Sorcerer Dice Pool Odds

[Lxndr]

Has anyone ever done calculations to suggest the rough odds for sorcerer dice pools based on the # of dice in each pool, and the # of sides used?  I'd be interested in seeing them somewhere, if they've been done, but I haven't been able to find them.  Perhaps I just don't know how to search.

[rafial]

I did up some probability graphs for Donjon, which uses almost the same die mechanic (Donjon just counts # of successes more generously).  But the probabilities of getting at least one success are the same for both systems.

Success is governed by the ratio of the size of the pools, that is 2d v 1d gets the same result as 6d v 3d.  The figures are approximate to a couple percentage points:

1:1 - 50%
3:2 - 60%
2:1 - 70%
3:1 - 80%
4:1 - 87%

[Lxndr]

Is that regardless of the die type used?  I was under the impression that there was a significant difference if I used, say, a d4 as opposed to a d20 or anything in between.

[Valamir]

There actually is a difference due to die size but its primarily at the margins.

For instance 8 dice vs 4 dice has a 70% chance of winning.  However, if the first die ties you set them aside and use the second die, which is basically the equivelent of 7 vs 3.  7 vs 3 being better than 2:1 there is a slightly better chance of winning the second die thatn there was the first.  If the second die is also a tie you wind up with going to the third die which makes the contest essentially 6 to 2.  Which is now 3:1 and an 80% chance.

The difference that smaller die sizes make then is to increase the frequency of ties, which skews the results slightly in favor of the larger die pool.  The skewing is most dramatic when 1) there is a large difference in die pool size (there's no skewing with equal pools), and 2) when one of the pools is very small.

The Sorcerer mechanic is one of the most opaque die pools systems out there in terms of being to accurately calculate odds.  Some folks whom I disagree with strenuously believe this to be a bad thing.  I find it MUCH more realistic and a superior game mechanic to only be able to get a rough sense of the odds.

[Lxndr]

I like the "only being able to figure out rough odds."  If I were a player, that's all I'd really want, the "more dice = better."  But as a GM, I'm interested in what my choice of die facings might mean.

So the general trend is "the larger the die type, the better chance the smaller pool has of winning" then?  I've noticed the d10 is a popular choice for sorcerer games, is that just aesthetic, or is there some sort of odds-related break point there?

(I should mention, the reason I became interested in this was when, on the indie-netgaming channel, someone used a dice bot to roll a d13.  Now, that can't happen in the real world, but online it's possible, and we all know the weird superstitions behind the 13.  It'd be neat in some games, thematically, but I was curious about the consequences of choosing 13 as opposed to 4 as opposed to 20 as opposed to 7.)

[Mike Holmes]

Here's the important thing. With all the common die types the skew is small enough that you'll never notice the difference in play. Meaning that the die that you have the most of is probably the best choice, or some such other consideration. It's just not worth worrying about, especially considering the opacity.

The big thing to know about in Sorerer is that as you get larger and larger discrepancies, the adjustmets get less and less. Basically, the lower pool always has a pretty decent chance of success. This is intentionally dramatic. You're never sure what's going to happen.

Mike

[rafial]

There actually is a difference due to die size but its primarily at the margins.

The only thing that die size controls is the probabilities relating to number of successes scored.  Smaller die sizes produce a flatter curve, with a greater likelihood of extreme results.  This is also obviously influenced by pool size.  Larger pools are likely to score more successes at the same pass/fail odds.  Die size begins to show its influence on the curve when the number of dice in the pool exceed the number of faces on a individual die.

However overall pass/fail probability is independent of die type and pool size.