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<blockquote data-quote="frisbeet" data-source="post: 1230211" data-attributes="member: 10287">So here are some numbers to start with.&nbsp; In this example I consider n=3,4,&amp;5; s=6, and d = 0,1,or 2.&nbsp; I've been thinking along the lines of:1). Count the ways of rolling the outcome with 3 dice.&nbsp; We've done this already in this thread.2).&nbsp; For each way of rolling an outcome, count the number of ways of replacing the highest dice with the discarded dice.Add, not multiply, the results of 1 &amp; 2.&nbsp; So # ways of getting a 6&nbsp; by 4d6 drop 1 = #ways of 3d6 getting a 6 + comb(3,0) + comb(3,0) + comb (3,1) + comb (3,1) + comb(3,2) = 21By a more brutal but accurate method I've determined the distributions for 4d6 drop1 and 5d6 drop 2.[CODE]oc&nbsp; &nbsp; &nbsp; 3d6&nbsp; &nbsp;&nbsp; 4d6&nbsp; &nbsp;&nbsp; 5d6&nbsp; &nbsp;&nbsp; 3d6 P&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 4d6 P&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 5d6 P18&nbsp; &nbsp; 1&nbsp; &nbsp; 21&nbsp; &nbsp; 276&nbsp; &nbsp; 0.004630&nbsp; &nbsp; 0.016204&nbsp; &nbsp; 0.03549417&nbsp; &nbsp; 3&nbsp; &nbsp; 54&nbsp; &nbsp; 610&nbsp; &nbsp; 0.013889&nbsp; &nbsp; 0.041667&nbsp; &nbsp; 0.07844716&nbsp; &nbsp; 6&nbsp; &nbsp; 94&nbsp; &nbsp; 935&nbsp; &nbsp; 0.027778&nbsp; &nbsp; 0.072531&nbsp; &nbsp; 0.12024215&nbsp; &nbsp; 10&nbsp; &nbsp; 131&nbsp; &nbsp; 1111&nbsp; &nbsp; 0.046296&nbsp; &nbsp; 0.101080&nbsp; &nbsp; 0.14287614&nbsp; &nbsp; 15&nbsp; &nbsp; 160&nbsp; &nbsp; 1155&nbsp; &nbsp; 0.069444&nbsp; &nbsp; 0.123457&nbsp; &nbsp; 0.14853413&nbsp; &nbsp; 21&nbsp; &nbsp; 172&nbsp; &nbsp; 1055&nbsp; &nbsp; 0.097222&nbsp; &nbsp; 0.132716&nbsp; &nbsp; 0.13567412&nbsp; &nbsp; 25&nbsp; &nbsp; 167&nbsp; &nbsp; 881&nbsp; &nbsp; 0.115741&nbsp; &nbsp; 0.128858&nbsp; &nbsp; 0.11329711&nbsp; &nbsp; 27&nbsp; &nbsp; 148&nbsp; &nbsp; 665&nbsp; &nbsp; 0.125000&nbsp; &nbsp; 0.114198&nbsp; &nbsp; 0.08552010&nbsp; &nbsp; 27&nbsp; &nbsp; 122&nbsp; &nbsp; 470&nbsp; &nbsp; 0.125000&nbsp; &nbsp; 0.094136&nbsp; &nbsp; 0.0604429&nbsp; &nbsp; 25&nbsp; &nbsp; 91&nbsp; &nbsp; 296&nbsp; &nbsp; 0.115741&nbsp; &nbsp; 0.070216&nbsp; &nbsp; 0.0380668&nbsp; &nbsp; 21&nbsp; &nbsp; 62&nbsp; &nbsp; 170&nbsp; &nbsp; 0.097222&nbsp; &nbsp; 0.047840&nbsp; &nbsp; 0.0218627&nbsp; &nbsp; 15&nbsp; &nbsp; 38&nbsp; &nbsp; 90&nbsp; &nbsp; 0.069444&nbsp; &nbsp; 0.029321&nbsp; &nbsp; 0.0115746&nbsp; &nbsp; 10&nbsp; &nbsp; 21&nbsp; &nbsp; 41&nbsp; &nbsp; 0.046296&nbsp; &nbsp; 0.016204&nbsp; &nbsp; 0.0052735&nbsp; &nbsp; 6&nbsp; &nbsp; 10&nbsp; &nbsp; 15&nbsp; &nbsp; 0.027778&nbsp; &nbsp; 0.007716&nbsp; &nbsp; 0.0019294&nbsp; &nbsp; 3&nbsp; &nbsp; 4&nbsp; &nbsp; 5&nbsp; &nbsp; 0.013889&nbsp; &nbsp; 0.003086&nbsp; &nbsp; 0.0006433&nbsp; &nbsp; 1&nbsp; &nbsp; 1&nbsp; &nbsp; 1&nbsp; &nbsp; 0.004630&nbsp; &nbsp; 0.000772&nbsp; &nbsp; 0.000129[/CODE]</blockquote>

[QUOTE="frisbeet, post: 1230211, member: 10287"] So here are some numbers to start with. In this example I consider n=3,4,&5; s=6, and d = 0,1,or 2. I've been thinking along the lines of: 1). Count the ways of rolling the outcome with 3 dice. We've done this already in this thread. 2). For each way of rolling an outcome, count the number of ways of replacing the highest dice with the discarded dice. Add, not multiply, the results of 1 & 2. So # ways of getting a 6 by 4d6 drop 1 = #ways of 3d6 getting a 6 + comb(3,0) + comb(3,0) + comb (3,1) + comb (3,1) + comb(3,2) = 21 By a more brutal but accurate method I've determined the distributions for 4d6 drop1 and 5d6 drop 2. [CODE] oc 3d6 4d6 5d6 3d6 P 4d6 P 5d6 P 18 1 21 276 0.004630 0.016204 0.035494 17 3 54 610 0.013889 0.041667 0.078447 16 6 94 935 0.027778 0.072531 0.120242 15 10 131 1111 0.046296 0.101080 0.142876 14 15 160 1155 0.069444 0.123457 0.148534 13 21 172 1055 0.097222 0.132716 0.135674 12 25 167 881 0.115741 0.128858 0.113297 11 27 148 665 0.125000 0.114198 0.085520 10 27 122 470 0.125000 0.094136 0.060442 9 25 91 296 0.115741 0.070216 0.038066 8 21 62 170 0.097222 0.047840 0.021862 7 15 38 90 0.069444 0.029321 0.011574 6 10 21 41 0.046296 0.016204 0.005273 5 6 10 15 0.027778 0.007716 0.001929 4 3 4 5 0.013889 0.003086 0.000643 3 1 1 1 0.004630 0.000772 0.000129 [/CODE] [/QUOTE]

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