Quick dice probability question

[Sammael]

When you roll 2*d20 and take the higher result, what is the average increase in result over rolling a single d20?

It's been 12 years since I had any probability/statistics classes, and I'm really rusty... the only things I can remember is that the chance of any given number occurring is increased from 5% to 10%, and that the chance of two identical numbers occurring is 0.25%.

The purpose of my original question is to eyeball the value of a feat that grants the ability to roll two dice for a check and take the larger value, versus a feat that grants a fixed bonus.

 

[Oldtimer]

Your average will increase with just a bit more than +3 (goes up from 10.5 to 13.825).

 

[ScottS]

Average on a d20 is 10.5, average on 2d20-drop-lowest is 13.8, i.e. it's roughly the same as a +3.

edit: ninja'd...

 

[Sammael]

Thanks!

The feat I'm trying to evaluate is Improved Initiative, by the way. However, in my version of the rules, all checks have a critical failure and critical success, so - what we'd get is a +3 bonus (instead of +4), coupled with the dramatic reduction of chance of critical failure (5% drops to 0.25%) and doubled chance of critical success (10% instead of 5%). I'm thinking it's pretty decent.

 

[fba827]

I know your question has been answered, but I am just doing this more as a mental excerise for myself ...

Total Possible Combinations: 400
Average Roll of 1d20: 10.5
Average Roll of 2d20, taking higher: 13.825
Chance of both rolls being equal: 20 in 400, or 5%
Chance of second roll being higher: 194 in 400, 48.5%
Chance of gaining equal or better from the second roll (total of the above two): 53.5%
Chance of second roll being lower (only relavent if order matters and you must take the second roll, for instance): 186 in 400, or 46.5%
Chance of either being a natural 20 (critical success, if an option): 39 in 400, or 9.75%
Chance of both being 1 (critical failure, if an option): 1 in 400, or 0.25%

Again, I know your question had been answered, just was scratching my brain for my own benefit of other facts that are related to what you wasked...

 

[Theo R Cwithin]

For this kind of stuff, I like AnyDice.

I has a pretty straightforward interface (see its wiki for help) and presents summary plots as well as the numbers.

 

[TarionzCousin]

You guys are completely failing to take into account that one of the d20's might be CURSED.

For example: Vrin's brown d20 never rolled above an 8 for him--so we snuck it into the DM's dice box in hopes that its bad fortune would rub off on his dice.

Hehe.

We'll see how the DM rolls tomorrow.

 

[hvg3akaek]

You guys are completely failing to take into account that one of the d20's might be CURSED.

Similar to this, I know for a fact that if I am DMing 4e, I will roll 15+ all night, with only one die. If I am playing 4e, I can roll 2d20, and gain a total which happily remains in single digits!

 

[jeffh]

Chance of second roll being higher: 194 in 400, 48.5%
Chance of second roll being lower (only relavent if order matters and you must take the second roll, for instance): 186 in 400, or 46.5%

These two should be the same, shouldn't they? So at least one of these numbers is wrong.

 

[Haltherrion]

Similar to this, I know for a fact that if I am DMing 4e, I will roll 15+ all night, with only one die. If I am playing 4e, I can roll 2d20, and gain a total which happily remains in single digits!

It does seem to work that way... although my rationale part says that is just because the ref rolls so many dice, you get to see more random streaks of good or bad luck.

I like 4E but one of things I miss about the older systems: at least there were some classes where you didn't have to roll to-hit rolls for those of us who seem to have exceptionally bad luck