and counted all the ways of rolling outcomes for each dice combo, using a little help from Excel and recognizing patterns. It was still a pain in the ass. Here's an example, for 4d6. oc___#ways___probability 4_____1______0.000771604938271605 5_____4______0.00308641975308642 6_____10_____0.00771604938271605 7_____20_____0.0154320987654321 8_____35_____0.0270061728395062 9_____56_____0.0432098765432099 10____80_____0.0617283950617284 11____104____0.0802469135802469 12____125____0.0964506172839506 13____140____0.108024691358025 14____146____0.112654320987654 15____140____0.108024691358025 16____125____0.0964506172839506 17____104____0.0802469135802469 18____80_____0.0617283950617284 19____56_____0.0432098765432099 20____35_____0.0270061728395062 21____20_____0.0154320987654321 22____10_____0.00771604938271605 23____4______0.00308641975308642 24____1______0.000771604938271605 The rest of the roll combo distributions can be found at [url]http://www.geocities.com/frisbeet/DandDandFightin.html[/url] Select the "Weapon Comparison" Excel file. Unhide the "rolls" worksheet. Hopefully this helps a little. [/QUOTE]

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