What's the effective bonus of a double d20 roll take the highest?

[DM-Rocco]

Thanks everyone for your answers... they were quite enlightening as I weigh whether to go with double rolls or single rolls with bonuses. I think that getting rid of bad rolls is definately a selling point for the double roll. What about straigth rerolls (i.e. I don't like this roll I'll take the next)? Would they have a higher effective bonus or lower one? Just curious...

You should just change your screen name to Can-O-Worms

It would depend on what they rolled on the first roll of course

 

[Nifft]

And Nifft, graphing it returns a *very* interesting result. (...) The graphing was a great idea.

What you graphed is (basically) the Probability Density Function, or "PDF", for that distribution. I find it's the best tool for getting an intuitive grasp on new distributions.

You can do similar things for conditional re-rolls, too.

Cheers, -- N

 

[Pielorinho]

Thanks everyone for your answers... they were quite enlightening as I weigh whether to go with double rolls or single rolls with bonuses. I think that getting rid of bad rolls is definately a selling point for the double roll. What about straigth rerolls (i.e. I don't like this roll I'll take the next)? Would they have a higher effective bonus or lower one? Just curious...

That one is much more difficult, because your question isn't defined. At what point will someone decide they don't like the current roll?

If someone rolls a 1 and decides to reroll, the approximate bonus is +9.5. At 2, the bonus is +8.5, and so on.

Decide what the highest number the first roll could be and still trigger a reroll, and average the bonuses for that number and all the ones beneath it, and you'll have your answer.

Daniel