Random Fiver Option?

[Sa'ar Chasm]

I recently helped her with an interesting little probability question: whether 1d8+1 beats 2d4+1 or not.

Average of 1d8+1: 5.5 Average of 2d4+1: 6. As far as damage goes, I'll take 6d1 over 1d6 any day.

Now tell me where I'm wrong.

[Gatac]

Well, on 1d8+1, you have a 12.5% chance for everything from 2 to 9. On 2d4+1, it's...

6.25% 3
12.5% 4
18.75% 5
25% 6
18.75% 7
12.5% 8
6.25% 9

...so it's more bell-curved. That means your probability is skewed towards middle-of-the-road results, which means you get truly good and truly bad rolls less...but 2d4+1 also gives you a higher minimum result.

Depending on whether getting the maximum roll allows you to activate a special ability (like, the die "explodes", to use Spycraft language), it may be a better deal, but I'm reasonably sure that the 2d4+1 option is better on average.

Gatac

[Zeke]

Wait a minute. 2d4 is two separate d4s? It's not "roll a d4 and double it"? Crap, that changes everything!

Originally Posted by Sa'ar Chasm

Now tell me where I'm wrong.

You're not. Averages (a.k.a. expected value) are exactly the way to answer a question like this. But I found a particularly nice way to get why it works (the way I thought originally), and that's what I'll be posting later.

[Gatac]

1d4 - roll 1 four-sided die.
2d4 - roll 2 four-sided dice.
2d4b1 - roll 2 four-sided dice, take best result.

That way, for example, the "Roll 4 d6, drop lowest" method of generating an attribute can be rendered as 4d6b3.

As far as I know, there's no standard notation to indicate that you should double a result.

Gatac

[Nate the Great]

It seems a monster has been created. Now I don't wonder so much why I never got into D&D. My sister did, incidentally, at least for awhile. Why? Because she had a huge string of luck when they were rolling together her character's initial stats.

I was just thinking about the geek heirarchy http://www.brunching.com/images/geekchartbig.gif
and how these "geek majors" are usually different. By the way, someone's gotta work the term "Kirk is an ocelot" into a fiver."