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Advantage and Disadvantage stacking
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<blockquote data-quote="Ferghis" data-source="post: 5962030" data-attributes="member: 40483"><p>I have no idea about the equation, but you're right on the money about the numbers. Damn my terrible memory. The benefit to crits of stacking advantages deteriorates at a much lower rate. Here are all my numbers rounded to the second place after the decimal point, from the spreadsheet:</p><p></p><p>Average of best of 2d20: 13.83</p><p>Average Improvement over 1d20: 3.33</p><p>Odds of critical: 9.75%</p><p>Crit odds improvement over 1d20: 4.75%</p><p></p><p>Average of best of 3d20: 15.49</p><p>Average Improvement over 1d20: 4.99</p><p>Average Improvement over 2d20: 1.66</p><p>Odds of critical: 14.26%</p><p>Crit odds improvement over 1d20: 9.26%</p><p>Crit odds improvement over 2d20: 4.51%</p><p></p><p>Average of best of 4d20: 16.48</p><p>Average Improvement over 1d20: 5.98</p><p>Average Improvement over 2d20: 2.66</p><p>Average Improvement over 3d20: 1.00</p><p>Odds of critical: 18.55%</p><p>Crit odds improvement over 1d20: 13.55%</p><p>Crit odds improvement over 2d20: 8.80%</p><p>Crit odds improvement over 3d20: 4.29%</p><p></p><p>Methodology: first four columns of the spreadsheet have the die rolls. The A column just repeats 1-20 over and over again, and each of these sets of 20 rows corresponds to one number of a d20 in the B column. This is repeated for the C and D columns, with increasingly longer series of the same digit (to include every possible iteration of the prior columns). This takes 160,000 rows (thank god for copy paste), which is 20 to the fourth power. In the E column I take the highest roll from the first two columns, in the F from the first three, and in the G from the first four (these are the actual results of advantage). Then, I calculate the average of columns E, F and G to obtain the average results of one, two and three advantages, respectively. To figure out the odds of a crit, I count the 20s in columns E, F and G using the COUNTIF formula. The improvements are simple subtraction. I use LibreOffice Calc.</p></blockquote><p></p>
[QUOTE="Ferghis, post: 5962030, member: 40483"] I have no idea about the equation, but you're right on the money about the numbers. Damn my terrible memory. The benefit to crits of stacking advantages deteriorates at a much lower rate. Here are all my numbers rounded to the second place after the decimal point, from the spreadsheet: Average of best of 2d20: 13.83 Average Improvement over 1d20: 3.33 Odds of critical: 9.75% Crit odds improvement over 1d20: 4.75% Average of best of 3d20: 15.49 Average Improvement over 1d20: 4.99 Average Improvement over 2d20: 1.66 Odds of critical: 14.26% Crit odds improvement over 1d20: 9.26% Crit odds improvement over 2d20: 4.51% Average of best of 4d20: 16.48 Average Improvement over 1d20: 5.98 Average Improvement over 2d20: 2.66 Average Improvement over 3d20: 1.00 Odds of critical: 18.55% Crit odds improvement over 1d20: 13.55% Crit odds improvement over 2d20: 8.80% Crit odds improvement over 3d20: 4.29% Methodology: first four columns of the spreadsheet have the die rolls. The A column just repeats 1-20 over and over again, and each of these sets of 20 rows corresponds to one number of a d20 in the B column. This is repeated for the C and D columns, with increasingly longer series of the same digit (to include every possible iteration of the prior columns). This takes 160,000 rows (thank god for copy paste), which is 20 to the fourth power. In the E column I take the highest roll from the first two columns, in the F from the first three, and in the G from the first four (these are the actual results of advantage). Then, I calculate the average of columns E, F and G to obtain the average results of one, two and three advantages, respectively. To figure out the odds of a crit, I count the 20s in columns E, F and G using the COUNTIF formula. The improvements are simple subtraction. I use LibreOffice Calc. [/QUOTE]
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Advantage and Disadvantage stacking
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