Article: 14177 of rec.games.frp.dnd Path: email!news.univie.ac.at!paladin.american.edu!howland.reston.ans.net!zaphod.mps.ohio-state.edu!sdd.hp.com!saimiri.primate.wisc.edu!usenet.coe.montana.edu!netnews.nwnet.net!news.uoregon.edu!dtyler1.uoregon.edu!bretwood From: bretwood@oregon.uoregon.edu (Bret Wood) Newsgroups: rec.games.frp.dnd Subject: Re: followup (4d6, 5d6, 6d6 probabilities) Date: Wed, 12 May 1993 20:19:11 GMT Organization: University of Oregon Lines: 151 Message-ID: References: <1993May11.182013.1@hmcvax.claremont.edu> <30695@galaxy.ucr.edu> NNTP-Posting-Host: dtyler1.uoregon.edu OK, here is the answer to the xd6 keep the highest three question for x = 3, 4, 5, 6, 7, 8, 9 I wrote a program in C called dice. It works like this: dice i j k (Gives the probabilities for the sum of the k highest i sided dice when j dice are rolled) I couldn't use a series of nested loops since the number of dice is undetermined, so it is recursive. If anyone wants a copy, send me e-mail -Bret Wood (bretwood@oregon.uoregon.edu) Here's the results: 3 dice, keep the highest 3 (I know, this one's easy) Value # of Hits %Chance ----- --------- ----------- 3 1 0.462963 4 3 1.388889 5 6 2.777778 6 10 4.629630 7 15 6.944445 8 21 9.722222 9 25 11.574074 10 27 12.500000 11 27 12.500000 12 25 11.574074 13 21 9.722222 14 15 6.944445 15 10 4.629630 16 6 2.777778 17 3 1.388889 18 1 0.462963 Total number of combinations -- 216 4 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.077160 4 4 0.308642 5 10 0.771605 6 21 1.620370 7 38 2.932099 8 62 4.783951 9 91 7.021605 10 122 9.413580 11 148 11.419753 12 167 12.885802 13 172 13.271605 14 160 12.345679 15 131 10.108025 16 94 7.253087 17 54 4.166667 18 21 1.620370 Total number of combinations -- 1296 5 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.012860 4 5 0.064300 5 15 0.192901 6 41 0.527263 7 90 1.157407 8 170 2.186214 9 296 3.806584 10 470 6.044239 11 665 8.551954 12 881 11.329733 13 1055 13.567387 14 1155 14.853395 15 1111 14.287552 16 935 12.024177 17 610 7.844650 18 276 3.549383 Total number of combinations -- 7776 6 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.002143 4 6 0.012860 5 21 0.045010 6 78 0.167181 7 207 0.443673 8 447 0.958076 9 914 1.959019 10 1677 3.594393 11 2706 5.799897 12 4135 8.862741 13 5646 12.101337 14 7056 15.123457 15 7770 16.653807 16 7551 16.184414 17 5535 11.863426 18 2906 6.228567 Total number of combinations -- 46656 7 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.000357 4 7 0.002501 5 28 0.010002 6 148 0.052869 7 469 0.167538 8 1141 0.407593 9 2745 0.980581 10 5747 2.052969 11 10409 3.718350 12 18159 6.486840 13 27979 9.994784 14 39277 14.030707 15 48798 17.431841 16 54096 19.324417 17 44121 15.761103 18 26811 9.577546 Total number of combinations -- 279936 8 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.000060 4 8 0.000476 5 36 0.002143 6 283 0.016849 7 1052 0.062633 8 2844 0.169324 9 8117 0.483265 10 19252 1.146214 11 38648 2.301002 12 76543 4.557173 13 132168 7.868941 14 206032 12.266613 15 286501 17.057529 16 358828 21.363693 17 322812 19.219393 18 226491 13.484690 Total number of combinations -- 1679616 9 dice, keep the highest 3 Value # of Hits %Chance ----- --------- ----------- 3 1 0.000010 4 9 0.000089 5 45 0.000447 6 547 0.005428 7 2340 0.023220 8 6948 0.068944 9 23806 0.236225 10 63612 0.631216 11 140049 1.389693 12 314245 3.118223 13 604863 6.001997 14 1037223 10.292263 15 1607641 15.952466 16 2257245 22.398424 17 2222676 22.055399 18 1796446 17.825960 Total number of combinations -- 10077696