 Challenge: Open-ended Dice on the HP-41 - Printable Version +- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: Challenge: Open-ended Dice on the HP-41 (/thread-155850.html) Challenge: Open-ended Dice on the HP-41 - Geir Isene - 09-06-2009 This challenge is derived from creating applications for the Amar role-playing game. It is a challenge involving the extension of the normal dice with 6 sides - a so called open-ended dice throw. Definition: Take a dice with 6 sides. Now we would like to extend the range of the numbers beyond the intrinsic 1 to 6. A way to accomplish that is to make the 1 and the 6 special cases. Whenever you throw a 6, you can extend the range by making another throw. A throw of 4 to 6 (50%) will add 1 to the original 6. Throw again and a result of 4 to 6 will again add 1 to the number (making it 8) etc. Every throw of 4 to 6 will add one until you get a 1, 2 or 3, then it stops. Conversely, throwing a 1 on the first throw is a special case. Throw again, and a result of 1 to 3 will subtract 1 from the original number. Keep throwing 1, 2 or 3 to subtract one... until you throw a 4, 5 or 6 - then it stops. Now we add a dimension; Whenever you throw two 6's consecutively it is marked as a "critical". A throw of two consecutive 1's is a "fumble". All this is called an "open-ended" dice throw. A normal dice roll is termed a D6, an open-ended roll is O6. Challenge: Create a program for the HP-41 that does open-ended dice rolls. It should show whether the roll also includes a "critical"/"fumble". Do this without using any storage registers - i.e. only using the stack (and the Alpha register if you wish). I will publish my solution for dissection in a few days :-) Re: Challenge: Open-ended Dice on the HP-41 - hugh steers - 09-06-2009 i was interested in how far out from [1,6] the "openness" might get. So i hacked up a quick program in Lua to print out a histogram. here's what i get after a million goes: the first column is the value and the second the percentage of trials hitting that value. ```1 8.2905 2 16.6888 3 16.6197 4 16.6964 5 16.7057 6 8.3628 7 4.1587 8 2.0964 9 1.0276 10 0.5105 11 0.264 12 0.1336 13 0.0652 14 0.0334 15 0.0141 16 0.0092 17 0.0041 18 0.0024 19 0.0011 20 0.0003 21 0.0002 22 0.0001 23 0.0002 -1 2.0857 0 4.1388 -2 1.0439 -3 0.5196 -4 0.2631 -5 0.1331 -6 0.0665 -7 0.0324 -8 0.0163 -9 0.0072 -10 0.0041 -11 0.0015 -12 0.0013 -13 0.0008 -14 0.0005 -15 0.0001 -16 0.0001 total 100 critical = 2.7771 fumble = 2.7606 ``` So we have a [2,4] plateau (1/6 as expected), then 50% falloff each side. However, it's interesting to note that the "critical" and "fumble" percentages are almost 1 in 36. This indicates that you don't really get much difference tracking consecutive 1's and 6's after the first go. Consequently, i modified my simulator to count a "critical" as 2 6's at the start and a "fumble" as 2 1's. here's what i get: ```1 8.2841 2 16.659 3 16.6423 4 16.7312 5 16.7244 6 8.2914 7 4.2017 8 2.0684 9 1.0386 10 0.5212 11 0.2641 12 0.1315 13 0.0618 14 0.0322 15 0.0185 16 0.0073 17 0.0041 18 0.002 19 0.0012 20 0.0006 22 0.0001 23 0.0001 24 0.0001 -7 0.0298 -8 0.0176 -9 0.0072 -10 0.0033 -11 0.0024 -12 0.0006 -13 0.0006 -14 0.0003 -1 2.0799 0 4.1518 -2 1.0266 -3 0.5313 -4 0.2638 -5 0.1286 -6 0.0701 -15 0.0002 total 100 critical = 2.7716 fumble = 2.7501 ``` Similar story. So i would say, for the purposes of generating values for Amar, you could simplify your algorithm on the 41c and not track consecutive values. which should shorten the program. here are my two versions. o6() is the "real" algorithm and "os6plain" is my hacked one. ```function d6() return math.floor(math.random()*6+1) end function o6() local v = d6() local d local crit = false local fumb = false local c = true if v == 6 then while true do d = d6() if d >= 4 then v = v + 1 if d == 6 then crit = c c = true else c = false end else break end end elseif v == 1 then while true do d = d6() if d < 4 then v = v - 1 if d == 1 then fumb = c c = true else c = false end else break end end end return v,crit,fumb end function o6plain() local v = d6() local crit = false local fumb = false if v == 6 then crit = d6() == 6 while d6() >= 4 do v = v + 1 end elseif v == 1 then fumb = d6() == 1 while d6() < 4 do v = v - 1 end end return v,crit,fumb end ``` Re: Challenge: Open-ended Dice on the HP-41 - hugh steers - 09-06-2009 Uh-oh! i made a mistake tracking the consecutive values. The difference is actually more - about 3% instead of 2.7 should be, ```function o6() local v = d6() local d local crit = false local fumb = false local c = true if v == 6 then while true do d = d6() if d >= 4 then v = v + 1 if d == 6 then if c then crit = true end c = true else c = false end else break end end elseif v == 1 then while true do d = d6() if d < 4 then v = v - 1 if d == 1 then if c then fumb = true end c = true else c = false end else break end end end return v,crit,fumb end ``` so, it depends on whether you really want to track consecutive values or not.