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Savage Worlds» Forums » General

Subject: Dice Probabilities rss

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Mike Holcomb
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I often hear from people that the dice mechanic of Savage Worlds is "broken". When I ask them to explain what they mean by this, they usually point out that you are more likely to Ace (roll the highest number) on a die with fewer sides. Somehow, this then implies that a skill or attribute of d4 is inherently better than a d6, and a d6 is inherently better than a d8, and so forth.

I have often challenged their reasoning by asking them if they would rather have a d4 or a d12 in a skill like fighting or shooting. Uncertainty usually crosses their faces. If a d4 is better than a d6, and a d6 is better than a d8, and so on up the chain, then certainly a d4 is much better than a d12, right? I mean, it is three times as likely to ace. But when so challenged, a gamer is likely to respond that a d12 is certainly more likely to roll a high value, like an 8 or better, when compared to a d4.

Muddying the waters further is the effect of the Wild Die. In Savage Worlds, you get to roll your trait die and a d6 Wild Die. Both can ace, and you take the better of the two die rolls. This makes the probabilities of getting a certain outcome harder to calculate.

In the absence of hard calculation, the probabilistic intuition of most players leaves them confused and uncertain. The unspoken expectation is that a d6 trait should always be better than a d4 trait in all circumstances. And a d8 trait should always be better than a d6, and so on up the ladder. So what is the truth of the matter?

I did the math.



This graph shows the probability (on the y-axis) of rolling a value of N or better (N on the x-axis) for each die type (different colored lines).

For an ordinary skill check in Savage Worlds, the Target Number for success is 4. However, in actual play, target numbers vary all over the place. When Fighting, the target number is the opponent's Parry, which is often higher than 4. When Shooting, the target number and the die roll itself are often modified by range, cover, aim, and the method of shooting the weapon (double tap, three round burst, full auto). So it's important to consider a range of possible results on the dice.

And we see something interesting. Generally, for any target number, a bigger die is better than a smaller one. But there are some small exceptions to this.

For a target number of 6, a d4 has a 32.29% chance of success, while a d6 has a 30.56% chance of success.

For a target number of 8, a d6 has a 25.85% chance of success, while a d8 has a 24.65% chance of success.

For a target number of 10, a d8 has a 18.36% chance of success, while a d10 has a 17.50% chance of success.

For a target number of 12, a d10 has a 11.53% chance of success, while a d10 has a 10.88% chance of success.

These are very narrow exceptions to the general rule, and the difference in probability is quite small. If a character with d4 shooting is firing at medium range (-2 penalty) at an opponent, he will hit about 323 times out of 1000. A character with a d6 in Shooting will hit about 306 times out of 1000 in the same circumstances. In all other situations, the d6 shooter will be more likely than the d4 shooter to hit.

If you really can't live with this, I'd recommend the following house rule to fix the probabilities:

When a die aces, roll it again and add the result minus one.

The highest value on a die is still an ace, and the die would continue to be rolled and added each time it aces, but you add one less than the number shown. For example, I have d8 in Fighting. My wild card character rolls:

Roll the d8 - a 7
Roll the d6 - a 6!
Roll the d6 again - another 6. I add (6-1)=5 to my original 6 for 11 and roll again.
Roll the d6 again - a 4. I add (4-1)=3 to my 11 for a Fighting total of 14.

Implementing this house rule eliminates the probability crossover that occurs in the rules as written, as you can see in the graph below.

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Excellent fix!

I think the term "broken" is too harsh, but it's clearly something of a flaw. Above all, it doesn't exactly inspire confidence in the system.
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Ben Vincent
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Another factor is that it is often but not always better to have a die roll bonus than a larger die size, so choosing an edge that gives a +1 bonus may be the best bang for your buck advancement. It varies by target number though, and in some cases the larger die is better.
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Jeremiah
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Broken? nah... It's a quirk that gives the system a little character... call it a hindrance

Also, the differences in probability for a given target are so small they are probably overshadowed by the bias in your dice.

Also, nice fix

EDIT: also, the probability is only greater for the lower die type for ONE target number. Unless the player really thinks that target number is going to come up a lot, and I don't think that is the case for any of the targets where this happens, I wouldn't worry about it too much.
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Michael Hopcroft
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Isn't Excel cool? You can do all sorts of business-related things on it, and use the same program to help you with your RPG chargen.
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Eric O. LEBIGOT
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Michael Hopcroft wrote:
Isn't Excel cool? You can do all sorts of business-related things on it, and use the same program to help you with your RPG chargen.
You mean "aren't spreadsheet programs cool?", no?
There are in fact quite a few "office" suites out there (like LibreOffice)… And isn't programming even cooler (e.g. with Python), as it allows one to do many more things often in a much more convenient way (except for very basic table handling, calculations and graphs)?
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Juhan Voolaid
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Don't you just love math! Fun, fun, fun.
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Blue Tyson
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Yes.
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Blue Tyson
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But yes, an obsession with oddball polyhedra combinations and modifiers should lead to oddball distributions.
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Timothy Heath
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Egads people...

Two things, this is a "role" playing game, not a "roll" playing game...

Number 1, Isn't your "role" in the game far more important then any "roll" you have to make in the game, eh?? clever, eh??

Number 2, We're talking at most 1-2 percentage points here... If half the players I personally know concentrated on their character's "role" in my game, than their last missed "roll" against the thug in the alley our collective game with all the player's would be a heck of a lot more fun....

If you "roll" players out there really want a game that emphasizes how well your "character" rolls, check out the game of Craps, now there's a game that will really benefit from all of this mathematical analysis and in turn earn all of those "roll" players a tidy profit...

So all of you "roll" players out there, unless you want to concentrate on the "role" of your character find a game where an emphasis on your "roll" is the crux of the game, k?!?!?! whistle
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Mavis
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hiroheathorpg wrote:
Number 1, Isn't your "role" in the game far more important then any "roll" you have to make in the game


Out of interest, for you, what role does dice rolling have in a role-playing game?
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3rik de πrik
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Mavis101 wrote:
hiroheathorpg wrote:
Number 1, Isn't your "role" in the game far more important then any "roll" you have to make in the game


Out of interest, for you, what role does does dice rolling have in a role-playing game?

Dice are randomizers. Rolling them to see what happens has little to do with whether you "play your role" or not. If you don't like randomizers in your game, you might want to consider going 'Diceless' (does not use dice or other randomizer).

Though the differences in probabilty are marginal and probably hardly noticeable in actual play, they *do* theoretically make Savage Worlds' task resolution counter-intuitive, for a higher skill does not always imply a better chance at succeeding.

Personally, I just think Dice Step (variable dice vs. static target) mechanics are ugly. I mean, just look at the way those graphs go all over the place! gulp But, that's just my personal opinon.
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Mavis
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3rik wrote:
Personally, I just think Dice Step (variable dice vs. static target) mechanics are ugly. I mean, just look at the way those graphs go all over the place! gulp But, that's just my personal opinon.

Whereas I love those graphs going all over the place.

I understand why some people don't like Savage Worlds because the dice probabilities are apparently slightly off but I think it is a positive quirk, designed to encourage players/characters to attempt to do something (especially with a d4 skill) rather than not.
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3rik de πrik
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Mavis101 wrote:
3rik wrote:
Personally, I just think Dice Step (variable dice vs. static target) mechanics are ugly. I mean, just look at the way those graphs go all over the place! gulp But, that's just my personal opinon.

Whereas I love those graphs going all over the place.

I understand why some people don't like Savage Worlds because the dice probabilities are apparently slightly off but I think it is a positive quirk, designed to encourage players to attempt to do something (especially with a d4 skill) rather than not.

I don't mind the dice probabilities being off. I mean, ignoring those marginal probability "anomalies", in general a higher skill still gives you a better chance at succeeding. I just don't like the shape of the graphs (even the "fixed" ones) and the uneven progression between different skill levels: the advantage of having a higher skill varies wildly depending on the target number. I find that ugly. It's just a personal quirk.

I don't agree with the part in your quote I emphasized. This was not intentional design. Rather, when the quirk was noticed/pointed out, it was deemed too marginal to bother with, which was probably a realistic assumption.


My personal main gripes with SW have to do with it being too fiddly and gamey to my taste.
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Mavis
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Hey stop editing your posts, I can't keep up!

3rik wrote:
I don't agree with the part in your quote I emphasized. This was not intentional design. Rather, when the quirk was noticed/pointed out, it was deemed too marginal to bother with, which was probably a realistic assumption.

Understood. Although it was not the intent of the design but in my experience the result has been to encourage players to be more proactive in attempting to do things.

I think that Savage Worlds system is geared heavily towards characters succeeding, which I think makes the failures incredibly important. That said this probably just reflects my style of GMing Savage Worlds, I am sure another GM would disagree.
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Timothy Heath
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Mavis101 wrote:
hiroheathorpg wrote:
Number 1, Isn't your "role" in the game far more important then any "roll" you have to make in the game


Out of interest, for you, what role does dice rolling have in a role-playing game?


My point was, this is a roleplaying game. People need to stop worrying about what dice, how many they get to throw, etc.

Players and GMs need to focus their attention on the story, developing their characters, and moving the story forward.

For the "roll" players, do you base your actions on how successful your die roll might be, or what your "character" would do??
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Timothy Heath
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3rik wrote:
Mavis101 wrote:
hiroheathorpg wrote:
Number 1, Isn't your "role" in the game far more important then any "roll" you have to make in the game


Out of interest, for you, what role does does dice rolling have in a role-playing game?

Dice are randomizers. Rolling them to see what happens has little to do with whether you "play your role" or not. If you don't like randomizers in your game, you might want to consider going 'Diceless' (does not use dice or other randomizer).

Though the differences in probabilty are marginal and probably hardly noticeable in actual play, they *do* theoretically make Savage Worlds' task resolution counter-intuitive, for a higher skill does not always imply a better chance at succeeding.

Personally, I just think Dice Step (variable dice vs. static target) mechanics are ugly. I mean, just look at the way those graphs go all over the place! gulp But, that's just my personal opinon.





Rolling them to see what happens has little to do with whether you "play your role" or not.

I disagree, "rolling them to see what happens" isn't the issue for me. The issue for me is, when players focus so much of their attention on the potential results of a die roll, they tend to make choices for their character based on die rolling probabilities as opposed to staying in character and doing what their character would do.
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Mavis
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hiroheathorpg wrote:
My point was, this is a roleplaying game. People need to stop worrying about what dice, how many they get to throw, etc.

Not everyone wants the same things out of a role-playing game. Some people do just enjoy sitting around a table rolling some dice with their mates and, although this would not be my preference as a player, I think it is a perfectly valid way to enjoy a game.

hiroheathorpg wrote:
Players and GMs need to focus their attention on the story, developing their characters, and moving the story forward.

What is the story and how does it appear?

In my experience character choices are part of it but so are dice rolls. The two feed off each other, the consequences of those dice rolls influence the decisions that the players make for their characters and equally can throw out unexpected results that can send 'the story' in unexpected directions, which can be as much a challenge to the GM as the players.

Also I have also tipped you 30GG so that you can purchase an avatar, please come join in the discussions in the RPGGeek General Forums, you will be most welcome.

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