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I am starting on a new home game this weekend. :-)
I can either use a 20 point buy, or roll 4 d6 seven times and drop the lowest d6 for each roll and drop the lowest roll all together. Rolling the dice seems the better choice, but I was wondering if there were any statistical geniuses out there that could tell me how much better off I am?
Or even what my average roll will be.
I am not following what you mean by total average. Are you asking for all six stats? If so it would be the same
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I am not following what you mean by total average. Are you asking for all six stats? If so it would be the same
Because I am allowed to roll 4 dice 7 times there is an extra roll. The smallest of the seven rolls is to be discarded and (I think) this will change the average roll value to something higher than 12.2446.
I would roll if it's re-roll 1s. If it's not, I would go point buy.
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I'm not convinced. Rolling 4d6 and dropping the lowest will give you an average of 11. Agreed, some will be higher and some lower. But the chances or rolling a 17 or 18 is very low.
If you were to take average across the board stats with point buy then you end up with 14 13 13 13 13 13. These are much better. You also have the flexibility to put a stat higher, or to make one lower for the extra points. I would go for the point buy.
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I'm not convinced. Rolling 4d6 and dropping the lowest will give you an average of 11. Agreed, some will be higher and some lower. But the chances or rolling a 17 or 18 is very low.
If you were to take average across the board stats with point buy then you end up with 14 13 13 13 13 13. These are much better. You also have the flexibility to put a stat higher, or to make one lower for the extra points. I would go for the point buy.
I see your point but the numbers for rolling are at least somewhat higher than you have suggested. Just rolling 4 and discarding the lowest pushes the average up to 12.2446. Dropping the overall lowest roll of 7 has to push the average even higher. What I haven't been able to compute yet is what that average would be.
Rolling 4 dice 7 times dropping the lowest each time will give you FAR greater results then 20 pt buy. I have never done the math and honestly, my brain is swimming already, but I know from experience. The problem I have always seen with rolling the dice is how incredibly polar the players can end up being.
What if you instead allowed your players to use 15 point buy and then gave them two rolls of a D6 which can each individually be added to a stat.
I have never done this, but as usual I am making this up as I go....
I'm a fan of point-buy, but I'm notoriously bad at rolling PC stats.
My dice like being behind the GM screen, not in front of it.
Also everyone gets a nice level playing ground.
16
12
12
15
16
10
Or in other words, 31 point buy. If you want a game that is that powerful, then have at it. Just know that typically point buy pales in comparison to most any "reroll..." method.
(Yes I just rolled that up)
EDIT:
By "pales" i meant is less powerful NOT BETTER. I prefer point buy
Point buy allows me to "tailor" a build if certain stats are needed. If I need an 18, then I use point buy even at 15 point buy because it's the only way I'll ever get 18. The same goes if I only need one stat to focus on, with all others at 10 or 9 at the worst.
But if I need multiple stats to be higher than 12, then I'd go for the 4D6 rolls. There's no way I can get three 13s or an 18 with some 14s on the side without 25 point buy and some serious min-maxing with racial bonuses and traits.
If your GM is "roll 4d6 drop the lowest and you can only roll once per stat" then you are screwed. Don't even make your character build until your rolls have been "witnessed", and be prepared for a fighter with a STR of 10 and a WIS of 4.
I was playing around with rolling the other day and comparing it to point buy and I usually ended up with about 20 point equivalent point buys. Occasionally I ended up with significantly less (around 10 point-buy equivalent and one time a -3 point buy). Might just be that they were lucky rolls.
If you're not up to playing the game of chance, then you're better off with the 20-point buy.
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Because I was bore and I love you all I did some calculations. I'm no mathematician so I might be wrong, but here is some numbers I came up with.
If you roll 4d6 and drop the lowest, here are the frequency of the totals.
-
3 - 1
4 - 4
5 - 10
6 - 21
7 - 38
8 - 62
9 - 91
10 - 122
11 - 148
12 - 167
13 - 172
14 - 160
15 - 131
16 - 94
17 - 54
18 - 21
Total: 1296
It seem that at least the mode average is higher than I thought.
RPG Superstar Season 9 Top 16, RPG Superstar 2015 Top 32
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I use this when I need to understand dice and number distribution.
13 has the highest probability when rolling 4d6 drop the lowest.
With the method of rolling you have access to, here is what I came up with:
I rolled them 6 times. I included the total of the bonuses as well.
16,13,13,12,11,7 (+6)
16,16,13,12,12,11 (+9)
16,16,13,13,11,9 (+8)
15,15,14,13,11,11 (+7)
16,15,13,11,11,10 (+6)
16,16,14,14,10,10 (+10)
Any of those would be great.
I haven't ran any of the numbers on a 20 point buy, but just some quick work and I was able to build a stat array with a total of +8 in bonuses, but the highest bonus was +3 and there was one -1.
I personally would roll.
Unless you plan to play a primary caster, especially one that will utilize save-or-X spells, you are going to do better with the rolling method.
And really, only a Wizard/Sorcerer/Witch suffers overmuch from not having a maxed casting stat. Clerics and Druids can be just fine with a 16.
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some good stuff . . .
It seem that at least the mode average is higher than I thought.
The math isn't that hard to complete what you have already done. Add up the totals that you already gave 1X3 + 4X4 + ... + 18X21 and then divide by 1296. That is how I arrived at an average of 12.2446. I am having a tough time deciding on how to approach the 2nd half of the problem. How much of an advantage do you get by being able to throw out the lowest of 7 rolls? I think that it will require that each of the 7 rolls has 1296 possibilities giving 6 x 10^21 total different dice combinations. I will write a little program in the morning to see if that will work to give me the answer that I am looking for. Unless there is someone out there that understands statisics and can show me a better way.
I think that depends on the class you wish to play!
By rolling you have a good chance that your average will be higher than with point buy.
But, you can't actually distribute, so chances are very good that your highest attribute will be lower than with point buy.
When I play a Fighter I would always go point buy, because all I need is an 18 Str and a not too sucky Con (14).
But if I would like to play a Monk/Bard/Paladine/Rogue I would go for rolling as you need multiple Attributes meduim high and this is what rolling usually delivers.
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So . . . I tried to write a computer program to find the final answer, but it isn't possible using only a brute force method. Using my desktop computer I worked out that it would take about 93 years to complete the calculations.
Any chance there are any advanced math types out there that can show me a better way?
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RPG Superstar Season 9 Top 16, RPG Superstar 2015 Top 32
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Here is a quick observation from looking at that program I posted the link to. The number you end up dropping is going to be lower then 12.
In the set that I posted I forgot to include the number that I dropped. Most of them were lower then 10, and several of the high numbers came up as the 7th number.
I wouldn't worry about the math of it all, with 4d6 drop lowest you have a higher chance of a number above 11 then below 11 for the simple reason that most 1s and 2s will be dropped. Considering that, you have a good chance that you will have an array that will have all positive modifiers and no negative modifiers.