With apologies if there have already been too many of these. Lets do an example of an opposed skill check using some non-combat skills (since combat skills are supposed to not be halved.)
We have a trollkin and a human using the skill.
Warning: I did this using the windows calculator which is kinda sucky and it's 9:00 pm at night. So although I think it is correct I might have made an error using that silly calculator.
Also note that there is some ambiguity in the rules on page 20. I assume, for example, that if both fail and get the same roll so that neither is "lowest" they just have to reroll. The rules do not make it clear, at least in that section of the rulebook.
(A) Scenario 1. Human has skill at 100 and trollskin has skill at 30. Then the trollskin wins the skill test if:
trollkin succeeds&human fails+trollkin succeeds&human succeeds but worse than trollkin+trollkin fails&human fails worse than trollkin
=(.30)(.05)+(.01)(.01+.02+...+.29)+(.01)(65(.05)+.04+.03+.02+.01)
=(.30)(.05)+(.01)(.01)(1+2+...29)+(.01)(.01)(69+70+....+100)
=(.30)(.05)+(.01)(.01)(29)(30)(.5)+(.01)(40(.30)+(29)(30)(.5)(.01))
=.015+.0435+.0335=.092
In other words, 9.2% of the time.
(B) Scenario 2: Human has skill at 120 and trollkin still has skill at 30. So we halve things to get new human skill 60 and new trollkin skill 15.
Along the same lines as above, the trollkin wins the skill test if:
=(.15)(.4)+(.01)(.01+.02+...+.15)+(.01)(45(.4)+.39+.38+...+.01)
=.06+.012+.258=.33
In other words, 33% of the time.
Again, with apologies if this has been done too much. I just wanted to give one concrete example at least.
We have a trollkin and a human using the skill.
Warning: I did this using the windows calculator which is kinda sucky and it's 9:00 pm at night. So although I think it is correct I might have made an error using that silly calculator.
Also note that there is some ambiguity in the rules on page 20. I assume, for example, that if both fail and get the same roll so that neither is "lowest" they just have to reroll. The rules do not make it clear, at least in that section of the rulebook.
(A) Scenario 1. Human has skill at 100 and trollskin has skill at 30. Then the trollskin wins the skill test if:
trollkin succeeds&human fails+trollkin succeeds&human succeeds but worse than trollkin+trollkin fails&human fails worse than trollkin
=(.30)(.05)+(.01)(.01+.02+...+.29)+(.01)(65(.05)+.04+.03+.02+.01)
=(.30)(.05)+(.01)(.01)(1+2+...29)+(.01)(.01)(69+70+....+100)
=(.30)(.05)+(.01)(.01)(29)(30)(.5)+(.01)(40(.30)+(29)(30)(.5)(.01))
=.015+.0435+.0335=.092
In other words, 9.2% of the time.
(B) Scenario 2: Human has skill at 120 and trollkin still has skill at 30. So we halve things to get new human skill 60 and new trollkin skill 15.
Along the same lines as above, the trollkin wins the skill test if:
=(.15)(.4)+(.01)(.01+.02+...+.15)+(.01)(45(.4)+.39+.38+...+.01)
=.06+.012+.258=.33
In other words, 33% of the time.
Again, with apologies if this has been done too much. I just wanted to give one concrete example at least.