tag:blogger.com,1999:blog-2657266526705426756.post7956670112918887995..comments2023-11-11T12:33:18.751-05:00Comments on The Wandering Gamist: Downtimejedavishttp://www.blogger.com/profile/08586249502818922886noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2657266526705426756.post-83631328332132999352017-12-23T09:11:55.183-05:002017-12-23T09:11:55.183-05:00Oh, ok - that makes a lot of sense in the context ...Oh, ok - that makes a lot of sense in the context of the apprentice discussion.jedavishttps://www.blogger.com/profile/08586249502818922886noreply@blogger.comtag:blogger.com,1999:blog-2657266526705426756.post-71551571742930529832017-12-23T08:06:02.181-05:002017-12-23T08:06:02.181-05:00Bah - sorry. The table I was looking at had the &#...Bah - sorry. The table I was looking at had the 'half time for formula' applied to it. (2.86/2==1.43), and I had meant to write 2.86 rather than 2.68. Severe posting failure :)<br />Koewnhttps://www.blogger.com/profile/01417138644425141883noreply@blogger.comtag:blogger.com,1999:blog-2657266526705426756.post-42149482138783352582017-12-22T20:57:05.743-05:002017-12-22T20:57:05.743-05:00That method makes sense, but it definitely doesn&#...That method makes sense, but it definitely doesn't converge to 1.43. The first ten terms sum to 2.68. I get around 2.86 with ten million terms, off by a factor of 2. Wolfram seems to agree, at https://www.wolframalpha.com/input/?i=sum+((1-0.35)%5Ek+*+0.35)+*+(1+%2B+1*k),+k%3D0..infinity ?jedavishttps://www.blogger.com/profile/08586249502818922886noreply@blogger.comtag:blogger.com,1999:blog-2657266526705426756.post-42074549214284601782017-12-22T19:29:30.309-05:002017-12-22T19:29:30.309-05:00Convergent series, evidently? Had I known I'd ...Convergent series, evidently? Had I known I'd be using this stuff some 20 years later, for the silly elf game no less, I'd have paid more attention in my various college math classes.<br /><br /> ((1-p)^k * p) * (f + f*k)<br /><br />where p is probability, f is the factor (base cost, base time), k is the answer we're getting.<br /><br />sum ((1-0.35)^k * 0.35) * (1 + 1*k), k=0..infinity<br /><br />in Wolfram Alpha will give you the goods; .35 being the probability of success at 14+, solving for time (1 week base) here.<br /><br />Being an unsubtle man, I brute force it in Perl when I want to generate a whole table.<br /><br /><br /><br />Koewnhttps://www.blogger.com/profile/01417138644425141883noreply@blogger.comtag:blogger.com,1999:blog-2657266526705426756.post-1025534299678433322017-12-22T17:50:55.054-05:002017-12-22T17:50:55.054-05:00Interesting! How did you get 1.43 / what summatio...Interesting! How did you get 1.43 / what summation did you do, exactly? I would expect 14+ to take something like 3x base cost and time (oh, divide that by 2 with 10+ as your baseline?).<br /><br />Yeah, we've never really considered apprentices viable; our 5th-6th level casters have enough trouble getting any research done. I really like having apprentices add a bonus to the master; I think that would make them worth using.<br /><br />I am explicitly not worried about preserving the continuity of projects / I like the idea of freely stopping, starting, and switching projects a lot. It's a poor simulation of real research work (because, like, mental cache effects), but v0v.jedavishttps://www.blogger.com/profile/08586249502818922886noreply@blogger.comtag:blogger.com,1999:blog-2657266526705426756.post-22738814388855401422017-12-22T17:25:32.263-05:002017-12-22T17:25:32.263-05:00One thing I've done recently is to apply a sum...<br />One thing I've done recently is to apply a summation calculation to magical research - so that instead of binary success/failure, there's just extra cost and time applied to the process based on the magical research throw - so a roll of 14+, for example, means a potion takes you 1,429 of base cost and 1.43 weeks, ignoring the chance to fail in exchange for upfront cost.<br /><br />At 14+ the 85% success guarantee happens around the 8th roll; 99% around the 11th roll - so it's certainly advantageous; and it kinda approaches base costs at 4+ (588gp/.59 weeks, these numbers with with formula/sample)<br /><br />The other thing it kinda showed me is that L0 apprentices leveling to Mage 1 via successful magical research is expensive, evidently, anywhere from 20x-4x expected costs at the high MRTs. I've modeled apprentices instead granting a +1/-1 on a successful throw to the base caster's chances via summation, and then split the XP accordingly by individual successes, the main pool going to the leader; and it 'feels' ok, at least.<br /><br />The consistent summation process would grant some verisimilitude to projects one can stop/start; maybe with the requirement an apprentice has to watch the oven, so to speak; and it has the advantage of at least singing along with the default assumed costs of things, if not fully in tune.<br /><br />I've bookmarked your fork; I'm glad someone's thought to do it.Koewnhttps://www.blogger.com/profile/01417138644425141883noreply@blogger.com