Not to crap on your program but I do trust AnyDice a bit more as it has been independently validated.
Anydice gives correct numbers for what it's calculating, but it calculates mean score, not mean point value. 4k3 has a mean point value of 12.24 but a mean point value of 5.03 (because of the higher value of stats above 13). It would probably be possible to make AnyDice generate net point value, but it would be a hassle.
It also shows us that the average roll is rougly 16, 14, 13, 12, 10, 9. This is pretty close to the D&D 3 elite array (15, 14, 13, 12, 10, 8) and the slightly boosted D&D 4 standard array (16, 14, 13, 12, 11, 10).
Yeah exactly....its pretty much the same as standard array. The part you forgot to include though:
Highest at least
One
Two
Three
18
9.34%
0.38%
0.01%
17
30.07%
4.03%
0.34%
16
56.76%
17.85%
3.26%
15
79.40%
42.16%
14.13%
14
92.80%
69.01%
36.29%
Is that you have a 79% chance to roll a 15. And only a 42% chance to have a second 15
Point Buy you have a 100% chance to have two 15s.
Overall Rolling is potentially better...but its just as likely it will be bad.
Optimus, now you're getting into my stuff. I have computed the results of "4d6 drop low" long hand (with the help of Excel) so I could really study the different probabilities. It is very difficult to do a fair analysis using most of the random number generators out there. It is true that when you just write a brute force routine and generate a million or so results you can generate enough trials to produce valid results, it just isn't the same for me as writing out the permutations and combinations and computing the probabilities for each outcome. But it's a lot of work, too.
At least, I think I did it right. For example ... after rolling 4d6 drop the low and repeating this five more times, I have 8.93% chance you will have an 18 and only one 18; a 0.37% chance you will have 2-18s and only 2-18s; and a 0.01% chance you will have 3-18s and only 3-18s. Does your 9.34% chance for getting an 18 also allow you to have more than one 18 in the final mix. If so, then I believe we match precisely to the third significant figure.
Now if we set the 15 or better as the target value I have a 37.23% chance that the player will get one number that is 15 or greater, but all other values are lower than 15. For two values of 15 or greater, the probability is 28.04% that the player will have two values greater than 14 and all other values will be 14 or less. Because of the manner in which I tabulated my final values I can't easily get to an answer for rolling two 15s or better, because my formulas are too specific to answer that question as tabulated. The reason I went through my work was to drill down and show that it isn't just getting the two 15s, but what else happens below that. Yes, in point buy I could get two 15s as an automatic result, but I also have to give away the possibility of getting good scores on four other stats. In the random 4d6 exercise, I can also get better numbers all the way down.
To do a proper probabilistic analysis of a set of numbers, you would have to give me the results you want to check (15, 14, 13, 12, 11, 10) say and I could give you the probability of getting exactly that, getting anything better than that, and the probability of getting anything worse than that.
But your other thesis is correct ... if you have a specific set of stats you can live with in point buy, you have a 100% chance of getting that with point buy and less than 100% chance of getting that with 4d6 drop low. But if I increase one stat above the array you want to get in point buy, you now have a zero chance of getting that in point buy and I have some chance of getting it in 4d6 drop low.
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Tbh I don’t know enough about math to argue about this, but I still think my system, 4d6 drop the lowest plus a freebie point pool so everyone gets a chance to boost their stats and customize their character, works pretty well. Everyone ends up with an above average character customized just the way they want. I used this system in a couple campaigns and I never had any trouble with players complaining about their stats (though granted we were all friends and it might’ve been different with strangers online).
You can always just use all 3 systems. Have your players roll the 4d6 and drop the lowest, if they don't like the scores they can then use either point buy or standard array as a fallback,
You can always just use all 3 systems. Have your players roll the 4d6 and drop the lowest, if they don't like the scores they can then use either point buy or standard array as a fallback,
What I would probably do is say, "You can either roll 4d6-drop-lowest, or you can use the standard array, but you have to pick before you roll."
Some people like gambling, some don't. I'd give them the chance to do whichever they want.
I do something like this with h.p. They can either roll for it, or take the default. But I also house ruled that 1s and 2s are re-rolled, so the roll is statistically a little better than the default. Still, three of the players take the default each level, and one of them rolls it. The roller, a Sorcerer, lucked out with 2 6s in the first 3 levels, so has very nice hp.
But what I don't do is let them roll it and then if they don't like the roll, take the default. If you roll, you're keeping it... you don't have to roll. If you fear the RNG gods, take the standard.
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WOTC lies. We know that WOTC lies. WOTC knows that we know that WOTC lies. We know that WOTC knows that we know that WOTC lies. And still they lie.
Because of the above (a paraphrase from Orwell) I no longer post to the forums -- PM me if you need help or anything.
It also shows us that the average roll is rougly 16, 14, 13, 12, 10, 9. This is pretty close to the D&D 3 elite array (15, 14, 13, 12, 10, 8) and the slightly boosted D&D 4 standard array (16, 14, 13, 12, 11, 10).
Yeah exactly....its pretty much the same as standard array. The part you forgot to include though:
Highest at least
One
Two
Three
18
9.34%
0.38%
0.01%
17
30.07%
4.03%
0.34%
16
56.76%
17.85%
3.26%
15
79.40%
42.16%
14.13%
14
92.80%
69.01%
36.29%
Is that you have a 79% chance to roll a 15. And only a 42% chance to have a second 15
Point Buy you have a 100% chance to have two 15s.
Overall Rolling is potentially better...but its just as likely it will be bad.
Optimus, now you're getting into my stuff. I have computed the results of "4d6 drop low" long hand (with the help of Excel) so I could really study the different probabilities. It is very difficult to do a fair analysis using most of the random number generators out there. It is true that when you just write a brute force routine and generate a million or so results you can generate enough trials to produce valid results, it just isn't the same for me as writing out the permutations and combinations and computing the probabilities for each outcome. But it's a lot of work, too.
At least, I think I did it right. For example ... after rolling 4d6 drop the low and repeating this five more times, I have 8.93% chance you will have an 18 and only one 18; a 0.37% chance you will have 2-18s and only 2-18s; and a 0.01% chance you will have 3-18s and only 3-18s. Does your 9.34% chance for getting an 18 also allow you to have more than one 18 in the final mix. If so, then I believe we match precisely to the third significant figure.
Now if we set the 15 or better as the target value I have a 37.23% chance that the player will get one number that is 15 or greater, but all other values are lower than 15. For two values of 15 or greater, the probability is 28.04% that the player will have two values greater than 14 and all other values will be 14 or less. Because of the manner in which I tabulated my final values I can't easily get to an answer for rolling two 15s or better, because my formulas are too specific to answer that question as tabulated. The reason I went through my work was to drill down and show that it isn't just getting the two 15s, but what else happens below that. Yes, in point buy I could get two 15s as an automatic result, but I also have to give away the possibility of getting good scores on four other stats. In the random 4d6 exercise, I can also get better numbers all the way down.
To do a proper probabilistic analysis of a set of numbers, you would have to give me the results you want to check (15, 14, 13, 12, 11, 10) say and I could give you the probability of getting exactly that, getting anything better than that, and the probability of getting anything worse than that.
But your other thesis is correct ... if you have a specific set of stats you can live with in point buy, you have a 100% chance of getting that with point buy and less than 100% chance of getting that with 4d6 drop low. But if I increase one stat above the array you want to get in point buy, you now have a zero chance of getting that in point buy and I have some chance of getting it in 4d6 drop low.
Thanks for the analysis! Learned something with this.
I should know better talking math with the DnD crowd lol!
Tbh I don’t know enough about math to argue about this, but I still think my system, 4d6 drop the lowest plus a freebie point pool so everyone gets a chance to boost their stats and customize their character, works pretty well. Everyone ends up with an above average character customized just the way they want. I used this system in a couple campaigns and I never had any trouble with players complaining about their stats (though granted we were all friends and it might’ve been different with strangers online).
I like this one the best honestly. It seems to even things it for the most part.
Bill Allan (from D&D with H.S. students) does roll 4-drop-lowest, but he also allows them to re-roll 1s after the drop. So if you roll, say, 4-3-1-1, you keep the 4-3 and re-roll one of the ones, and drop the other one. They end up with pretty good stats.
Rollback Post to RevisionRollBack
WOTC lies. We know that WOTC lies. WOTC knows that we know that WOTC lies. We know that WOTC knows that we know that WOTC lies. And still they lie.
Because of the above (a paraphrase from Orwell) I no longer post to the forums -- PM me if you need help or anything.
Bill Allan (from D&D with H.S. students) does roll 4-drop-lowest, but he also allows them to re-roll 1s after the drop. So if you roll, say, 4-3-1-1, you keep the 4-3 and re-roll one of the ones, and drop the other one. They end up with pretty good stats.
Hm. That's a tad hard to do with AnyDice but isn't too hard to just math out. Rolling 2 1s is a bit rare (1-1-1-1 is 1/1296, 1-1-1-x is 20/1296 (5 values, 4 possible orders), 1-1-x-x is 250/1296 (25 values, 10 possible orders) so overall it's a 271/1296 chance of adding an average of 2.5 points, or +0.52 to the average for a mean stat of 12.76.
It's interesting that most people who like to roll stats also like to use die rolling conventions that produce significantly more powerful characters than RAW. Perhaps their actual objection to points or standard array is that they think the stats are too low?
allowing for rerolls when you roll poorly is much more common than forcing someone to reroll when they've done "too well"
it creates a situation where the squeaky wheels get the grease. As someone who is not very assertive or confrontational, I'm much more likely to end up with garbage than someone who is aggressive or whiny about it
it creates an unbalanced party. standard array/point buy caters to specialists who fill out a niche for their party which gives them all a chance to shine. in rolled parties you always have that guy who is better than everyone at everything, and/or the guy that sucks at almost everything and his "chances to shine" are forced, thinly veiled acts of charity and everyone knows it.
it can negate progression choices that would have otherwise been meaningful. Guys come in to Tips & Tactics saying stuff like, "I'm a rogue and rolled 20/18/16/16/14/12 for stats. What should I do with all my ASI's?" It's like they're done before they even start. They have less to look forward to or be excited about.
I'm not going to rage against it or anything, but I honestly don't see a single thing that it improves about the game, especially once Tasha's drops. If we want to play at a higher power level, having higher stats is just about the most boring way I can think of to achieve that, and unbalanced parties are just never going to fly at my table because they objectively make the game worse.
However if you enjoy it, go for it. The best thing about D&D is that you can change it however you like to fit the preferences of your table.
Everyone wants to roll for stats until they get a 6.
Perhaps this is true for many, but one of the best characters I have seen in years of gaming was a fighter with an 18.87 Strength and a 4 Int. Yes, I know that shows how long ago this was. The point is that the player embraced the challenges presented by his character. Throm was strong, but stupid and just liked to hit things. He became a rallying point for his entire party and the source of many side encounters, such as the rogue deciding to "have a talk with that nice merchant who had given his buddy such a great deal on supplies" or the mayors pretty daughter growing frustrated when the "Hero" who had slain the beast and saved her was oblivious to her flirting.
This is a role-playing game. Struggles and limitations are part of the fun.
No offense, but being a strong but dumb fighter is not exactly a challenge or struggle. It's kind of a trope, and being bad at something your class doesn't need isn't really a penalty.
It also sounds like he was roleplaying closer to 8 INT, because 4 is more like you can't even speak beyond grunts and gestures and don't understand concepts like "supplies" or "money." So this is a roleplay option that is completely achievable without rolling stats. Just put an 8 somewhere and play it up.
Everyone wants to roll for stats until they get a 6.
Perhaps this is true for many, but one of the best characters I have seen in years of gaming was a fighter with an 18.87 Strength and a 4 Int. Yes, I know that shows how long ago this was. The point is that the player embraced the challenges presented by his character. Throm was strong, but stupid and just liked to hit things. He became a rallying point for his entire party and the source of many side encounters, such as the rogue deciding to "have a talk with that nice merchant who had given his buddy such a great deal on supplies" or the mayors pretty daughter growing frustrated when the "Hero" who had slain the beast and saved her was oblivious to her flirting.
This is a role-playing game. Struggles and limitations are part of the fun.
No offense, but being a strong but dumb fighter is not exactly a challenge or struggle. It's kind of a trope, and being bad at something your class doesn't really need isn't really a penalty.
It also sounds like he was roleplaying closer to 8 INT, because at 4 is more like a level where you can't even speak beyond grunts and gestures. So this is a roleplay option that is completely achievable without rolling stats. Just put an 8 somewhere and play it up.
I thought it sounded like a good role playing experience.
Also, the way @Eriniel described it Throm was naive as well as dumb. He didn’t get that the mayor’s daughter was flirting with him.
There's nothing wrong with that, but 18/85 strength and 4 Int on a fighter is rolling really good stats. I'm pretty sure playing 16 strength and 4 int would have been less fun...
Bill Allan (from D&D with H.S. students) does roll 4-drop-lowest, but he also allows them to re-roll 1s after the drop. So if you roll, say, 4-3-1-1, you keep the 4-3 and re-roll one of the ones, and drop the other one. They end up with pretty good stats.
Hm. That's a tad hard to do with AnyDice but isn't too hard to just math out. Rolling 2 1s is a bit rare (1-1-1-1 is 1/1296, 1-1-1-x is 20/1296 (5 values, 4 possible orders), 1-1-x-x is 250/1296 (25 values, 10 possible orders) so overall it's a 271/1296 chance of adding an average of 2.5 points, or +0.52 to the average for a mean stat of 12.76.
It's interesting that most people who like to roll stats also like to use die rolling conventions that produce significantly more powerful characters than RAW. Perhaps their actual objection to points or standard array is that they think the stats are too low?
I think that could be the main reason. Does that mean those DMs should consider boosts the point-buy's point and increase the maximum as an alternative?
Yeah, it seems to me - from reading many of these discussions - that of the people who say they like "4d6 drop lowest", a pretty big chunk actually use "4d6 drop lowest, but then reroll or add numbers or change things around if [various conditions]".
Yeah, it seems to me - from reading many of these discussions - that of the people who say they like "4d6 drop lowest", a pretty big chunk actually use "4d6 drop lowest, but then reroll or add numbers or change things around if [various conditions]".
... and that is exactly why I think the real average of 4d6 drop low is much higher than people think. Most DMs have empathy to let a player reroll if they get something that just doesn't look exciting enough. So the average and high for a typical PC in this method is going to be higher than the math says it should be.
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Fair enough!
Optimus, now you're getting into my stuff. I have computed the results of "4d6 drop low" long hand (with the help of Excel) so I could really study the different probabilities. It is very difficult to do a fair analysis using most of the random number generators out there. It is true that when you just write a brute force routine and generate a million or so results you can generate enough trials to produce valid results, it just isn't the same for me as writing out the permutations and combinations and computing the probabilities for each outcome. But it's a lot of work, too.
At least, I think I did it right. For example ... after rolling 4d6 drop the low and repeating this five more times, I have 8.93% chance you will have an 18 and only one 18; a 0.37% chance you will have 2-18s and only 2-18s; and a 0.01% chance you will have 3-18s and only 3-18s. Does your 9.34% chance for getting an 18 also allow you to have more than one 18 in the final mix. If so, then I believe we match precisely to the third significant figure.
Now if we set the 15 or better as the target value I have a 37.23% chance that the player will get one number that is 15 or greater, but all other values are lower than 15. For two values of 15 or greater, the probability is 28.04% that the player will have two values greater than 14 and all other values will be 14 or less. Because of the manner in which I tabulated my final values I can't easily get to an answer for rolling two 15s or better, because my formulas are too specific to answer that question as tabulated. The reason I went through my work was to drill down and show that it isn't just getting the two 15s, but what else happens below that. Yes, in point buy I could get two 15s as an automatic result, but I also have to give away the possibility of getting good scores on four other stats. In the random 4d6 exercise, I can also get better numbers all the way down.
To do a proper probabilistic analysis of a set of numbers, you would have to give me the results you want to check (15, 14, 13, 12, 11, 10) say and I could give you the probability of getting exactly that, getting anything better than that, and the probability of getting anything worse than that.
But your other thesis is correct ... if you have a specific set of stats you can live with in point buy, you have a 100% chance of getting that with point buy and less than 100% chance of getting that with 4d6 drop low. But if I increase one stat above the array you want to get in point buy, you now have a zero chance of getting that in point buy and I have some chance of getting it in 4d6 drop low.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
Tbh I don’t know enough about math to argue about this, but I still think my system, 4d6 drop the lowest plus a freebie point pool so everyone gets a chance to boost their stats and customize their character, works pretty well. Everyone ends up with an above average character customized just the way they want. I used this system in a couple campaigns and I never had any trouble with players complaining about their stats (though granted we were all friends and it might’ve been different with strangers online).
You can always just use all 3 systems. Have your players roll the 4d6 and drop the lowest, if they don't like the scores they can then use either point buy or standard array as a fallback,
I like this. Consider it stolen.
All things Lich - DM tips, tricks, and other creative shenanigans
What I would probably do is say, "You can either roll 4d6-drop-lowest, or you can use the standard array, but you have to pick before you roll."
Some people like gambling, some don't. I'd give them the chance to do whichever they want.
I do something like this with h.p. They can either roll for it, or take the default. But I also house ruled that 1s and 2s are re-rolled, so the roll is statistically a little better than the default. Still, three of the players take the default each level, and one of them rolls it. The roller, a Sorcerer, lucked out with 2 6s in the first 3 levels, so has very nice hp.
But what I don't do is let them roll it and then if they don't like the roll, take the default. If you roll, you're keeping it... you don't have to roll. If you fear the RNG gods, take the standard.
WOTC lies. We know that WOTC lies. WOTC knows that we know that WOTC lies. We know that WOTC knows that we know that WOTC lies. And still they lie.
Because of the above (a paraphrase from Orwell) I no longer post to the forums -- PM me if you need help or anything.
Thanks for the analysis! Learned something with this.
I should know better talking math with the DnD crowd lol!
I like this one the best honestly. It seems to even things it for the most part.
My DM uses a stolen house rule from another DM. The rule is the following:
He doesn't like point buy nor standard array because players can't get 16.
Bill Allan (from D&D with H.S. students) does roll 4-drop-lowest, but he also allows them to re-roll 1s after the drop. So if you roll, say, 4-3-1-1, you keep the 4-3 and re-roll one of the ones, and drop the other one. They end up with pretty good stats.
WOTC lies. We know that WOTC lies. WOTC knows that we know that WOTC lies. We know that WOTC knows that we know that WOTC lies. And still they lie.
Because of the above (a paraphrase from Orwell) I no longer post to the forums -- PM me if you need help or anything.
That is effectively 'roll 4d5, keep 3, and add 3'. It produces a mean stat of 13.43 (1.19 better than 4k3).
Hm. That's a tad hard to do with AnyDice but isn't too hard to just math out. Rolling 2 1s is a bit rare (1-1-1-1 is 1/1296, 1-1-1-x is 20/1296 (5 values, 4 possible orders), 1-1-x-x is 250/1296 (25 values, 10 possible orders) so overall it's a 271/1296 chance of adding an average of 2.5 points, or +0.52 to the average for a mean stat of 12.76.
It's interesting that most people who like to roll stats also like to use die rolling conventions that produce significantly more powerful characters than RAW. Perhaps their actual objection to points or standard array is that they think the stats are too low?
Not a fan because:
I'm not going to rage against it or anything, but I honestly don't see a single thing that it improves about the game, especially once Tasha's drops. If we want to play at a higher power level, having higher stats is just about the most boring way I can think of to achieve that, and unbalanced parties are just never going to fly at my table because they objectively make the game worse.
However if you enjoy it, go for it. The best thing about D&D is that you can change it however you like to fit the preferences of your table.
My homebrew subclasses (full list here)
(Artificer) Swordmage | Glasswright | (Barbarian) Path of the Savage Embrace
(Bard) College of Dance | (Fighter) Warlord | Cannoneer
(Monk) Way of the Elements | (Ranger) Blade Dancer
(Rogue) DaggerMaster | Inquisitor | (Sorcerer) Riftwalker | Spellfist
(Warlock) The Swarm
No offense, but being a strong but dumb fighter is not exactly a challenge or struggle. It's kind of a trope, and being bad at something your class doesn't need isn't really a penalty.
It also sounds like he was roleplaying closer to 8 INT, because 4 is more like you can't even speak beyond grunts and gestures and don't understand concepts like "supplies" or "money." So this is a roleplay option that is completely achievable without rolling stats. Just put an 8 somewhere and play it up.
My homebrew subclasses (full list here)
(Artificer) Swordmage | Glasswright | (Barbarian) Path of the Savage Embrace
(Bard) College of Dance | (Fighter) Warlord | Cannoneer
(Monk) Way of the Elements | (Ranger) Blade Dancer
(Rogue) DaggerMaster | Inquisitor | (Sorcerer) Riftwalker | Spellfist
(Warlock) The Swarm
I thought it sounded like a good role playing experience.
Sure, I'm just saying you don't need to roll stats to play a dumb guy. 8 INT is as dumb as you want it to be.
My homebrew subclasses (full list here)
(Artificer) Swordmage | Glasswright | (Barbarian) Path of the Savage Embrace
(Bard) College of Dance | (Fighter) Warlord | Cannoneer
(Monk) Way of the Elements | (Ranger) Blade Dancer
(Rogue) DaggerMaster | Inquisitor | (Sorcerer) Riftwalker | Spellfist
(Warlock) The Swarm
Okay, I can see your point
Also, the way @Eriniel described it Throm was naive as well as dumb. He didn’t get that the mayor’s daughter was flirting with him.
There's nothing wrong with that, but 18/85 strength and 4 Int on a fighter is rolling really good stats. I'm pretty sure playing 16 strength and 4 int would have been less fun...
I think that could be the main reason. Does that mean those DMs should consider boosts the point-buy's point and increase the maximum as an alternative?
Yeah, it seems to me - from reading many of these discussions - that of the people who say they like "4d6 drop lowest", a pretty big chunk actually use "4d6 drop lowest, but then reroll or add numbers or change things around if [various conditions]".
... and that is exactly why I think the real average of 4d6 drop low is much higher than people think. Most DMs have empathy to let a player reroll if they get something that just doesn't look exciting enough. So the average and high for a typical PC in this method is going to be higher than the math says it should be.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt