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Force
2012-04-18, 02:03 PM
OK, I'm no math wizz, so I thought I'd turn to GiantITP for some help.

One of the (online) games I've playing right now a Council game, run by turns. Each turn, we have 10 actions we can take; success or failure of the action is determined by a d100 (higher is better). We can choose to focus on certain rolls by spending two rolls on one action. In this case, the DM rolls two d100 and subtracts 25 from each, then adds them together. He does transparent rolls via invisible castle, so we tend to know how well we're doing.

One of the things I've noticed is that we tend to not do so well with those rolls, and I know that the GM is not fudging. What I'm asking is, is the probability of getting a result higher than 50 with the double roll -50 less than it is with a single roll?

Morithias
2012-04-18, 02:07 PM
According to Online dice roller..

2d100 - 50
min -48 / median 51 / max 150

Source http://www.brockjones.com/dieroller/dice.htm

So you are slightly better off...but only 1 point.

Force
2012-04-18, 02:11 PM
He basically says that if we get a negative total it's equivalent to just a 1. Considering that the worst 2 rolls we've had so far (a 3 and a 4) ended up with us going to war, once with a Reaper and its attendant Zerg brood (Mass Effect Fusion game), and currently with the rest of the galaxy, I don't even want to know what he'd come up with given a 1.

Pinnacle
2012-04-18, 02:16 PM
It's higher, but only very very slightly.

Average roll on d100 is 50.5.

Average 50.5 - 25 + Average 50.5 - 25 = Average 51.

On a die as big as that, I'd call that .5 difference in average negligible for most purposes.
What this does give you is a bit more of a bell curve--on a d100, you have an equal chance of any number from 1 to 100. On 2d100, you're somewhat more likely to get rolls closer to the average--a high roll and a low roll balance out. If you're worrying about avoiding rolling a low number, that's in your favor; if you need a high one, it actually hurts.
You've also got a much wider range--anywhere from -48 to 150. You can eliminate that last part by using 2d50 instead (since you're using Invisible Castle). That's got the same average of 51 but a range of 2 to 100, so almost the same as 1d100 and slightly in your favor.

EDIT: Okay, eliminating results between -48 and 0 does increase your average, but if it just sets them all to 1 and those are still failures I don't think it really makes any practical difference.

Rorrik
2012-04-18, 05:13 PM
With a 25% chance of getting a 1 on either roll, a 2 has a 12.5% chance, 12.5 times the probability it would have on a single die, though the possibility of a 1 is eliminated. The rest of the numbers will be distributed with a slightly higher than 1% probability near 50 or 51. The probability of getting 150 is .1% and the total probability of getting anything over 100 is about 12.5%. Wish I had MatLab on this computer, could graph the whole distribution in a minute or two.

The gist is that you will get a 2 one out of 8 rolls, you'll roll over 100 one out of 8 rolls and the other six rolls will be distributed in between, half below 50, half 50 and above.

Jay R
2012-04-18, 06:26 PM
It improves the chances of any roll where the probability is less than 1/2.

Prob (X > 60) = 40% with 1 die, but 41.86% with 2 dice
Prob (X > 80) = 20% with 1 die, but 25.256% with 2 dice
Prob (X > 90) = 10% with 1 die, but 18.3% with 2 dice
Prob (X > 95) = 5% with 1 die, but 15.4% with 2 dice
Prob (X >= 100) = 1% with 1 die, but 13.26% with 2 dice

Specifically, it greatly improves the chances of an extremely low number or an extremely high number, primarily because anything lower than 1 is a 1, and (presumably) anything higher than 100 is 100.

Prob (X <= 1) = 1% with 1 die, but 12.75% with 2 dice.

If it a simple success/failure roll, and the number you need is higher than 51, you should roll two dice. The higher the number you need, the more help it gives you.

But if the roll affects how good the success or failure is, specifically if any roll 1 or less is a fumble, they you are greatly increasing the probability of those rolls.

TheOOB
2012-04-18, 09:56 PM
A more sensical way of doing it would be to roll 2 d100's and take the better of the two results.

Techsmart
2012-04-18, 11:34 PM
From a purely random point? Let's look at the statistics of it.
1d100
Average: 50.5
Range: 1 to 100
% chance of a roll: 1% always

2d100 - 50
Average: 51
Range: -48-150 (minimum roll is 1 and 1)
Standard deviation: 40.8

Translation: in 2d100-50, your chances of rolling between 10 and 91 are about 68% (approximation made here), whereas in 1d100, your chances are 81%. the remaing 31.8% chance on the 2d100-50 is split evenly between higher and lower scores. What does this mean? Not a whole lot, to be honest... Your chances of getting an average roll with the 2d100-50 is less likely, since your chances are spread over a much larger range. The average itself, however, is marginally higher, due to the second die making the minimum 1 point higher.

From a programming point of view? Most RNGs are done very poorly, and love giving low numbers. It's just a problem we face with digital dice-rolling. I would probably run with the one dice-roll most of the time, since if I get one good value, im probably not going to risk losing that good roll to a bad roll, which is more likely than not to happen. Personally, I would go with the other post of seeing if the DM is willing to give you the option to roll 2 and take the better of those.

ShneekeyTheLost
2012-04-18, 11:45 PM
I tend to employ a broader bell curve by employing a handful of dice rather than just a couple.

As an example:

In the game I am making, your basic check is xdy where x is your die pool and y is your die size. There are no static modifiers in the game, most of your modifiers are to the number of dice in your pool, although there are a couple of abilities which can affect die size by one category, with a hard cap.

If a skill is a primary skill, the die size is a d8. If it's a secondary skill, then it's a d6. If it's a cross-class skill, then it's a d4.

So, anyone can pick up any skill, but a stealthy type class is going to be better at sneaking around than a warrior is.

Your attribute modifier cannot ever exceed your base die pool for the action. Therefore, even if you have capped the relevant stat, a starting character is not going to have more bonuses from stats than from skill.

So say you have a mid-level fighter trying to swing his sword at his opponent. He's got 4 ranks in his skill, a +2 die modifier from his stats, a +1 die modifier from an enchanted weapon, and a +1 die modifier from a buff. He's got an 8 die pool. Since swinging a sword is a primary skill for a fighter, he rolls 8d8, targeting his opponent's defense number.

8d8 gives you a very broad bell curve. You've got enough dice in your hand that the odds of coming up all 1's or all 8's is extremely remote. You're more likely to hit somewhere in the middle, which means extremely lucky shots are rather memorable, but not something to count on.