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<blockquote data-quote="Cadence" data-source="post: 8530893" data-attributes="member: 6701124">tldr;&nbsp; The expected value under the situation I think you're agreeing to is 11.8125, not 10.5-----------------------In the table below, #Con out of 216 is the number out of 216 rolls that would end up with each consitution.&nbsp; So there is a 21/216 chance of rolling an 8, for example.The columns C through T indicate if the class is allowed based on that roll.&nbsp; With a con of 8 you can be a Cleric, not a Dwarf, an Elf if Int is 9+, a Fighter, not a Halfling, a Magic-User, or a Thief.[ATTACH=full]150998[/ATTACH]Case 1:Consider selecting the class randomly from all of those allowed.&nbsp; For a Con below 9, a Dwarf can never be selected.&nbsp; For a Con of 9 or higher, the chance of picking a Dwarf is 27/175&nbsp; (Each of the C, D, F, M, and T can happen all of the time, while the E and H need to have a 9+ in a specified other skill, so the chance of that happening is 20/27.&nbsp; So the chance of a Dwarf is 1/(5+2*(20/27))=1/(175/27)=27/175.Now consider rolling 1400 characters. The expected number of Dwarves for each Con of 9 or higher is calculated by taking 1400*(#/216)*(27/175). This is in the column labeled #Dwarf out of 1400.&nbsp;&nbsp; (It is 0 for below 9, because there aren't any).There are a total of 160 Dwarves rolled out of the 1400 characters.The expected value (mean) of the Cons is:(25/160)*9+(27/160)*10+(27/160)*11+(25/160)*12+(21/160)*13+(15/160)*14+(10/160)*15+(6/160)*16+(3/160)*17+(1/160)*18which is 1890/160 = 11+13/16 = 11.8125.Case 2:Consider choosing to play a Dwarf whenever it is allowed.&nbsp; In that case column J becomes the number of Dwarves out of 216 rolled.&nbsp; There are still 160 Dwarves, and the math for the expected value doesn't change.Case 3:Rerolling until you get a 9+ on Con.&nbsp; The numbers in column J out of 160 are the chance that you get the Con for that row, and the math for the expected value doesn't change.</blockquote>

[QUOTE="Cadence, post: 8530893, member: 6701124"] tldr; The expected value under the situation I think you're agreeing to is 11.8125, not 10.5 ----------------------- In the table below, #Con out of 216 is the number out of 216 rolls that would end up with each consitution. So there is a 21/216 chance of rolling an 8, for example. The columns C through T indicate if the class is allowed based on that roll. With a con of 8 you can be a Cleric, not a Dwarf, an Elf if Int is 9+, a Fighter, not a Halfling, a Magic-User, or a Thief. [ATTACH type="full" alt="1643642597320.png"]150998[/ATTACH] Case 1: Consider selecting the class randomly from all of those allowed. For a Con below 9, a Dwarf can never be selected. For a Con of 9 or higher, the chance of picking a Dwarf is 27/175 (Each of the C, D, F, M, and T can happen all of the time, while the E and H need to have a 9+ in a specified other skill, so the chance of that happening is 20/27. So the chance of a Dwarf is 1/(5+2*(20/27))=1/(175/27)=27/175. Now consider rolling 1400 characters. The expected number of Dwarves for each Con of 9 or higher is calculated by taking 1400*(#/216)*(27/175). This is in the column labeled #Dwarf out of 1400. (It is 0 for below 9, because there aren't any). There are a total of 160 Dwarves rolled out of the 1400 characters. The expected value (mean) of the Cons is: (25/160)*9+(27/160)*10+(27/160)*11+(25/160)*12+(21/160)*13+(15/160)*14+ (10/160)*15+(6/160)*16+(3/160)*17+(1/160)*18 which is 1890/160 = 11+13/16 = 11.8125. Case 2: Consider choosing to play a Dwarf whenever it is allowed. In that case column J becomes the number of Dwarves out of 216 rolled. There are still 160 Dwarves, and the math for the expected value doesn't change. Case 3: Rerolling until you get a 9+ on Con. The numbers in column J out of 160 are the chance that you get the Con for that row, and the math for the expected value doesn't change. [/QUOTE]

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