11-24-2011, 02:38 PM | #31 |
Join Date: Aug 2004
Location: The ASS of the world, mainly Valencia, Spain (Europe)
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Re: The bell-curve for Luck
Emily, that's not the lazy option, the lazy option is to go to anydice.com and get this:
http://anydice.com/program/c40 Oh, and it does it by probability exploration, not by doing a gazillion trials ;) Oh, and it is fast! EDIT: Ninjaed by PseudoFenton! EDIT2: Anydice is just so nice... you can get nice tables, bar graphs, line graphs,... check "graph" and "at most" for the curves for GURPS probabilities |
11-24-2011, 04:24 PM | #32 |
Join Date: Oct 2009
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Re: The bell-curve for Luck
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11-24-2011, 05:10 PM | #33 |
Banned
Join Date: Oct 2007
Location: Europe
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Re: The bell-curve for Luck
If Bruno can't, it's presumably possible to do it in the Troll dice rolling analysis programming lanuage, by computer scientist Torben Mogensen.
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11-24-2011, 06:08 PM | #34 | |
Join Date: Sep 2004
Location: Canada
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Re: The bell-curve for Luck
Quote:
Here's 4d6 drop lowest 2 Code:
2: 0.08% 0.08% 3: 0.32% 0.40% 4: 1.15% 1.55% 5: 2.47% 4.02% 6: 5.05% 9.07% 7: 8.35% 17.42% 8: 13.28% 30.70% 9: 17.31% 48.01% 10: 20.08% 68.09% 11: 18.76% 86.85% 12: 13.15% 100.00% Code:
3: 0.01% 0.01% 4: 0.07% 0.08% 5: 0.19% 0.27% 6: 0.55% 0.82% 7: 1.15% 1.98% 8: 2.19% 4.17% 9: 3.81% 7.98% 10: 6.05% 14.03% 11: 8.52% 22.54% 12: 11.35% 33.90% 13: 13.49% 47.39% 14: 14.86% 62.24% 15: 14.30% 76.54% 16: 12.05% 88.59% 17: 7.87% 96.46% 18: 3.54% 100.00% Code:
2: 0.01% 0.01% 3: 0.07% 0.08% 4: 0.40% 0.48% 5: 1.03% 1.51% 6: 2.69% 4.20% 7: 5.19% 9.39% 8: 10.01% 19.39% 9: 15.38% 34.78% 10: 21.88% 56.65% 11: 23.69% 80.35% 12: 19.65% 100.00% 6d6 drop lowest 3 Code:
3: 0.002% 0.002% 4: 0.01% 0.01% 5: 0.05% 0.07% 6: 0.17% 0.23% 7: 0.44% 0.68% 8: 0.94% 1.62% 9: 1.95% 3.56% 10: 3.63% 7.19% 11: 5.81% 13.00% 12: 8.85% 21.85% 13: 12.08% 33.93% 14: 15.10% 49.03% 15: 16.67% 65.70% 16: 16.19% 81.89% 17: 11.89% 93.78% 18: 6.22% 100.00%
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11-24-2011, 09:51 PM | #35 |
Never Been Pretty
Join Date: Jan 2005
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Re: The bell-curve for Luck
Since Bruno's numbers are worked examples, rather than the actual probabilities, they do not always match the probabilities. And since I'm doing this by hand, I'll just show an example.
4d6 drop the two lowest 2: 0.08% 0.08% 3: 0.31% 0.39% 4: 1.16% 1.55% 5: 2.47% 4.02% Instead of 2: 0.08% 0.08% 3: 0.32% 0.40% 4: 1.15% 1.55% 5: 2.47% 4.02% |
11-25-2011, 01:26 AM | #36 |
Join Date: Oct 2004
Location: Yorkshire, UK
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Re: The bell-curve for Luck
Yep, the lazy way is much easier - and at 10million iterations is going to be close enough for most reasonable (rpg) scenarios. (ignoring 300d6 scenarios!)
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11-25-2011, 04:22 AM | #37 |
Join Date: Oct 2004
Location: Yorkshire, UK
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Re: The bell-curve for Luck
Here is a look at Success probabilities with Luck, accounting for succeeding without luck, and using Luck on a Failure.
For a given Target number, the first % column is the standard Success rate on 3d6; the second % column is the Success rate using Luck; the third % column is the % Success Rate of using Luck on an initial failure. Code:
Target Before Luck After Luck (% Successful Luck Usage) 3 0.4630% 1.3825% ( 0.9238%) 4 1.8519% 5.4533% ( 3.6694%) 5 4.6296% 13.2558% ( 9.0449%) 6 9.2593% 25.2851% ( 17.6612%) 7 16.2037% 41.1598% ( 29.7818%) 8 25.9259% 59.3558% ( 45.1303%) 9 37.5000% 75.5859% ( 60.9375%) 10 50.0000% 87.5000% ( 75.0000%) 11 62.5000% 94.7266% ( 85.9375%) 12 74.0741% 98.2574% ( 93.2785%) 13 83.7963% 99.5746% ( 97.3744%) 14 90.7407% 99.9206% ( 99.1427%) 15 95.3704% 99.9901% ( 99.7857%) 16 98.1481% 99.9994% ( 99.9657%) Last edited by SCAR; 11-25-2011 at 04:45 AM. Reason: To explain source of data |
11-25-2011, 04:44 AM | #38 | |
Join Date: Oct 2004
Location: Yorkshire, UK
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Re: The bell-curve for Luck
Quote:
I looked at rolling an extra 'Luck' d6 with the main 3d6; and Luck could be used to swap the Luck die for one of the 3d6; it's not as good as standard Luck (although pretty close for a Target number of 3 to 6), but you know before you use Luck if it's going to work for you! Charted as per standard Luck above: Code:
Target Before Luck After Luck (% Successful Luck Usage) 3 0.4630% 1.6204% ( 1.1628%) 4 1.8519% 5.7870% ( 4.0094%) 5 4.6296% 13.0401% ( 8.8188%) 6 9.2593% 23.1481% ( 15.3061%) 7 16.2037% 35.4938% ( 23.0203%) 8 25.9259% 48.7654% ( 30.8333%) 9 37.5000% 61.6512% ( 38.6420%) 10 50.0000% 73.0710% ( 46.1420%) 11 62.5000% 82.4846% ( 53.2922%) 12 74.0741% 89.5062% ( 59.5238%) 13 83.7963% 94.2901% ( 64.7619%) 14 90.7407% 97.2222% ( 70.0000%) 15 95.3704% 98.8426% ( 75.0000%) 16 98.1481% 99.6142% ( 79.1667%) Code:
Target Before Luck After Luck (% Successful Luck Usage) 3 0.4630% 3.5494% ( 3.1008%) 4 1.8519% 11.3940% ( 9.7222%) 5 4.6296% 23.4182% ( 19.7006%) 6 9.2593% 37.7058% ( 31.3492%) 7 16.2037% 52.5592% ( 43.3855%) 8 25.9259% 66.1265% ( 54.2708%) 9 37.5000% 77.4563% ( 63.9300%) 10 50.0000% 86.0082% ( 72.0165%) 11 62.5000% 92.0525% ( 78.8066%) 12 74.0741% 95.8591% ( 84.0278%) 13 83.7963% 98.0453% ( 87.9365%) 14 90.7407% 99.2027% ( 91.3889%) 15 95.3704% 99.7299% ( 94.1667%) 16 98.1481% 99.9228% ( 95.8333%) |
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11-25-2011, 05:16 AM | #39 |
Join Date: Apr 2010
Location: Land of the Britons
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Re: The bell-curve for Luck
Heh, they seem interesting though. I quite like doing the maths behind various exploding and imploding die methods to see how they'd alter the outcome of probabilities - although I can't say I've done this for Luck yet. It'd be fun to draw up a few alternative "Luck" advantages that had different statistical outcomes and mechanics and base the CP cost around the probability distribution accordingly. Fun in an utterly geeky sort of way, of cause.
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...like a monkey with a wrench. |
11-25-2011, 05:29 AM | #40 | |
Join Date: Oct 2004
Location: Yorkshire, UK
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Re: The bell-curve for Luck
Quote:
I think I was trying to avoid additional rolling, roll once (3d6+1d6) instead of: roll once then if using luck rolling twice more. |
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