Author Topic: 4d6 or 1d20?  (Read 6440 times)

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Lo77o

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4d6 or 1d20?
« on: January 26, 2011, 09:53:35 AM »
Friend suggested an odd house rule. He wants to use 4d6 instead of 1d20 for all attacks.

Now im sure we will end up with a bigger average hit, but we will still be using "natural 20" to indicate an allways hit.

Im trying to figure out the probability of rolling a "20" with 4d6.

There would be (6*6*6*6) outcomes, or 1296 outcomes. But how many of those would be 20's?

6662
6653
6644
6554
5555

And then a number of variations of the numbers, but im getting my self confused i think.

Well, what i would like help with, is first to figure out the number of outcomes that sums up to 20, and if there is any way i could get a bigger benefit out of this then the monsters we would be meeting. Seems like weapons with 18-20 crit range would be odd in this system, seeing as if you roll 22, it might be a hit, but not a possible crit.
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Maat_Mons

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Re: 4d6 or 1d20?
« Reply #1 on: January 26, 2011, 10:21:22 AM »

Sinfire Titan

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Re: 4d6 or 1d20?
« Reply #2 on: January 26, 2011, 10:33:42 AM »
All it does is help the noncasters (and CoDzilla, not that they need it). Unless it applies to Skills and other d20 rolls, I see very little reason to not test this out.


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Re: 4d6 or 1d20?
« Reply #3 on: January 26, 2011, 10:41:28 AM »
My work
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Lo77o

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Re: 4d6 or 1d20?
« Reply #4 on: January 26, 2011, 11:01:48 AM »
Are you sure he didn't mean 3d6?

Ya im sure its 4d6, or a 20 would never be rolled.

And im trying to figure out the exact probability of rolling a total of 20. I guess i could make a spreadsheet and just start writing the different numbers and adding them up when done, but then i stand a chance of missing a number or two. And if we decided to play with it, we might change natural 20 to "20-22" or something, and then ill have to count it all over again. I was hoping someone might have a little math insight, and could help me figure it out so i can take the "results" to the table next time. That way we could have an informed discussion about if we should add this house rule.
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Maat_Mons

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Re: 4d6 or 1d20?
« Reply #5 on: January 26, 2011, 11:13:22 AM »

Or you could use Google to find one of the online tools that will give you the answer with essentially no effort. 

cru

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Re: 4d6 or 1d20?
« Reply #6 on: January 26, 2011, 11:28:50 AM »
d204d64d6 probability
14-85.4
2-179-13rest
18186.17
19194.32
2020-245.4
http://anydice.com/
Of course, d20 probability is 5%

If you need to identify rolls like 15, 16, 17, that's not easy to map and it would not be as precise.
« Last Edit: January 26, 2011, 11:32:04 AM by cru »

Lo77o

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Re: 4d6 or 1d20?
« Reply #7 on: January 26, 2011, 11:34:56 AM »

Or you could use Google to find one of the online tools that will give you the answer with essentially no effort. 

That is true, but how would i learn anything then?
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cru

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Re: 4d6 or 1d20?
« Reply #8 on: January 26, 2011, 11:40:08 AM »
odds of rolling 24: 1/1296
6666 - 1

odds of rolling 23: 4/1296
6665 - 4

odds of rolling 22: 10/
6664 - 4
6655 - 6

odds of rolling 21: 20/
6663 - 4
6654 - 12
6555 - 4

odds of rolling 20: 35/
6662 - 4
6653 - 12
6644 - 6
6554 - 12
5555 - 1

cumulative odds of rolling 20 and above: add all of the above = 70/1296 = 5.4 %

Lo77o

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Re: 4d6 or 1d20?
« Reply #9 on: January 26, 2011, 11:48:17 AM »
odds of rolling 24: 1/1296
6666 - 1

odds of rolling 23: 4/1296
6665 - 4

odds of rolling 22: 10/
6664 - 4
6655 - 6

odds of rolling 21: 20/
6663 - 4
6654 - 12
6555 - 4

odds of rolling 20: 35/
6662 - 4
6653 - 12
6644 - 6
6554 - 12
5555 - 1

cumulative odds of rolling 20 and above: add all of the above = 70/1296 = 5.4 %

Thanks a bunch, i can take that with me to the table and we can work from that.
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Re: 4d6 or 1d20?
« Reply #10 on: January 26, 2011, 12:50:06 PM »
so what does rolling a 24 get you?
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Re: 4d6 or 1d20?
« Reply #11 on: January 26, 2011, 01:23:10 PM »
so what does rolling a 24 get you?

Instant claim to an additional slice of pizza from the ones present, pickers choice? ;)
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Re: 4d6 or 1d20?
« Reply #12 on: January 27, 2011, 12:10:19 AM »
I hate math. Math lies, like cake.

Odds of 4d6 rolling a 20: 2.70061728395%
Source: http://anydice.com/

Odds of 4d6 rolling a 20: 2.701%
Source: http://topps.diku.dk/torbenm/troll.msp

Odds of 4d6 rolling a 20: 0.02701%
Source: http://www.anwu.org/games/dice_calc.html

Odds of 4d6 rolling a 20: 5.7%
Source: Cru

Odds of 4d6 rolling a 20: 5%
Source: Me, 4~24 equals 20 possible outcomes therefor any particular one has a 5% chance of happening.
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Re: 4d6 or 1d20?
« Reply #13 on: January 27, 2011, 12:12:02 AM »
Odds of 4d6 rolling a 20: 5%
Source: Me, 4~24 equals 20 possible outcomes therefor any particular one has a 5% chance of happening.
See, the problem with that is that (using 3d6 for an example) a 3 can only occur through one combination of dice, while a 10 or 11 can occur with more than one combination.

Nytemare3701

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Re: 4d6 or 1d20?
« Reply #14 on: January 27, 2011, 12:13:27 AM »
UA has a 3d6 variant, that uses a bell curve to keep rolls near the middle. 18 is the new "crit" but you are far more likely to roll near the center. It essentially stabilizes the chaos of normal d20 rolling.

elint

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Re: 4d6 or 1d20?
« Reply #15 on: January 27, 2011, 12:44:30 AM »
I hate math. Math lies, like cake.

Odds of 4d6 rolling a 20: 2.70061728395%
Source: http://anydice.com/

Odds of 4d6 rolling a 20: 2.701%
Source: http://topps.diku.dk/torbenm/troll.msp

Odds of 4d6 rolling a 20: 0.02701%
Source: http://www.anwu.org/games/dice_calc.html

Odds of 4d6 rolling a 20: 5.7%
Source: Cru

Odds of 4d6 rolling a 20: 5%
Source: Me, 4~24 equals 20 possible outcomes therefor any particular one has a 5% chance of happening.


Actually, all those sources (except your own) are correct, and roughly equivalent.

2.70061728395% and 2.701% are equal, just different levels of precision.  Your third source (0.02701) is not a percentage, it's a probability adding up to 1, so multiply by 100 to get a percentage, or 2.701%.  And finally, cru was not quoting odds of rolling a 20, he was totaling the odds of rolling anything between 20-24 inclusively, which is 2.701+1.543+0.772+0.309+0.077 =5.402%, which he rounded to 5.4%.

Your odds of 20 being 5% are wrong because there are multiple combinations of 4d6 that equal 20, but only a single combination that equals 4 (1,1,1,1), so 20 comes up much more often (for the same reason 7 is much more common in craps (2d6) than snake-eyes).

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Re: 4d6 or 1d20?
« Reply #16 on: January 27, 2011, 12:50:53 AM »
Nevermind that 4d6 has 21 possible results, not 20.  So even your own screwed up attempt at math is wrong.

Soda

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Re: 4d6 or 1d20?
« Reply #17 on: January 27, 2011, 01:58:09 AM »
Why 4d6, again?

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Re: 4d6 or 1d20?
« Reply #18 on: January 27, 2011, 08:38:10 AM »
chart that shows the likelihood of rolling each possible outcome relative to other outcomes with 1, 2, 3 and 4 d6's
[spoiler][/spoiler]
so you might want to widen your crit range...

the formula for getting the number of ways of getting any sum of k with 4d6
[spoiler][/spoiler]

the numbers on the graph are a little hard to read, here are the exact odds
[spoiler]
roll   
 |     number of ways out of 1296 to get that roll
 |     |                odds of getting a specific number
 |     |                 |
4     1               1/1296
5     4               4/1296
6     10             10/1296
7     20             20/1296
8     35             35/1296
9     56             56/1296
10   80             80/1296
11   104           104/1296
12   125           125/1296
13   140           140/1296
14   146           146/1296
15   140           140/1296
16   125           125/1296
17   104           104/1296
18   80             80/1296
19   56             56/1296
20   35             35/1296
21   20             20/1296
22   10             10/1296
23   4               4/1296
24   1               1/1296
[/spoiler]

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Lo77o

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Re: 4d6 or 1d20?
« Reply #19 on: January 27, 2011, 08:54:22 AM »
Im not sure why he suggested 4d6, but we usually consider suggestions from the players around the table. Besides, it seems like 4d6 might be fun to try out, maybe even for all d20 rolls, including skills and so on.
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