Auspicious Marking statistics

[3d6]

There are 6 feats in Races of Stone that allow a character to roll two dice and pick the best one for various rolls. I was wondering if anyone with more statistics knowledge than I could figure out how much that actually helps. For example, is the feat that allows you to roll two dice for your initiative better or worse than Improved Initiative?

 

[Hypersmurf]

There are 6 feats in Races of Stone that allow a character to roll two dice and pick the best one for various rolls. I was wondering if anyone with more statistics knowledge than I could figure out how much that actually helps. For example, is the feat that allows you to roll two dice for your initiative better or worse than Improved Initiative?

The average roll of 2d20, drop 1, is 13.825. Min 1, Max 20. It's more likely to be close to the average though, and more likely to be 20 than 1.

The average roll of 1d20+4 is 14.5. Min 5, Max 24. The distribution is uniform - you're exactly as likely to roll a 24 as you are to roll a 5.

-Hyp.

 

[3d6]

When you say average, do you mean median or mean?

On second thought, I'm not even sure if that makes any difference.

 

[Shadowdweller]

The average roll of 2d20, drop 1, is 13.825. Min 1, Max 20. It's more likely to be close to the average though, and more likely to be 20 than 1.

Wow. I don't suppose there's any chance you might be willing to explain how this number was arrived at, Mr. Hypersmurf? At least, assuming something other than direct experimentation? (me am literate in something up to basic calculus if necessary, although not how to apply it in such a case-- if used here once again).

 

[rkanodia]

2d20, drop lowest. result : chance of occurring : chance of getting this or better

1 : 1/400 : 400/400
2 : 3/400 : 399/400
3 : 5/400 : 396/400
4 : 7/400 : 391/400
5 : 9/400 : 384/400
6 : 11/400 : 375/400
7 : 13/400 : 364/400
8 : 15/400 : 351/400
9 : 17/400 : 336/400
10 : 19/400 : 319/400
11 : 21/400 : 300/400
12 : 23/400 : 279/400
13 : 25/400 : 256/400
14 : 27/400 : 231/400
15 : 29/400 : 204/400
16 : 31/400 : 175/400
17 : 33/400 : 144/400
18 : 35/400 : 111/400
19 : 37/400 : 76/400
20 : 39/400 : 39/400
21 : 0/400 : 0/400
22 : 0/400 : 0/400
23 : 0/400 : 0/400
24 : 0/400 : 0/400

1d20+4. result : chance of occurring : chance of getting this or better
1 : 0/400 : 400/400
2 : 0/400 : 400/400
3 : 0/400 : 400/400
4 : 0/400 : 400/400
5 : 20/400 : 400/400
6 : 20/400 : 380/400
7 : 20/400 : 360/400
8 : 20/400 : 340/400
9 : 20/400 : 320/400
10 : 20/400 : 300/400
11 : 20/400 : 280/400
12 : 20/400 : 260/400
13 : 20/400 : 240/400
14 : 20/400 : 220/400
15 : 20/400 : 200/400
16 : 20/400 : 180/400
17 : 20/400 : 160/400
18 : 20/400 : 140/400
19 : 20/400 : 120/400
20 : 20/400 : 100/400
21 : 20/400 : 80/400
22 : 20/400 : 60/400
23 : 20/400 : 40/400
24 : 20/400 : 20/400

So basically what Hypersmurf said. Note that the 2d20 drop lowest method does have a slightly better chance of being '15 or above' than 1d20+4. I'd take Improved Initiative myself, though, since I like the guaranteed minimum of 5. Not knowing what the other feats are, I can't really comment on them. However if you have the choice between 2d20 drop lowest and 1d20+5, definitely take the solid bonus as it will be superior all the way across that right column. At 1d20+3, I would call it a toss-up; at 1d20+2, the second roll is probably your best bet.

 

[Patryn of Elvenshae]

Of course, you could take *both*...

 

[Hypersmurf]

When you say average, do you mean median or mean?

Mean.

Wow. I don't suppose there's any chance you might be willing to explain how this number was arrived at, Mr. Hypersmurf?

About two minutes in Excel - nothing fancy

Two columns of 400 numbers - 20x1, 20x2, 20x3, etc, in column A, and 1-20 repeated 20 times in column B.

Column C is the max of A and B; sum column C and divide by 400.

-Hyp.

 

[Darklone]

You guys know that statistical calculations can be done without listing all possibilities ?

 

[Hypersmurf]

You guys know that statistical calculations can be done without listing all possibilities ?

Absolutely. But with a fill-down, listing all the possibilities took less than thirty seconds. It was simpler than trying to remember or derive a formula

-Hyp.

 

[Darklone]

Absolutely. But with a fill-down, listing all the possibilities took less than thirty seconds. It was simpler than trying to remember or derive a formula

-Hyp.

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