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I'm asking here because I know there are lots of smart gamers here who might enjoy helping me solve this. I'm trying to work out the probabilities of hitting a target number when rolling a set of d6s. But not just a standard bell curve. The method I'm looking at is borrowed from another game - Heavy Gear, I believe. It is to roll a number of D6, take the highest die as your result. If any of the other dice match that die, then add +1 to the result. So, for example, rolling 3 d6, and getting a 5, a 4 and a 1 would be a result of 5. Rolling a result of a 5, a 4 and another 5 would be a result of 6 (5+1 for the second 5 =6) 1,1,1 = 3 1,1,4= 4 6,6,6= 8 etc, etc. I was able to work out the probabilities with using two, three and four d6 manually - here are my charts: Number of each result 1 2 3 4 5 6 7 8 9 1d 1 1 1 1 1 1 2d 3 5 7 9 11 1 3d 3 16 34 58 88 16 1 4d 38 137 319 609 167 21 1 Chance to hit Target Number TN 2 TN 3 TN 4 TN 5 TN 6 TN 7 TN 8 TN 9 1d 83.3% 66.7% 50.0% 33.3% 16.7% 0.0% 0.0% 0.0% 2d 100.0% 91.7% 77.8% 58.3% 33.3% 2.8% 0.0% 0.0% 3d 100.0% 98.6% 91.2% 75.5% 48.6% 7.9% 0.5% 0.0% 4d 100.0% 97.1% 86.5% 61.8% 14.6% 1.7% 0.1% But doing it manually for any further amounts of dice is going to be far too time consuming, considering that 5d6 has 7776 different combinations, and 6d6 has 46656, and I'm looking to go to as many as 12d6, which is 2 trillion or so combinations. So the puzzle I'm looking to solve right now is designing a formula to build the next rows on my top chart. Which is going to be a chore, because figuring out complex formula's like that is not my strong suit, nor is coding them into Excel. Any help is appreciated, if you want to give it.
I've got a long term project on the go - I'm designing a skirmish game, set in a slightly-fantasyish 14th century England. It's a slow process, but I've made a start, and I'll be working on it whenever I get spare time. If you fancy a look, I've started a small blog to document the development process here: http://ravensrodd.com/ And because posting just a link to a blog is a bit naughty, here's a couple of pics of minis for the project... Anyway, thanks if you take the time to look, and any feedback is appreciated; either here, or by email. cheers, Michael