Quick math question

[James McMurray]

I'm contemplating the paragon feat that lets you roll initiative twice and take the highest, but I don't know what the expected result is. Anyone know offhand what the average result is for 2d220, take the highest?

 

[Nifft]

I'm contemplating the paragon feat that lets you roll initiative twice and take the highest, but I don't know what the expected result is. Anyone know offhand what the average result is for 2d220, take the highest?

That's a case where mean ≠ mode, so "average" is misleading.

Danger Sense is great at avoiding low rolls, so take it if you already have a decent Initiative bonus (Dex 18+ or Improved Initiative or both).

Cheers, -- N

 

[James McMurray]

I'll have dex 15 and improved init when I pick it up, if I do. But I have to weigh it against all the other sweet paragon feats for a wizard.

 

[baberg]

Assuming no modifiers, rolling 2d20 and taking the highest gives the following results:

Chances of rolling a 20: 39/400, 9.75% (compared to 5%)
Chances of rolling 18 or greater: 111/400, or 27.75% (compared to 15%)
Chances of rolling 15 or greater: 209/400, or 52.25% (compared to 30%)
Chances of rolling 11 or greater: 300/400, or 75% (compared to 50%)
Chances of rolling 5 or less: 25/400, or 6.25% (compared to 25%)

So you've basically got a coinflip chance to get a 15 or higher on one of your 2d20 rolls.

[sblock]

Value/Combinations
==================
1	 1
2	 3
3	 5
4	 7
5	 9
6	 11
7	 13
8	 15
9	 17
10	 19
11	 21
12	 23
13	 25
14	 27
15	 29
16	 31
17	 33
18	 35
19	 37
20	 39

[/sblock]

 

[James McMurray]

Thanks! Looks like I've found my next feat to swap out. I'll be going from crap initiative (+8) to fairly decent (2d20+12). Having gone last several times with my controller, I now understand the pain of wanting to mold a battlefield to my liking but coming up a few seconds short.

 

[Staffan]

A quick Excel spreadsheet shows that the average of taking the highest of 2d20 is 13.5.

 

[James McMurray]

Cool. Looks like it's a lower bonus on average than Improved Initiative, but pushes the curve up higher at the ends. Or I should say it creates a curve with high ends, since a straight d20 is a line.

 

[cdrcjsn]

More importantly, it stacks with Improved Initiative

 

[Nifft]

Here.

Brilliant graphs on page 3.

Cheers, -- N

 

[Vurt]

I think that the way it works for rolling two dice and taking the best result is that what you end up with is better than average 75% of the time.

For example, if you roll a d2, then your average is 1.5. Rolling twice, you only have a 25% chance of rolling 2 ones, and a 75 % chance of rolling at least 1 two.

If you roll a d4, the average is 2.5. Rolling twice, you have a 1/16 chance of them both coming up ones, a 3/16 chance of coming up with a two or lower, and a 12/16 chance (i.e. 75%) of coming up with at least one of the dice more than two.

If you roll a d6, the average is 3.5. Rolling twice, you have a 1/36 chance of coming up with 2 ones, a 3/36 chance of coming up with a two or lower, a 5/36 chance of coming up with a 3 or lower, and therefore a 27/36 chance (again 75%) of coming up with a four or higher.

etc.

EDIT:

I had a "well duh" moment while falling asleep last night. The odds of rolling less than average on each roll is 50%, so the odds of rolling less than average on both of them is 25%. Therefore the probability of rolling better than average on at least one of the rolls is 75%.