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<blockquote data-quote="ichabod" data-source="post: 1010686" data-attributes="member: 1257">Sure, spreadsheet is attached. I tested the idea on easy to check things, like 3d3 drop 1, and 4d6 drop 1. I'm going out tonight to celebrate 13 years without a cig, but now that I have the python code finished I can check the whole thing. I'll also try to program in the formula, and test it, but I may get distracted. In any case, I think I forgot to mention that the formula depends on treating 0^0 as 1. It could be rewritten without that assumption, but it would make the formula even messier.The spreadsheet is set up only for keeping 3d6 and rolling up to 9d6. Enter the number of dice into '# of dice', and it should give you the whole distribution. The patterns in the combinatorics took me a long time to figure out, but I finally realized that once you're dropping more than one die, you have to start summing multinomials.In the spreadsheet, all the sorted three die combinations are on the left. Then there are four collumns showing calculating the possible combinations for the four possible was the three dice could be equal: all 3 equal, top 2 equal, low 2 equal, and none equal. These are taken using an offset on the tables to the far right, where the summing of multinomials is done. Then the 'Combos' collumn figures out which equality situation actually exists, and then gets the correct number of combinations. The chart with the distributions sums up all the combos with the correct number is the 'Total' collumn.</blockquote>

[QUOTE="ichabod, post: 1010686, member: 1257"] Sure, spreadsheet is attached. I tested the idea on easy to check things, like 3d3 drop 1, and 4d6 drop 1. I'm going out tonight to celebrate 13 years without a cig, but now that I have the python code finished I can check the whole thing. I'll also try to program in the formula, and test it, but I may get distracted. In any case, I think I forgot to mention that the formula depends on treating 0^0 as 1. It could be rewritten without that assumption, but it would make the formula even messier. The spreadsheet is set up only for keeping 3d6 and rolling up to 9d6. Enter the number of dice into '# of dice', and it should give you the whole distribution. The patterns in the combinatorics took me a long time to figure out, but I finally realized that once you're dropping more than one die, you have to start summing multinomials. In the spreadsheet, all the sorted three die combinations are on the left. Then there are four collumns showing calculating the possible combinations for the four possible was the three dice could be equal: all 3 equal, top 2 equal, low 2 equal, and none equal. These are taken using an offset on the tables to the far right, where the summing of multinomials is done. Then the 'Combos' collumn figures out which equality situation actually exists, and then gets the correct number of combinations. The chart with the distributions sums up all the combos with the correct number is the 'Total' collumn. [/QUOTE]

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