Just how good is rolling twice?

Remember, there is also the chance to stack multiple feats together. Skill Focus becomes less useful if you have one of the other feats that gives you a smaller feat bonus [but a secondary effect]. The reroll from Agile Athlete, for example, works fine with the feat that lets you make standing long jumps and gives a +1 to Athletics. Compared to an effective +2 from Skill Focus, Agile Athlete is a better choice. There is also the wood-elf feat that gives another way to stabilize the checks, it probably works better with fixed bonuses [that, when added to 8, get you what you want] while rolling 2 just makes the 1 nigh impossible.
 

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I just wrote a quick script to see what the average actually is for this.

Running a million iterations a couple different times comes out to an average result of 13.825, which is effectively (on average) slightly better than a +3 bonus over the 10.5 average of one d20.

So over your character's lifetime, the agile athlete feat would be slightly better than skill focus in both of those skills.

For the heck of it I also ran it with more rerolls:
1d20 avg: 10.5
Best of 2d20: 13.825
3d20: 15.49
4d20: 16.48

I proved the 13.825 number abstractly, you didn't need to run a million experiments.
 



My party has an elven cleric (laser). We haven't played that much so far, only almost lvl 3... but I cant remember a single time she has failed with a reroll from elven accuracy... (maybe she just has hot dice but from a non-maths gut feeling I think 2 rolls is potent)
 

Elven Accuracy is a little bit of a different ballgame, since you only use it on known misses.
Exactly!

My party has an elven cleric (laser). We haven't played that much so far, only almost lvl 3... but I cant remember a single time she has failed with a reroll from elven accuracy... (maybe she just has hot dice but from a non-maths gut feeling I think 2 rolls is potent)
No, the dice are probably hot. :)

When considered on its own, Elven Accuracy has exactly the same chance of hitting as your normal attack (unless you take the elven racial feat, of course).
 


Exactly!


No, the dice are probably hot. :)

When considered on its own, Elven Accuracy has exactly the same chance of hitting as your normal attack (unless you take the elven racial feat, of course).

lets not forget stradagy of use...If I roll 16 and miss, I don't use elvenaccuracy, on the other hand if I roll a 4 and the GM says "So close but a miss"...well then I reroll.
 

Now, when there isn't a target number, like in initiative, then a reroll of a d20 gives expected value of 13.825, which is less than the 14.5 you get from improved initiative. However, there is less variance in the reroll, i.e., you're less likely to roll mega low or mega high when you have a reroll. This makes your initiative more predictable, which is better for you as a player (if you're designing a character to win fights. If you're designing him to have fun playing then maybe having a lot of swing factor is cool for you).

hmmh i am not sure here... of course you are rolling more predictable with a reroll, but you can´t roll lower than 5 with improved initiative and you have the chance to roll 24...
 

hmmh i am not sure here... of course you are rolling more predictable with a reroll, but you can´t roll lower than 5 with improved initiative and you have the chance to roll 24...

+4 to a roll that is being compared to other rolls is a different ballgame than a single roll being rolled against a target number.
 

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