What's the chance to roll 18 from 4 six sided dice where of course only the 3 highest are chosen?
I just want to put it into perspective for someone.
My math isn't that good or even correct for what I know. I know its 1/6 per die and then i think 3 dices with all 6s is like 1/216 I believe. But I'm unsure of what changes if it's 4 dice that are being rolled if it changes anything?
https://www.omnicalculator.com/statistics/dice seems pretty good for calculating simple rolls, and I usually look at https://statmodeling.stat.columbia.edu/2014/07/12/dnd-5e-advantage-disadvantage-probability/ for the d20 table, but I'm not aware of a pre-generated table that would tell you 4d6k1 or whatever else. The omnicalculator tells me that the odds of rolling a 6 on 3 of 4 d6's would be 0.015432 (about 1.5%), but I'm not really sure how you'd use omnicalculator to figure that odds of mixed rolls that don't need three dice of the same face value.
There are 1,296 different unique ways to roll 4D6's. 6 possibilities per die, so 6^4 different permutations. Of these, there are 21 different ways to roll at least 3 out of 4 as 6's, as follows. The first 3 dice as 6's, then the fourth can be from 1 to 5 (so 5 total possibilities for the 4th die being the non-six) plus the same 5 possibilities for each of the other 3 dice to be the non 6. This gives 20 different possibilities for exactly 3 6's, plus the one possibility that there are all four dice 6's, for a total of 21 ways to roll at least 3 of 4 as 6's. Divide 21/1,296 and you get 1.62%. The 1.54% is equal to 20/1,296, which would be the percent chance to get exactly 3 of 4 dice as 6's (since it's exactly 3 of 4, the 4th dice in this scenario cannot be a six; this removes one possibility from the numerator). Since all 4 being 6's would give the desired result, it's 1.62%.
What's the chance to roll 18 from 4 six sided dice where of course only the 3 highest are chosen?
I just want to put it into perspective for someone.
My math isn't that good or even correct for what I know. I know its 1/6 per die and then i think 3 dices with all 6s is like 1/216 I believe. But I'm unsure of what changes if it's 4 dice that are being rolled if it changes anything?
Exactly 7/432, or roughly 1.62% (rounding slightly down). Note that as other people have pointed out, rolling for your stats will tend to give you a better statline than using point buy. Note also that this is usually not the question you want the answer to; usually, what you really want to know is what your odds are of having at least one 18 in a stat (remember, the actual procedure is to roll for 6 stats, and then you sort them in priority order, so if you want an 18 in a stat you like, you have 6 chances to do so). This is exactly 1-(1-7/432)^6, or about 9.34% (rounding slightly up).
Also, rolling for your stats means you have a (low) chance of generating a 3 in a stat, which can cause issues - e.g. Int 3 will make you dumber than many beasts. I've had GMs employ various house rules to stop PCs from entering game with a stat that low, and different house rules will impact the odds of an 18 differently.
I think that betting on an 18 isn't a requirement... but getting at least 2 scores of 15 or higher is. Having your dump stats swing higher or lower is fun but not fundamental, but trying to play a Barbarian with starting 12's across the board is gonna be a Bad Time.
That's been my experience with rolled stats. I often roll more 13's and 14's than I have a right to, but not having one or two at 15 or above can really slow down your Tier 1 and Tier 2 progression.
Yeah, few characters need more than 3 or 4 good stats, but all characters need 1 or 2 great stats.
If I can get at least 1 16-17 and 2 14-15s while rolling, I've rolled well. The other 3 could be less than 10 and I'd keep that. A few flaws make characters interesting.
Thanks everyone, I just wanted to know the chances. I'm often looked at in the group as someone trying to cheat with these rolls, like "no you cheated you can't have a 17 or 16". I have never received an 18 either through computer generated rolls or using real dice. Mostly I am assumed the cheater because I'm trying to make a decent character so I look for threads where people have min-maxed certain classes. Like I even have 3 source books on dnd beyond and apparently that's cheating because I'm using it, so I gave them all access to it in the campaign so they'll stop complaining.
I just thought it was funny when one of the people who I added to my campaign for source book access has both characters with 18s and one with two 18s, but apparently I'm a cheater with my rolls who has never gotten a 18 so far. So he got mad when my rolls where all positive modifiers as if I have to have something below 9.
We're all fairly new and most of them just want to use the phb only, because its easy but I want to start using tasha and xanadar and new rules and have all the crazy stuff i hear on reddit and youtube, not just we walk into a dungeon we hit a group of kobolds repeat until boss, find loot, leave./rant
Aha, so I was right, your question was about the odds of having at least one 18.
It is "cheating" for different PCs in a campaign to play by different rules - standard practice is for a GM to declare a given sourcebook legal or illegal for a campaign, and then all PCs in the campaign are expected to abide by that ruling. Same thing can be done for any specific rule, of course. My point is that all PCs should share the same ruleset.
For example, since rolling for your stats genuinely provides a higher average than point buy, but also allows a lower minimum, it's bad form to force some PCs to point buy, force some to roll, and allow some to choose. All PCs should be subject to the same ruleset.
The only "exception" that comes to mind is official material like Curse of Strahd that alters the in-game economy, radically altering class balance based on how much money various classes need to function. But even so, the economy is changed for all PCs equally, so the only concern is that it's routine for that campaign for PCs to not find out they won't be able to afford their gear until after the campaign has started and suddenly the monk is gloating and the wizard is contemplating rolling a new character.
The chance of getting at least 1 ability score at 18 (before racials) after rolling 4d6 drop lowest is 9.34% - if I haven't messed my maths up - which is pretty close to 1 in 11. So if 11 players rolled for stats at a table - you'd have good odds that one of the players would have at least one 18.
What's the chance to roll 18 from 4 six sided dice where of course only the 3 highest are chosen?
I just want to put it into perspective for someone.
My math isn't that good or even correct for what I know. I know its 1/6 per die and then i think 3 dices with all 6s is like 1/216 I believe. But I'm unsure of what changes if it's 4 dice that are being rolled if it changes anything?
https://www.omnicalculator.com/statistics/dice seems pretty good for calculating simple rolls, and I usually look at https://statmodeling.stat.columbia.edu/2014/07/12/dnd-5e-advantage-disadvantage-probability/ for the d20 table, but I'm not aware of a pre-generated table that would tell you 4d6k1 or whatever else. The omnicalculator tells me that the odds of rolling a 6 on 3 of 4 d6's would be 0.015432 (about 1.5%), but I'm not really sure how you'd use omnicalculator to figure that odds of mixed rolls that don't need three dice of the same face value.
dndbeyond.com forum tags
I'm going to make this way harder than it needs to be.
Weird, using the omni calculator CC linked, I got 0.016204 (about 1.6%) as the odds of rolling 3 out of 4 6s. I wonder what we did differently.
I got that the second time too. Not sure what I did wrong the first time, maybe I changed an entry but the calculation didn't update?
dndbeyond.com forum tags
I'm going to make this way harder than it needs to be.
And I got the "0.015432" same as CC... Interesting.... =D
Edit: Checked a bit and the 0,015 is for "exactly 3 dice = 6" and the 0,016 is for "at least 3 dice = 6".
It's 1.62037%. Probability wise:
There are 1,296 different unique ways to roll 4D6's. 6 possibilities per die, so 6^4 different permutations. Of these, there are 21 different ways to roll at least 3 out of 4 as 6's, as follows. The first 3 dice as 6's, then the fourth can be from 1 to 5 (so 5 total possibilities for the 4th die being the non-six) plus the same 5 possibilities for each of the other 3 dice to be the non 6. This gives 20 different possibilities for exactly 3 6's, plus the one possibility that there are all four dice 6's, for a total of 21 ways to roll at least 3 of 4 as 6's. Divide 21/1,296 and you get 1.62%. The 1.54% is equal to 20/1,296, which would be the percent chance to get exactly 3 of 4 dice as 6's (since it's exactly 3 of 4, the 4th dice in this scenario cannot be a six; this removes one possibility from the numerator). Since all 4 being 6's would give the desired result, it's 1.62%.
Exactly 7/432, or roughly 1.62% (rounding slightly down). Note that as other people have pointed out, rolling for your stats will tend to give you a better statline than using point buy. Note also that this is usually not the question you want the answer to; usually, what you really want to know is what your odds are of having at least one 18 in a stat (remember, the actual procedure is to roll for 6 stats, and then you sort them in priority order, so if you want an 18 in a stat you like, you have 6 chances to do so). This is exactly 1-(1-7/432)^6, or about 9.34% (rounding slightly up).
Also, rolling for your stats means you have a (low) chance of generating a 3 in a stat, which can cause issues - e.g. Int 3 will make you dumber than many beasts. I've had GMs employ various house rules to stop PCs from entering game with a stat that low, and different house rules will impact the odds of an 18 differently.
I think that betting on an 18 isn't a requirement... but getting at least 2 scores of 15 or higher is. Having your dump stats swing higher or lower is fun but not fundamental, but trying to play a Barbarian with starting 12's across the board is gonna be a Bad Time.
That's been my experience with rolled stats. I often roll more 13's and 14's than I have a right to, but not having one or two at 15 or above can really slow down your Tier 1 and Tier 2 progression.
dndbeyond.com forum tags
I'm going to make this way harder than it needs to be.
Yeah, few characters need more than 3 or 4 good stats, but all characters need 1 or 2 great stats.
If I can get at least 1 16-17 and 2 14-15s while rolling, I've rolled well. The other 3 could be less than 10 and I'd keep that. A few flaws make characters interesting.
Thanks everyone, I just wanted to know the chances. I'm often looked at in the group as someone trying to cheat with these rolls, like "no you cheated you can't have a 17 or 16". I have never received an 18 either through computer generated rolls or using real dice. Mostly I am assumed the cheater because I'm trying to make a decent character so I look for threads where people have min-maxed certain classes. Like I even have 3 source books on dnd beyond and apparently that's cheating because I'm using it, so I gave them all access to it in the campaign so they'll stop complaining.
I just thought it was funny when one of the people who I added to my campaign for source book access has both characters with 18s and one with two 18s, but apparently I'm a cheater with my rolls who has never gotten a 18 so far. So he got mad when my rolls where all positive modifiers as if I have to have something below 9.
We're all fairly new and most of them just want to use the phb only, because its easy but I want to start using tasha and xanadar and new rules and have all the crazy stuff i hear on reddit and youtube, not just we walk into a dungeon we hit a group of kobolds repeat until boss, find loot, leave./rant
Aha, so I was right, your question was about the odds of having at least one 18.
It is "cheating" for different PCs in a campaign to play by different rules - standard practice is for a GM to declare a given sourcebook legal or illegal for a campaign, and then all PCs in the campaign are expected to abide by that ruling. Same thing can be done for any specific rule, of course. My point is that all PCs should share the same ruleset.
For example, since rolling for your stats genuinely provides a higher average than point buy, but also allows a lower minimum, it's bad form to force some PCs to point buy, force some to roll, and allow some to choose. All PCs should be subject to the same ruleset.
The only "exception" that comes to mind is official material like Curse of Strahd that alters the in-game economy, radically altering class balance based on how much money various classes need to function. But even so, the economy is changed for all PCs equally, so the only concern is that it's routine for that campaign for PCs to not find out they won't be able to afford their gear until after the campaign has started and suddenly the monk is gloating and the wizard is contemplating rolling a new character.
The chance of getting at least 1 ability score at 18 (before racials) after rolling 4d6 drop lowest is 9.34% - if I haven't messed my maths up - which is pretty close to 1 in 11.
So if 11 players rolled for stats at a table - you'd have good odds that one of the players would have at least one 18.
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