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Ignoring the extreme success case for now, and supposing the skill gives a probability p of success, then the probabilities of succeeding on the skill roll and then failing the learning roll (that ...
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#2: Post edited
by
tommi
·
2023-10-30T06:08:51Z (7 months ago)
- Ignoring the extreme success case for now, and supposing the skill gives a probability p of success, then the probabilities of succeeding on the skill roll and then failing the learning roll (that is, getting the increase) is p(1-p). This is a parabel with top at 1/2 and zeros at 0 and 1. It is symmetric as all parabels are. (The function is a second degree polynomial with a negative highest order term.)
However, if you get to test the skill several times, say n times, then you have n chances to succeed, while you still only get a single test to confirm that you fail. I can calculate the probabilities if desired, but the main point is that lower skills are indeed favoured - any of the rolls succeeding gives the advancement chance, while there is only a single try at "failing" that one.
- Ignoring the extreme success case for now, and supposing the skill gives a probability p of success, then the probabilities of succeeding on the skill roll and then failing the learning roll (that is, getting the increase) is p(1-p). This is a parabel with top at 1/2 and zeros at 0 and 1. It is symmetric as all parabels are. (The function is a second degree polynomial with a negative highest order term.)
- However, if you get to test the skill several times, say n times, then you have n chances to succeed, while you still only get a single test to confirm that you fail. I can calculate the probabilities if desired, but the main point is that lower skills are indeed favoured - any of the rolls succeeding gives the advancement chance, while there is only a single try at "failing" that one.
- The extreme success case happens rarely and essentially gives two attemps at the test to fail, so it will not affect the big picture, but it will somewhat improve the chances of success, especially where the skill level is high. A reasonable relative change, but still a small absolute one.
#1: Initial revision
by
tommi
·
2023-10-30T06:06:52Z (7 months ago)
Ignoring the extreme success case for now, and supposing the skill gives a probability p of success, then the probabilities of succeeding on the skill roll and then failing the learning roll (that is, getting the increase) is p(1-p). This is a parabel with top at 1/2 and zeros at 0 and 1. It is symmetric as all parabels are. (The function is a second degree polynomial with a negative highest order term.) However, if you get to test the skill several times, say n times, then you have n chances to succeed, while you still only get a single test to confirm that you fail. I can calculate the probabilities if desired, but the main point is that lower skills are indeed favoured - any of the rolls succeeding gives the advancement chance, while there is only a single try at "failing" that one.