Probabilities for opposed skill checks

[kamosa]

An easier way to do it, is to make the "defender"'s skill bonus+10 the target number, basically like an AC score. The check is rolled like an attack, with the exception of tie going to the defender.

So a person trying to sense motive +5 (the attacker) against a person with bluff +7, needs to make a s.m. check against DC 17.

This is basically a variation on a rules variation offered in Unearthed Arcana, for players to "defend themselves" by rolling enemie's attack rolls (well, actually, they roll their ACbonus+d20 vs 10+enemies Attack Bonus, but... that is a tale for another time)

Easier on you, but much harder on the players. Essentially you are saying that the NPC always takes 10 on their check. Say the player and the defender have the same skill level then you are saying that you want the skill to fail over 50% of the time. That is pretty harsh.

 

[Gnimish88]

Thanks for the information!
As far as why I asked, it came up in a game recently that the amount of time actually roleplayed through probably accounted for about 10% of the time that would characters would actually have been spent interacting. Bear in mind that this includes a lengthy ocean voyage at the start of the campaign.
Over the course of the first several sessions, a couple of the characters were played as less then honest, nothing particularly bad. Eventually, they ended up getting paid for attempting to kill us (impersonated our would be assassins). With all the players at the table, one stated that he was taking 20 of the 50 gp out of the bag and told the other one he would split it with him. When they rejoined the party, they told of being paid. When asked how much, one said "Let's see" and dumped out the bag. Since this constituted a deception, a Sense Motive check was called for by one of the players. This caused an uproar, with them saying we should trust them and that we have no reason to make sense motive checks. Granted that several things were handled wrong in this instance, but that is pretty much how it went down.

The arguement mostly went that since they hadn't actually been caught lying by party members in the past, we had no reason to distrust them in this case.

It seems reasonable that the behavior of the characters in that 10% represents their behavior the other 90%. Given this, it is quite likely that they would have been dishonest at other times and no one gets lucky on the dice forever. That got me started on the mental exercise of how often one can, in fact, lie to all of the people. Thus did I come here, looking for satisfaction to my curiousity. The in game problems are being resolved and certainly nothing in the game rests on the statistics in question.

Sorry for the somewhat disjointed response and thanks again for the replies.

 

[Quasqueton]

the amount of time actually roleplayed through probably accounted for about 10% of the time that would characters would actually have been spent interacting.

New thread coming up.

Quasqueton

 

[Plane Sailing]

Your probability of winning an opposed check can be calculated as follows, assuming the defender wins ties.

D = (your bonus) - (opponent's bonus).

%victory = 0.475 + (41D-D^2)/800.

I could explain the whole formula, but that's the distillation. If your skill is 7 and your opponent's is 3, -> D=4, your probability of victory on any given roll is 66%.

Dan, Just wanted to say thanks for the good work here. I've often wondered how to easily (!) compute the probability of two competing skills winning a match in the d20 system but never got the time together to work it out. Now I don't have to! I'm particularly glad that you included the derivation of the formula too.

Cheers