11-24-2011, 01:00 PM | #11 |
Join Date: Aug 2009
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Re: The bell-curve for Luck
One important subtlety about how the Luck advantage works (without modifiers) is that when you use it, you have already made a bad roll. Therefore, a more accurate probabilistic analysis would take into account that the first roll failed, and then look at the likelihood of the two next rolls having at least one success. This can get a bit complicated of course since now you can't really ignore what your effective skill was.
The probability curve given in this thread is the one you get if you choose the Active limitation on Luck, which is still a very instructive analysis. :-) |
11-24-2011, 01:06 PM | #12 | |
Join Date: Nov 2007
Location: The City of Subdued Excitement
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Re: The bell-curve for Luck
Quote:
So, if p is the probability of rolling T or less, the probability of getting T or less at least once in 3 rolls is 1-(1-p)^3. (As usual when I'm working with probabilities, I checked this with my wife, who teaches college statistics.) Using that formula, your probability for at least one success, expressed at a percentage, are: Code:
Luck Regular 3: 1.38% 0.5% 4: 5.45% 1.8% 5: 13.26% 4.6% 6: 25.29% 9.2% 7: 41.16% 16.1% 8: 59.36% 25.9% 9: 75.59% 37.4% 10: 87.50% 49.9% 11: 94.73% 62.4% 12: 98.26% 74.1% 13: 99.57% 83.8% 14: 99.92% 90.7% 15: 99.99% 95.4% 16: 99.9994% 98.2% However, you usually use luck when you've already failed once (edit: bcd is a ninja), so it's usually more useful to ask what the odds of succeeding with the two rolls you have left are. The formula in this case is 1-(1-p)^2. Code:
Luck Regular 3: 0.92% 0.5% 4: 3.67% 1.8% 5: 9.04% 4.6% 6: 17.66% 9.2% 7: 29.78% 16.1% 8: 45.13% 25.9% 9: 60.94% 37.4% 10: 75.00% 49.9% 11: 85.94% 62.4% 12: 93.28% 74.1% 13: 97.37% 83.8% 14: 99.14% 90.7% 15: 99.79% 95.4% 16: 99.97% 98.2% Last edited by Grouchy Chris; 11-24-2011 at 01:11 PM. Reason: Darned ninjas. |
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11-24-2011, 01:10 PM | #13 |
Join Date: Oct 2009
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Re: The bell-curve for Luck
I guess I could check the book myself, but doesn't Luck give you 4 rolls in total? 1 failed original roll and 3 rerolls?
So, I'd rather look at the curve for 4 rolls, exaggerating it even further. This is your chance when you're willing to use Luck. (How often will you then actually use the advantage? Easy: Failure rate at effective skill.) Ts Last edited by Ts_; 11-24-2011 at 01:12 PM. Reason: typo |
11-24-2011, 01:11 PM | #14 | |
Join Date: Sep 2004
Location: Canada
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Re: The bell-curve for Luck
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Fortunately my computer at home and at work are good enough that I can do a substantial statistical sampling conveniently. If I were at home, I'd have based this on my multithreaded mass-dice-roller that I have there, and then since I'd be using all six cores, I probably would have kicked it up to 1k million rolls since it would still run pretty quickly. It's easy to just slap a few zeroes onto the end of my stop condition. It's hard to figure out probability. Cool.
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11-24-2011, 01:13 PM | #15 |
Join Date: Aug 2009
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Re: The bell-curve for Luck
It seems a bit unfair to give probabilities for Luck on the premise "the first roll has already failed", side by side with probabilities for normal use without that premise. Properly therefore, the "Regular" column should be all zeros to be comparable. :P
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11-24-2011, 01:13 PM | #16 | ||
Join Date: Sep 2004
Location: Canada
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Re: The bell-curve for Luck
Quote:
Quote:
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11-24-2011, 01:17 PM | #17 | |
Join Date: Sep 2004
Location: Canada
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Re: The bell-curve for Luck
Quote:
What I did, was show you what "best of three rolls" looks like. The first roll could be the best. These are not skill checks, these are the curve for "best of three rolls". The actual luck usage case is, as you've noted, different. I think it might actually skew things further towards the end.
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11-24-2011, 01:19 PM | #18 | |
Join Date: Sep 2004
Location: Canada
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Re: The bell-curve for Luck
Quote:
For example, I just tested the "best of 4" scenario and no 17s or 18s ever came up :) Code:
4x Luck 3x Luck Regular 3: 1.8375% 1.3832% 0.5% 4: 5.3775% 4.0677% 1.389% 5: 10.0936% 7.8090% 2.740% 6: 14.9343% 12.0218% 4.616% 7: 18.5378% 15.8806% 6.945% 8: 19.2047% 18.2009% 9.736% 9: 14.7819% 16.2288% 11.564% 10: 8.9922% 11.9093% 12.473% 11: 4.2772% 7.2197% 12.509% 12: 1.5167% 3.5351% 11.649% 13: 0.3788% 1.3187% 9.736% 14: 0.0607% 0.3452% 6.920% 15: 0.0069% 0.0706% 4.626% 16: 0.0002% 0.0089% 2.795% 17: 0.0006% 1.391% 18: 0.0000% 0.458%
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All about Size Modifier; Unified Hit Location Table A Wiki for my F2F Group A neglected GURPS blog |
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11-24-2011, 01:20 PM | #19 |
Join Date: Oct 2009
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Re: The bell-curve for Luck
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11-24-2011, 01:22 PM | #20 |
Join Date: Jan 2005
Location: Charlotte, North Caroline, United States of America, Earth?
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Re: The bell-curve for Luck
How do you people do this stuff?!
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