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View Full Version : Contested Roll success propability in OWoD Storyteller system.



Gulian
2017-04-04, 03:25 AM
So, I'm trying to figure out the mathematics of winning a contested roll with varying dicepools in oWoD, in particular for the 2nd Valeren dot, Anesthetic Touch. I understand that the higher the difficulty, the less difference there is between each new die added to one side or the other, however I definitely don't remember my school statistics, and I'd like to know the numbers a bit more specifically.

Let's suppose we have a vampire with 8 willpower attempting to forcefully put to sleep a mortal with 4 willpower. I'd like to know the chances that both of them have at victory with a difficulty of 8 for both of their rolls.

Please help!

Knaight
2017-04-04, 03:33 AM
Take a look at Anydice - it's a minimalist dice probability specific online programming system, and it's usually the easiest way to deal with more complicated probability problems.

Pauly
2017-04-04, 03:56 AM
Easiest way is to do a cumulative total based on a grid.

Human rolls a 1. 1 chance of a tie. 7 chances of a loss
Human rolls a 2. 1 chance of a win, 1 chance of a tie, 6 chances of a loss
Human rolls a 3. 2 chances of a win. 1 chance of a tie and 5 chances of a loss
Human rolls a 4. 3 chances of a win, 1 chance of a tie and 4 chances of a loss.

Totals.
6 chances of winning
4 chances of tieing
22 chances of losing
32 chances in total.

jindra34
2017-04-04, 06:34 AM
Easiest way is to do a cumulative total based on a grid.

Human rolls a 1. 1 chance of a tie. 7 chances of a loss
Human rolls a 2. 1 chance of a win, 1 chance of a tie, 6 chances of a loss
Human rolls a 3. 2 chances of a win. 1 chance of a tie and 5 chances of a loss
Human rolls a 4. 3 chances of a win, 1 chance of a tie and 4 chances of a loss.

Totals.
6 chances of winning
4 chances of tieing
22 chances of losing
32 chances in total.

Except each of those sub variants doesn't have equal probablity. This isn't d4 versus d8 it 4d10 record any above 7 (iirc) versus 8d10 record any above 7...

Knaight
2017-04-04, 11:48 AM
Except each of those sub variants doesn't have equal probablity. This isn't d4 versus d8 it 4d10 record any above 7 (iirc) versus 8d10 record any above 7...

I'm not super familiar with oWoD (more familiar with nWoD, and I didn't get that familiar with either due to not being all that interested in their settings and hating the mechanics I do remember), but I'm pretty sure it's not a binomial distribution - a 1 counts against you. That makes it a trinomial distribution between -1, 0, and 1, with probabilities of .1, .5, .4, respectively. It also makes it that much harder to deal with mathematically, which is why I suggested anydice - even if doing it analytically, I wouldn't do it by hand.

meschlum
2017-04-04, 09:08 PM
I'm not super familiar with oWoD (more familiar with nWoD, and I didn't get that familiar with either due to not being all that interested in their settings and hating the mechanics I do remember), but I'm pretty sure it's not a binomial distribution - a 1 counts against you. That makes it a trinomial distribution between -1, 0, and 1, with probabilities of .1, .5, .4, respectively. It also makes it that much harder to deal with mathematically, which is why I suggested anydice - even if doing it analytically, I wouldn't do it by hand.

But math is fun!


So I went through the operations, wrote up a bit of code to help, and got the odds! I'll spare you the details this time.

Summary: bad.

The Facts of Life at difficulty 8 (on both sides): you're going to fail. A lot.

With 8 dice, you have a 75% chance of getting at least one success - a bit more than a quarter of the time, you fail in your area of expertise. You also botch a bit more than 10% of the time (botch meaning you have a negative total, so a lot of 1s can mean a botch even if you rolled some successes).

With 4 dice, you have a 60% chance of getting at least one success - the expert has invested 4 dice into succeeding 25% more often. You also botch 13.3% of the time, so it's barely worse than the expert.

Assuming you are the attacker with 8 dice, and need to score successes for your attack to be relevant, your attack works ~53% of the time. A 4 dice attacker succeeds 8% of the time. So you are better, but it's still not really overwhelming - mostly because the attacker fails pretty often, making defense less relevant.