01-20-2016, 07:13 PM | #1 |
Join Date: Sep 2004
Location: Medford, MA
|
Gathering Successes Thresholds (Call for Math Wizards)
Hi All You Math Wizards!
There is this thing that I do in my GURPS campaigns for long skill tasks while in combat time that makes everything very exciting. It is sort of inspired by other game systems but also inspired by energy gathering magic from Thaumatology. Let's say there is a fire fight going on. Some PCs are shooting, trying to hold off the bad guys...while one PC is trying to search a computer for incriminating information. How long does that take? I like to make the hero roll against the relevant skill (say Computer Hacking), and gather a certain amount of margin of successes before the task is complete. They also get 1 for a success and 2 for a Critical Success. So, maybe the Hacker needs to gather a margin of success of 10. Turn 1 she succeeds by 4. With it 1 for the success she has a total of 5 and she needs to gather another 5 margin of successes before she finds the hidden info. Then the other players shoot, aim, whatever. Next turn she succeeds by 3...she'll need one more turn...and turn 3 she gets what she needs and now the team can start retreating. Failure results in no progress. Crit fail either results in loss of all accumulated successes, or you can no longer do the task depending on what makes sense. So far this has been really fun and the players have all enjoyed it. So what am I asking of the math wizards? You who know probabilities? So on average, given x skill level, how many turns will it take to achieve y success margins? How would one construct a chart or table that could be made with the x axis being skill level, y axis success margins and the then data in the table the average number of turns it would take? If I had that I could decide on difficulty levels. Thanks math wizards! |
01-20-2016, 08:04 PM | #2 |
Join Date: Dec 2013
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
I tried to assemble a table with this information, using the assumption that Critical Failures have no effect other than not adding a success (it would complicate things greatly):
Code:
Skill Average Successes\Threshold 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3 0.023 44 87 131 174 218 261 305 348 392 435 479 522 566 609 653 696 740 783 827 870 4 0.0414 25 49 73 97 121 145 170 194 218 242 266 290 315 339 363 387 411 435 459 484 5 0.0875 12 23 35 46 58 69 80 92 103 115 126 138 149 160 172 183 195 206 218 229 6 0.1798 6 12 17 23 28 34 39 45 51 56 62 67 73 78 84 89 95 101 106 112 7 0.3415 3 6 9 12 15 18 21 24 27 30 33 36 39 41 44 47 50 53 56 59 8 0.6004 2 4 5 7 9 10 12 14 15 17 19 20 22 24 25 27 29 30 32 34 9 0.975 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 10 1.4746 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11 11 12 13 13 14 11 2.0992 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 12 2.8413 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 8 13 3.6806 1 1 1 2 2 2 2 3 3 3 3 4 4 4 5 5 5 5 6 6 14 4.5893 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 15 5.5719 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 16 6.6007 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 17 7.5833 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 18 8.5659 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 Code:
Skill Chance of CritFail\Rolls 1 2 3 4 5 6 7 8 9 10 15 20 25 30 45 50 75 100 150 200 3 0.2589 0.26 0.45 0.59 0.7 0.78 0.83 0.88 0.91 0.93 0.95 0.99 1 1 1 1 1 1 1 1 1 4 0.1617 0.16 0.3 0.41 0.51 0.59 0.65 0.71 0.76 0.8 0.83 0.93 0.97 0.99 0.99 1 1 1 1 1 1 5 0.0923 0.09 0.18 0.25 0.32 0.38 0.44 0.49 0.54 0.58 0.62 0.77 0.86 0.91 0.95 0.99 0.99 1 1 1 1 6 0.0461 0.05 0.09 0.13 0.17 0.21 0.25 0.28 0.31 0.35 0.38 0.51 0.61 0.69 0.76 0.88 0.91 0.97 0.99 1 1 7 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 8 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 9 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 10 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 11 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 12 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 13 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 14 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 15 0.0184 0.02 0.04 0.05 0.07 0.09 0.11 0.12 0.14 0.15 0.17 0.24 0.31 0.37 0.43 0.57 0.6 0.75 0.84 0.94 0.98 16 0.0046 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.07 0.09 0.11 0.13 0.19 0.21 0.29 0.37 0.5 0.6 17 0.0046 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.07 0.09 0.11 0.13 0.19 0.21 0.29 0.37 0.5 0.6 18 0.0046 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.07 0.09 0.11 0.13 0.19 0.21 0.29 0.37 0.5 0.6 Last edited by Eukie; 01-21-2016 at 08:18 PM. |
01-20-2016, 10:56 PM | #3 |
Join Date: Sep 2004
Location: Medford, MA
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
That's amazing. Could you explain how you did the math so I could learn something about this?
|
01-21-2016, 01:50 AM | #4 | |
Join Date: Sep 2011
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
Quote:
[php]effective skill Successes/Roll Rolls/Success 3 -0.250 4 -0.120 5 -0.005 6 0.134 7.448 7 0.324 3.086 8 0.583 1.714 9 0.958 1.043 10 1.458 0.686 11 2.083 0.480 12 2.605 0.384 13 3.662 0.273 14 4.569 0.219 15 5.551 0.180 16 6.579 0.152 17 7.560 0.132 18 8.556 0.117[/php] As to the math, this would apply to both Eukie's tables and mine, allowing for our different assumptions. The probability for threshold margins of success for any effective skill level is the sum of probabilities for each possible die roll and the probability for each die roll is (margin of success +1 [or +2, if a critical success] x probability of that die roll). For example, for skill level 18, a roll of 6 has a threshold probability of 12 [margin of success]+2 [for being a critical success] = 14 x 10/216 (probability of rolling a 6 on 3d6) = 0.648 to 3 decimal places. For skill level 18, a roll of 7 has a threshold probability of 11 [margin of success] +1 [for being an ordinary success] = 12 x 15/216 (probability of rolling a 7 on 3d6) = 0.833 to three decimal places. The probability for skill level 18 as a whole is the sum: 0.079 [probability of a 3] + 0.222 [probability of a 4] + 0.417 [5]+ 0.648 [6] + 0.833 [7] + 1.069 [8] + 1.157 [9] + 1.125 [10] + 1 [11] + 0.810 [12] + 0.583 [13] + 0.347 [14] + 0.185 [15] + 0.083 [16] +0 [17] -0.005 [18] = 8.556 successes gained on any given roll. The number of rolls/success is the reciprocal of the number of successes/roll or 1/(successes/roll). Where Eukie and I differ is in calculating the effects of a critical failure. Eukie treated them as ordinary failures, giving a probability of zero. I treated them as giving a value of -1, effectively undoing one success. While this isn't strictly accurate as a critical failure removes all the successes, it's useful in determining which skill levels are likely to accumulate more critical failures than successes (whether critical or ordinary).As can be seen in my table, any time the effective skill is reduced to 5 or less, there is very little hope of getting even a single success. My tables don't provide a lookup for the number of turns to garner y successes but the rolls/success for skill levels 6-9 and the successes/roll for skills 10+ should provide a useful guide for judging that. Last edited by Curmudgeon; 01-21-2016 at 02:46 AM. Reason: hit submit by accident |
|
01-21-2016, 04:19 AM | #5 | |
Join Date: Dec 2013
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
Quote:
|
|
01-21-2016, 05:06 AM | #6 | ||
Join Date: Sep 2011
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
Quote:
Quote:
I'd interpret that as succeeding by the skin of your teeth, so you're not better positioned than simple success would indicate while someone with a margin of success of 1 succeeded and has managed gain one or more minor advantages into the bargain, so that he's competitively better off. |
||
01-21-2016, 11:01 AM | #7 | |
Join Date: Aug 2004
Location: Nashville, TN
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
Quote:
__________________
I didn't realize who I was until I stopped being who I wasn't. Formerly known as Bookman- forum name changed 1/3/2018. |
|
01-21-2016, 11:33 AM | #8 |
Join Date: Aug 2005
Location: Denmark
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
I have used it for great effect in D&D 4e. I hadn't really thought much of using it in GURPS but i's a really good idea. Gives lot more interesting thins to do for none-combat characters. Good idea!
|
01-21-2016, 12:21 PM | #9 | |
Join Date: Sep 2011
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
Quote:
|
|
01-21-2016, 12:32 PM | #10 |
Join Date: Sep 2004
Location: Medford, MA
|
Re: Gathering Successes Thresholds (Call for Math Wizards)
I'm thinking about writing this up as a quick little article for Pyramid...but I do have one thing I go back and forth on...and that is the result of failure, and I'd love people's thoughts.
So far I have ruled that a failure results in no progress, crit fail wipes out all progress and/or no longer allows for any more attempts (you jam the lock, your terminal is disconnected from the mainframe, etc). This is somewhat generous to the players because there is no negative consequences for a failure beyond taking more time. Here is my question: do you think there should be some sort of penalty for failure? -1 to accumulated MoS? Should it mirror the positive side and give -1 and the Margin of Failure on a failed roll? Do you think it is more fair to mirror the the positive and the negative completely? What you gain is what you can lose? This would allow for contests of skills to work in this system like a tug of war. Thoughts? |
Thread Tools | |
Display Modes | |
|
|