OT math question for the math guru's (dice %)

[Toadmaster]

I've been reading through some older RPG's I've got and some use unconventional die rolling (not d20, % or 3d6 which seem to be the most common). I know there are some here who are good at figuring die rolling odds statistics (and even some who seem to it like too, sicko's :eek: ). So if you don't mind I'd like the odds of rolling various outcomes for:

2d6
2d8
2d10 (2-20 not %)
3d6 (HERO, Gurps)
3d8
3d10
4d6

I assume d20 and d% are a straight 5%, 1% if not I'd be interested in how those roll.

Thanks

[Gary]

Originally posted by Toadmaster
I've been reading through some older RPG's I've got and some use unconventional die rolling (not d20, % or 3d6 which seem to be the most common). I know there are some here who are good at figuring die rolling odds statistics (and even some who seem to like too). So if you don't mind I'd like the odds of rolling various outcomes for:

2d6
2d8
2d10 (2-20 not %)
3d6 (HERO, Gurps)
3d8
3d10
4d6

I assume d20 and d% are a straight 5%, 1% if not I'd be interested in how those roll.

Thanks

If you're interested, I have a spreadsheet to calculate all dice probabilities for d6's up to 24d6. It was designed to calculate the average damage through defenses for normal and killing attacks, and to calculate con stunning probabilities. I can probably adapt it to d8's and d10's with a little work.

Just give me an email address. Warning, it's a big spreadsheet. ;)

[Insaniac99]

dude, I want it too!


Insaniac99@charter.net

[Gary]

Originally posted by Insaniac99
dude, I want it too!


Insaniac99@charter.net

Just emailed it.

[BenKimball]

Originally posted by Toadmaster
2d6
2d8
2d10 (2-20 not %)
3d6 (HERO, Gurps)
3d8
3d10
4d6

I assume d20 and d% are a straight 5%, 1% if not I'd be interested in how those roll.

<b>2d6</b>
2: 35:1 against (2.8%)
3: 17:1 against (5.6%)
4: 11:1 against (8.3%)
5: 8:1 against (11.1%)
6: 6.2:1 against (13.9%)
7: 5:1 against (16.7%)
8: 6.2:1 against (13.9%)
9: 8:1 against (11.1%)
10: 11:1 against (8.3%)
11: 17:1 against (5.6%)
12: 35:1 against (2.8%)

<b>2d8</b>
2: 63:1 against (1.6%)
3: 31:1 against (3.1%)
4: 20.3:1 against (4.7%)
5: 15:1 against (6.7%)
6: 10.8:1 against (7.8%)
7: 9.7:1 against (9.4%)
8: 8.1:1 against (10.9%)
9: 7:1 against (12.5%)
10: 8.1:1 against (10.9%)
11: 9.7:1 against (9.4%)
12: 10.8:1 against (7.8%)
13: 15:1 against (6.7%)
14: 20.3:1 against (4.7%)
15: 31:1 against (3.1%)
16: 63:1 against (1.6%)

<b>2d10</b>
2: 99:1 against (1%)
3: 49:1 against (2%)
4: 32.3:1 against (3%)
5: 24:1 against (4%)
6: 19:1 against (5%)
7: 15.7:1 against (6%)
8: 13.3:1 against (7%)
9: 11.5:1 against (8%)
10: 10.1:1 against (9%)
11: 9:1 against (10%)
12: 10.1:1 against (9%)
13: 11.5:1 against (8%)
14: 13.3:1 against (7%)
15: 15.7:1 against (6%)
16: 19:1 against (5%)
17: 24:1 against (4%)
18: 32.3:1 against (3%)
19: 49:1 against (2%)
20: 99:1 against (1%)

<b>3d6</b>
3: 215:1 against (0.5%)
4: 71:1 against (1.4%)
5: 35:1 against (2.8%)
6: 23:1 against (4.2%)
7: 11:1 against (8.3%)
8: 9.3:1 against (9.7%)
9: 8:1 against (11.1%)
10: 7:1 against (12.5%)
11: 7:1 against (12.5%)
12: 7.6:1 against (11.6%)
13: 9.3:1 against (9.7%)
14: 13.4:1 against (6.9%)
15: 20.6:1 against (4.6%)
16: 35:1 against (2.8%)
17: 71:1 against (1.4%)
18: 215:1 against (0.5%)

<b>3d8</b>
3: 511:1 against (0.2%)
4: 169.7:1 against (0.6%)
5: 84.3:1 against (1.2%)
6: 38.4:1 against (2.5%)
7: 33.1:1 against (3.0%)
8: 27.4:1 against (3.5%)
9: 17.3:1 against (5.5%)
10: 13.2:1 against (7.0%)
11: 10.4:1 against (8.8%)
12: 10.1:1 against (9.0%)
13: 9.7:1 against (9.4%)
14: 9.7:1 against (9.4%)
15: 10.1:1 against (9.0%)
16: 11.2:1 against (8.2%)
17: 13.2:1 against (7.0%)
18: 17.3:1 against (5.5%)
19: 23.4:1 against (4.1%)
20: 27.4:1 against (3.5%)
21: 50.2:1 against (2.0%)
22: 84.3:1 against (1.2%)
23: 169.7:1 against (0.6%)
24: 511:1 against (0.2%)

<b>3d10</b>
3: 999:1 against (0.1%)
4: 332.3:1 against (0.3%)
5: 165.7:1 against (0.6%)
6: 82.3:1 against (1.2%)
7: 54.6:1 against (1.8%)
8: 46.6:1 against (2.1%)
9: 34.7:1 against (2.8%)
10: 26.8:1 against (3.6%)
11: 22.8:1 against (4.2%)
12: 17.2:1 against (4.5%)
13: 14.9:1 against (6.3%)
14: 13.5:1 against (6.9%)
15: 12.2:1 against (7.6%)
16: 12.3:1 against (7.5%)
17: 12.3:1 against (7.5%)
18: 12.7:1 against (7.3%)
19: 12.9:1 against (7.2%)
20: 14.9:1 against (6.3%)
21: 17.2:1 against (5.5%)
22: 21.2:1 against (4.5%)
23: 26.8:1 against (3.6%)
24: 34.7:1 against (2.8%)
25: 46.6:1 against (2.1%)
26: 65.7:1 against (1.5%)
27: 99:1 against (1.0%)
28: 165.7:1 against (0.6%)
29: 332.3:1 against (0.3%)
30: 999:1 against (0.1%)

<b>4d6</b>
4d6 is left as an exercise for the reader. :)

Cheers!
Ben

P.S. These numbers are guaranteed to be mostly correct. ;)

[Xandarr]

Someone posted this site once on RPG.net and I saved it to my harddrive because it was so useful. Not sure what his/her name was, but I'm sure you will find it on the site.

Here's the URL:

http://ojaste.dhs.org/~ojastej/dice.html

I think you'll find it most useful for your questions on dice probabilities.

Helpfully,
Steve

[Toadmaster]

Thanks for the help everybody.

Gary, I have a slow dial up connection and the dice calculator looks like it will be pretty helpful for my future needs, but thanks for the offer, if I ever get around to DSL I'll take you up on it. Thanks.

[Steve]

Originally posted by Gary
If you're interested, I have a spreadsheet to calculate all dice probabilities for d6's up to 24d6. It was designed to calculate the average damage through defenses for normal and killing attacks, and to calculate con stunning probabilities. I can probably adapt it to d8's and d10's with a little work.

Just give me an email address. Warning, it's a big spreadsheet. ;)

Since this sort of math question pops up every now and then, maybe the file could be posted to the Hero Games site as a free download? This sounds like something that would be useful to many GMs and players.

[Dauntless]

Here's a general rule of thumb, take your die type divide it by two, and add .5, then multiply by the number of dice you roll to obtain the "average" number you will role.

For example, 3d6 would be, 6/2 = 3 + .5 = 3.5.
Multiplied by number of dice is 3 x 3.5 = 10.5

Another example, 2d10 would be 10/2 = 5 + .5 = 5.5
Multiplied by number of dice is 2 x 5.5 = 11

so 10.5 is the average number (in other words averaged out over many rolls, the average will equal 10.5). This is why the "average" skill roll is 11 or less.

I've always preferred multiple dice that are added together over straight percentile rolls for one reason. In a straight percentile roll, it is just as easy to roll a 01 as it is to roll a 100 as it is to roll a 50. In other words, your chance to roll a 29 or a 100 are exactly the same...1 in 100. Some will say, but if you need a 50 or less, that's the same as saying you need a 7 or less in a 2d6 system. Not quite...due to statistical deviation, or what happens at the extremes. If you roll 1d100 a hundred thousand times, it will be a mostly flat line with roughly 1000 marks between 1 and 100.

In a 3d6 system, it is not as easy to roll a 3 as it is to an 18 as it is to 11. A multiple die system takes into account the bell curve, which basically means that extremely high and low outcomes are rare, and things tend to fall more in the middle. This makes catastrophic errors or outstanding success much harder than percentile systems. If you roll 3d6 a hundred thousand times, you'll get the vast majority of the rolls centered between 9 and 12 and slowly tapering down both directions. The upshot of this is that multiple die systems reward mediocrity :D

[Arthur]

Originally posted by Toadmaster
[B
Gary, I have a slow dial up connection and the dice calculator looks like it will be pretty helpful
[/B]

I am stuck with dialup also, and it DL'd in about two seconds. It's 12K. Even at 14.4, you'd be looking at about a ten-second DL.

[Le Schtroumpf]

A refinement to Dauntless's post is to add the minimum possible roll to the maximum possible roll and divide by 2

5d4 for example
minimum: 5
maximum: 20
average: (5+20)/2 = 12.5

[Gary]

Originally posted by Steve
Since this sort of math question pops up every now and then, maybe the file could be posted to the Hero Games site as a free download? This sounds like something that would be useful to many GMs and players.

I'm willing to donate the spreadsheet.