Savage Worlds: Question for Ari

[Greg K]

Ari,
Not long ago you had mentioned trying out Savage Worlds using the Solomon Kane supplement. I don't recall there being a follow up with your impressions so I was just wondering what your impressions were of the system.

 

[Mouseferatu]

Still not sure, to be honest. We've only played about 1.5 games so far. (We got about half a game in after character creation.) Granted, game two was fairly combat heavy, but I still don't think I've given the system a fair shake.

With that understood, my impression so far is, "Huh." There's a lot to recommend it, and it flows simply and quickly enough. Definitely positive in that respect. I'm not sold on some of the specific implementation, though. For instance, it's way too easy to build a character who's not good at some of what he's supposed to be good at, and the death spiral is absolutely unforgiving. I don't mind systems that are deadlier than D&D's hit points, but the penalties for being wounded build up far too quickly for a system in which it can take weeks of game time to heal.

And I think there are times, thanks to the exploding dice, where it's actually statistically better to be rolling a d4 than a d6. Not sure of that--I'm not a math guy--but it's an impression I've gotten.

But again, these are just initial impressions after a single experience and from someone who doesn't yet grasp all the specifics. So all of this, both the positive and negative, are subject to change.

 

[thatdarnedbob]

And I think there are times, thanks to the exploding dice, where it's actually statistically better to be rolling a d4 than a d6. Not sure of that--I'm not a math guy--but it's an impression I've gotten.

This is actually something to be concerned about. If your target number is a die size, then you are better off rolling the die one size lower than that die. For example, if you're shooting for 10, then don't roll a d10, roll a d8. My intuition tells me that these four points are the only such points where the math is weird, but my intuition could be wrong. I'll test this a bit more and get back if I am mistaken.

 

[Ainamacar]

And I think there are times, thanks to the exploding dice, where it's actually statistically better to be rolling a d4 than a d6. Not sure of that--I'm not a math guy--but it's an impression I've gotten.

That's not true if you don't know the target number beforehand, but it could be if you do.

Obviously a d1 in an exploding system wins everything, but after that using larger dice is always at least as good as using lower dice (assuming you don't know the result you need). And the equality holds only when comparing a d2 and a d3, so if the lowest dice in the game is a d3, using a larger one is always better on average.

The calculation is this, where d is the size of the die:
The probability of getting exactly i exploding rolls followed by exactly one non-exploding roll is p=(1/d)^i * (1-1/d). Every single possible roll can be described this way.

The average value of a roll that explodes i times and then doesn't explode is v=i*d + d/2. (In other words, If I rolled a d4 which exploded once I certainly have 1*4 from the first roll, and the second roll which didn't explode, and thus must be either 1, 2, or 3, has an average of 2).

My expected roll is the sum of the contribution from each possible roll times its probability of occurring, in other words the sum of all the possible p*v's. This is a sum from i=0 to infinity which, happily, can be calculated exactly: d/2 + 1/(d-1) + 1.

d   exp (exact)  exp (approximate)
2   3            3
3   3            3
4   10/3         3.33
5   15/4         3.75
6   21/5         4.2
7   14/3         4.67
8   36/7         5.14
9   45/8         5.63
10  55/9         6.11
11  33/5         6.6
12  78/11        7.09
13  91/12        7.58
14  105/13       8.08
15  60/7         8.57
16  136/15       9.07
17  153/16       9.56
18  171/17       10.06
19  95/9         10.56
20  210/19       11.05

Obviously that isn't the whole story, as the distribution about the expected values is important as well. I didn't calculate anything, but I did simulate it briefly (also to check the numbers above, which are correct.) For d>=3 every increase in dice size leads to the usual modest increase in the standard deviation. Going from d=2 to 3 actually decreases the standard deviation a slight amount, which is kinda interesting: the d2 is "swingier" than a d3, but they have the same average result. Also, even though going from a d3 to a d4 increases the standard deviation, for the d4 it is still less than it is for a d2.

Of course, since actually using "dice" smaller than a d4 in play is pretty rare those little anomalies will pretty much never show up at the table.

Back to the matter at hand, if you need a 6 and you know it, then you have a 1/6 (.1667) chance of getting at least that with a d6, and a 3/16 (.1875) chance with a d4. Similarly for other target numbers exactly equal to dice sizes.

Edit: Now that I think about it, interpreting this in terms of one's a priori knowledge of the needed result instead of just acknowledging the raw probabilities tacitly assumes one is trying to optimize the roll and is free to roll a smaller die if desired. I've never played Savage Worlds, but I'm guessing you can't do that. In which case the math has some wonky points, end of statement. Which is just what thatdarnedbob said in a considerably more concise fashion.

 

[thatdarnedbob]

That's not true if you don't know the target number beforehand, but it could be if you do.

This is more a philosophical point than anything, but it doesn't matter whether the die roller is aware of the statistics behind his actions. Anyway, good data and analysis. You posted just as I was getting my program chugging, so I'll graciously say you saved me work instead of frustrating me.

 

[Ainamacar]

This is more a philosophical point than anything, but it doesn't matter whether the die roller is aware of the statistics behind his actions. Anyway, good data and analysis. You posted just as I was getting my program chugging, so I'll graciously say you saved me work instead of frustrating me.

Yeah, I was definitely framing the issue the wrong way. It's a valid way to look at the problem if we're trying to find the optimal strategy for what kind of dice to roll, but that isn't what we're doing at all! I was actually reading a textbook on statistical modeling and information theory for a few hours just before I saw all this, and in retrospect I had been thinking along those lines all night. The fact that I failed to make the necessary distinction here will actually help keep me alert to it in the future. Thanks EN World, you're helping science even while you divert me from it.

Anyway, glad to have helped.

 

[TheNovaLord]

SK can be a little combat heavy, if you follow the plot point campaign in the book
we have completed europe and are in the middle of the africa quests

it can feel a little 'monster' of the week but the fights are pretty challenging and you need fair tactics, and tricks to beat some of the beasties

 

[Mouseferatu]

SK can be a little combat heavy, if you follow the plot point campaign in the book
we have completed europe and are in the middle of the africa quests

We're not. In fact, we're deliberately avoiding it.

 

[Greg K]

The other thing to consider regarding d4 vs d6 is the odds of getting raises. The first raise requires an 8, the second a 12, etc. Someone want to do determine the odds for that?

 

[coyote6]

For d4, it's 1 in 16 (6.25%); d6 is 5 in 36 (13.89%).

Of course, with a d8 it's 1 in 8 (12.5%) -- little wonkiness.