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Sploosh
2010-09-29, 11:06 PM
Hi there,

I'm just curious what the average PB would be for a roll formula rolling 4d6, rerolling 1s and turning the highest stat into a 18.

Could anyone help me with this?

Peregrine
2010-09-30, 04:24 AM
Okay, that's a tricky question. However, I like tricky maths questions. :smallsmile: I just wrote a short program to calculate point buy equivalents for rolling methods, and here's what I came up with. (Note that I'm working with 3e point buy at the moment, because it's what I know. I have a 4e PHB on hand and will adjust my answers as necessary, once I'm done.)

Standard 4d6 drop lowest gives an average point buy of about 4.755 per score, or 28.5 points for all six scores.

4d6, reroll 1s and drop lowest gives an average point buy of about 6.24 per score, or 37.4 points for all six scores.

I'm still working on the "replace the best roll with 18" part of your request, but it will be better than rolling five scores (at 6.24 points each) and taking an 18 for the sixth, which averages 47.2 points.

Edit: The hard part about calculating this is that doing it the long way, there's 4.7 quintillion stat arrays to consider. I'm trying to trim that number down somewhat.

Edit again: Okay, I've gotten it down to 16.7 million, but I'm not sure of my maths and it'll still probably take a few minutes.

Edit yet again: While waiting for this computer to churn out my results, I-- oh, wait, it just finished. And it's wrong, so clearly I was right to doubt my maths and I have to go back and fix my program. But I'm wondering whether it really is better than rolling five and taking 18 for the sixth? I think it might actually be exactly the same...

Edit once more: Actually it's worse. It's a little tricky to explain, but basically, if your sixth roll is worse than your previous best roll, you've reduced your overall result.

Edit one last time: Okay, I can't seem to get this to work. I think my brain is temporarily toasted. There's only one way I can get an answer for "replace the best roll with 18" that's even the right order of magnitude, and it logically cannot be right. For what it's worth, it gives me an answer of 33.7, which is somewhat lower than expected. Anyway, I'll come back to this tomorrow, try and fix my program, and also give you the correct 4e numbers.

Edit because I can't stay away: *facepalm* I am such an idiot. I was taking the mean of weighted values, when the weighting was such that I should just be taking the sum to find the mean... The hopefully correct version of the program is running now. There's still one part that doesn't make sense to me, but I'm just rolling with it (ha ha) for now.

And the result is... *drumroll* ...41.0 by 3e rules. I'm putting in the 4e point buy rules right now.

Edit with 4e results: Okay, assuming I've done this right, I-- you know what? This is getting ridiculous. I'm making a new post.

GoodbyeSoberDay
2010-09-30, 05:57 AM
A while ago I ran a Monte Carlo simulation (100,000 trials I think) that suggested 4d6 drop lowest 6 times had a greater 'point buy value' (aka how many points you'd have to have to buy that value, assuming you can subtract past 8 and get more points that way), so this machination has to be much better. I'll edit in the results in a second once I create and run it.

For simplicity I'm going to assume you mean re-roll *all* ones, so it's like rolling a bunch of d5+1s.

Edit: I just remembered how much of a pain it is to map all that stuff in matlab, so I had to reduce the trial size to 10000 and export all the fully-calculated stat gens to excel and map the point buy values there. I got an average of 36 point buy, while the PHB lists 22 as your standard. This is a significant increase in power, though as always there's a lot of variance in the dice.

Leolo
2010-09-30, 07:31 AM
If i do not calculated something wrong the average value of 4d6 drop lowest, reroll every 1 should be 13,4

If you set one score to 18 fix and the other 5 ability scores to 2x14 3x13 this would be equivalent to a point buy of 2+(2*5)+(3*3)+16=37

(You should note that this is a minimum point buy value for this average score. You could also have the same average score of 13.4 (ignoring the 18) if you have rolled 2x18 and 2x10+1x11. But this would result in a Point buy value of 51. )

Peregrine
2010-09-30, 08:46 AM
I got an average of 36 point buy, while the PHB lists 22 as your standard. This is a significant increase in power, though as always there's a lot of variance in the dice.

Note that in 4e, the starting array for point buys is an 8 and five 10s, so you've already "spent" 10 points before those 22. (Anti-min-maxing protection, I guess.)

And yes, my calculations assumed that rolled scores of 3 to 7 were worth minus one point for each step away from 8.

Sploosh
2010-09-30, 10:16 AM
Wow guys, that is a lot of tough math. Thank you so much though. :D

My friend is doing a 4e dark sun campaign journal and whatnot and we talked about stats. He came up with that dice roll for stats, or 28 point buy and I knew that it should be a little higher than that.

Peregrine
2010-09-30, 10:30 AM
Okay, the results are in. If my calculations are correct...

By 3rd edition point-buy rules, 4d6 drop lowest is actually worth an average of 28.5 points. I guess they figured that the less random results of point buy were worth the slightly lesser power. With rerolling 1s, it's worth 37.4 points.

By 4th edition point-buy rules, 4d6 drop lowest is worth a meagre 18.8 points, on average. I suppose the "reroll if it's awful" rule is its saving grace, as otherwise you'd be unquestionably better off using the standard point-buy rules. With rerolling 1s, it's worth 28.6 points.

Rerolling 1s and changing the best score to 18 is worth 41.0 points in 3rd edition, or 35.0 points in 4th edition.

I can show my working if you like...

BlckDv
2010-09-30, 10:31 AM
Wow guys, that is a lot of tough math. Thank you so much though. :D

My friend is doing a 4e dark sun campaign journal and whatnot and we talked about stats. He came up with that dice roll for stats, or 28 point buy and I knew that it should be a little higher than that.

"should" there gets dicey. (pun not intended) While it is true that if one were to cost-out what scores randomly rolled would be; it must be remembered that they are still random.

While a set of 16,16,15,15,15,13 would be quite a high value set, for many character concepts an 18, 16, 10, 10, 10, 8 set might actually be a more "valuable" set to the player, and conversely while an 18,18,12,10,8,6 might make some concepts jump for joy, a three score build would cringe at trying to make those work, and might prefer a 16,16,15,10,10,6 despite the loss of the two 18's.

When comparing random rolls to point buy, one must also consider how many "points" is it worth to be able to guarantee getting the exact balance of stats, not just total value, for the character you want to play.

Just food for thought when trying to decide if a given point buy is "equal" in player value to a roll.

(For the record I'm an old dice monkey myself and prefer to roll, then make a PC to fit the stats... some very memorable PCs have been born from seeing single digits numbers come up.)

Sploosh
2010-09-30, 10:58 AM
Haha, I dont think I could get the math behind the numbers if I tried. Besides, I am sure you did it perfectly.

As far as not doing the exact half way and giving a bit of a float for bad rolls and whatnot..do you have a good suggestion for handling that? I'm a dice monkey old edition style too sometimes and so I only use PB in really mechanically focused games or RPGA.

I'd love to have them be fair though.

Thanks guys, you are the best!

Peregrine
2010-09-30, 11:06 AM
As far as not doing the exact half way and giving a bit of a float for bad rolls and whatnot..do you have a good suggestion for handling that? I'm a dice monkey old edition style too sometimes and so I only use PB in really mechanically focused games or RPGA.

I'd love to have them be fair though.

Well, if we assume that Wizards' own rules are the baseline of "fair", then we can say that, for example, in 3rd edition the certainty of point buy is worth 3.5 points (because a 25-point buy and 4d6 drop lowest, which is 28.5 points on average, are meant to be equivalent). It's harder to do this with 4e, though, thanks to the standard point buy being generally better than 4d6 drop lowest by a decent margin. To properly figure that out, I'd have to rework my program to account for starting over if stats are unacceptably low. (I really ought to do that for 3e as well, before saying things like "certainty is worth 3.5 points".)

Sploosh
2010-09-30, 11:16 AM
Yikes, that sounds like a lot of work.

Kurald Galain
2010-09-30, 12:07 PM
My friend is doing a 4e dark sun campaign journal and whatnot and we talked about stats. He came up with that dice roll for stats, or 28 point buy and I knew that it should be a little higher than that.
That doesn't compare well.

In point buy, high scores are expensive because otherwise, pretty much everyone would put an 18 in their primary and secondary attribute (few 4E builds actually require a tertiary attribute).

This comparison assumes that all stat distributions with the same point buy value are equal. But they're not: 18/14/11/10/10/8 (the standard "specialist" array) is much better in practice than 14/14/13/13/13/13. And, point buy has the added safety feature that you won't end up with a 12-point or a 42-point character.

Frankly I fail to see the appeal of random stats generation, and have failed to see this appeal ever since second edition.

Susano-wo
2010-09-30, 01:15 PM
I really do like gambling rolling dice. And I think that's the basic appeal. YOu get to see that 18 roll, and go "woo hoo!"

After having done one game in PB(A 4E game), and making a pathfinder char with point buy for an up and coming campaign, I am warming up to it. Actually, though the excitement of rolling good stats goes away, the numbers themselves are more impressive to me. (As in, when I have to pay points for it, and it might actually be better to have 17 so I can raise another stat, that 18 means so much more. Its a sacrifice, not free money)

Also, I think this helps the sad state of heavy armor in the games I've played. WHen you get stats so high that plenty of people have, say 16 dex, the question of is -10ft a rnd worth a point of AC starts to be reeeealy easy to answer.

Finally PB is nice for the simple fact of making builds easy to evaluate, since they don't require good luck with the dice to play.

[sorry, this had nothing to do with the topic...though on that all I have to say is that being able to secure stats rather than have the chance to get screwed definitely has value. Also I haven't looked at 4E darksun yet (I'm scared and interested :P), but darksun is supposed to be harsh, and higher points/dice should be allowed for it]

GoodbyeSoberDay
2010-10-01, 04:55 PM
That doesn't compare well.

In point buy, high scores are expensive because otherwise, pretty much everyone would put an 18 in their primary and secondary attribute (few 4E builds actually require a tertiary attribute).

This comparison assumes that all stat distributions with the same point buy value are equal. But they're not: 18/14/11/10/10/8 (the standard "specialist" array) is much better in practice than 14/14/13/13/13/13. And, point buy has the added safety feature that you won't end up with a 12-point or a 42-point character.

Frankly I fail to see the appeal of random stats generation, and have failed to see this appeal ever since second edition.Oh, I agree that point buy is 'safer,' and you can often do more with point buy with fewer equivalent points than with a rolled result. That's why, given risk averse and/or optimizing players, rolling stats should yield a higher expected point buy total. That said, the OP's die rolling method is *far* greater in expected point buy value to your standard 22 point buy (or even 28 point buy), and it even guarantees an 18 in your primary. Any discrepancy for dice variance and optimization is small in comparison.

Peregrine: I took the 8 10 10 10 10 10 thing into account; I guess more technically I should say that in order to come up with a sane metric I allowed something like 7 7 10 10 10 10 to be equivalent to a -4 point buy in 4e. However, when I run the same monte carlo on the standard 4d6 drop lowest, I get about 21 point buy equivalent. That might have to do with the variance, but it seems unlikely at 10,000 trials. Either way, 4d6b3 sucks in 4e.

term1nally s1ck
2010-10-01, 06:27 PM
35.1, by my calculations. Difficult problem.

Kurald Galain
2010-10-01, 06:31 PM
I really do like gambling rolling dice. And I think that's the basic appeal. YOu get to see that 18 roll, and go "woo hoo!"
It's kind of funny - 4d6-drop-lowest was considered generous a couple editions ago, and now the baseline is 5d6-drop-lowest-two-and-gain-a-free-18. That's markedly less gambling than it used to be.

Just remember that the original methods for rolling for attributes did not allow you to swap them around!

Kylarra
2010-10-01, 06:32 PM
3D6 in order no minimums.

term1nally s1ck
2010-10-01, 07:58 PM
3d6 is 15pb. 4d6 drop lowest is 28, iirc.

GoodbyeSoberDay
2010-10-02, 03:25 AM
It's kind of funny - 4d6-drop-lowest was considered generous a couple editions ago, and now the baseline is 5d6-drop-lowest-two-and-gain-a-free-18. That's markedly less gambling than it used to be.

Just remember that the original methods for rolling for attributes did not allow you to swap them around!The funny thing is I think the OP's stat gen is even more generous than this, as it rerolls 1s.