Just rolled up my new character and (someone with math skills needed)....

[Bastoche]

Asuming you systematically reroll:

the probability to get a 6 on the first die is one half. The probability to get a 5 is 2/9th, to get a 4 is 4/27th, to get a 3 is 1/18th, a 2 is 7/216th and a 1 is 1/216th.

So the average on the first die is:

6*0.5 + 5*2/9 + 4*4/27 + 3/18 + 14/216+ 1/216 = 4.93981

For the second die, the probability to get a 6 is 12/36th, a 5 is 8/36th a 4 is 7/36th a 3 is 5/36th a 2 is 3/36th and a 1 is 1/36th

So the average is:

6*1/3 + 5*8/36 + 4*7/36 + 3*5/36 + 2*3/36 + 1/36 = 4.5

The average of the last die is a simple 3.5

So on averge, you get 12.93981. Let's say 13.

Your average should be higher, because once in a while, you would get some possibilities wherre you don't want to reroll. Like getting a 16 on the first roll.

 

[Conaill]

Yeah, I messed up in my original estimate.

Out of 1 million rolls, I'm getting 13.2650 if you reroll on a 3 or less, 13.4209 if you do the 2-reroll on a 4 or or less, the 1-reroll on 3 or less.

BTW, It's not entirely unambiguous how you do the optional rerolls. For example, if you get 6,6,2 as your first rolls and decide not to reroll the 6, do you still get to reroll the 2 *two* times? I.e. do you have to skip the 2-reroll altogether? (that's what I assumed in my calculation, and what Dakkareth's algorithm suggests as well)

 

[MerakSpielman]

I assumed I got to reroll that die twice if I liked.

 

[Conaill]

Ah. Yes, that would make a difference. Hang on, results coming up...

If you reroll the two lowest rolls on a 4 or less, then the last one on a 3 or less, the average (over 2 million rolls) comes to 13.5608.

PS: you could also argue that you take the *lowest* dice at any point. So if you roll 3,2,1, then reroll a 6 and 5, you would get to reroll that first 3.

 

[MerakSpielman]

For the record, these are the exact numbers I rolled:

1:
Rolled 2, 5, 6. Rerolled the 2 and got a 4. Stopped rerolling: 15

2:
Rolled 5, 6, 6. Kept as is: 17

3:
Rolled 6, 4, 4. Rerolled one of the 4s. Got a 6. Stopped rerolling: 16

4:
rolled 2, 5, 6. Rerolled the 2. Got a 6. Stopped rerolling: 17

5:
Rolled 6, 3, 1. Rerolled the 3 and 1. Got two sixes. Stopped rerolling: 18

6:
Rolled 2, 4, 5. Rerolled the 2 and 4. Got 2, 3. Rerolled them. Got 4, 5. No more rerolls: 14


Now that I think about it, roll #6 is the only one that didn't have a 6 in it to start out. It's also the only set where I even bothered rerolling the second time.

Cool.

 

[MerakSpielman]

...you could also argue that you take the *lowest* dice at any point. So if you roll 3,2,1, then reroll a 6 and 5, you would get to reroll that first 3.

Ah. It was assumed that once we kept a number, it was kept forever and could not be rerolled.

 

[Conaill]

6:
Rolled 2, 4, 5. Rerolled the 2 and 4. Got 2, 3. Rerolled them. Got 4, 5. No more rerolls: 14

This one looks iffy. Are you saying that you rerolled 2 dice *twice*?

 

[MerakSpielman]

Hey, my notes are pretty sketchy. Good to know I'm under surveillance.

Truth be told, for that roll, I only wrote down the original numbers and the final result. At that time, I didn't know I was going to be telling anybody my exact rolls, so when I typed it in, I just made up how I got from the first rolls to the final number. I know I did it legit when I did it, I just messed up typing it in.

Blast... Now you don't trust me! It's true, I swear...

 

[Dakkareth]

You get quite nice stats with this method, but I'd rather use 39 point buy - safer and more freedom for character customization.

Some nice stats I got while playing around

13,16,13,14,17,17 - nice cleric

14,15,15,16,13,18 - even nicer sorcerer

16,16,15,15,13,13 - nice fighter type


If someone else wants to play, too, I attached my program - remove the .txt and run it through a python interpreter (www.python.org).

 

[Conaill]

Actually, if you do the rerolls the way Dakkareth and I were doing it originally, this method gives almost exactly the same results as 5d6-drop-2, except that it has a slightly lower standard deviation. Your way of rerolling makes it even more powerful than 5d6.