Quick dice probability question

[arscott]

Something to keep in mind is that it's not nearly so simple as the 13.825 average result would suggest.

Rolling two dice and keeping the highest varies widely in effectiveness depending on the target number. For example, when you need an 11+ on the die to succeed, rolling two dice and keeping the highest is equivalent to a +5 bonus. But when need a natural 20 to succeed, rolling twice is only equivalent to a +1 bonus.

[Sblock]

needed		2d20
roll	1d20	keep 1	improvement
2+	95%	100%	5%
3+	90%	99%	9%
4+	85%	98%	13%
5+	80%	96%	16%
6+	75%	94%	19%
7+	70%	91%	21%
8+	65%	88%	23%
9+	60%	84%	24%
10+	55%	80%	25%
11+	50%	75%	25%
12+	45%	70%	25%
13+	40%	64%	24%
14+	35%	58%	23%
15+	30%	51%	21%
16+	25%	44%	19%
17+	20%	36%	16%
18+	15%	28%	13%
19+	10%	19%	9%
20	5%	10%	5%

[/Sblock]

Given that most rolls in D&D have a target in the mid ranges, rolling twice and keeping the highest is generally better than a +4 bonus.

However, because initiative is an opposed roll, you'll get target numbers across the spectrum--which means the 3.825 number is alright for your purposes.

 

[hvg3akaek]

The big difference is that the rolling twice only increases your d20 roll average. You still end with a value between 1 and 20.

Improved Initiative increases your min and max, too, so your value is between 5 and 24. The outside rolls are also important, as a straight +4 will mean you won't roll really terrible, and on some rare occasions you will roll really well. 2d20 means you roll above average more often.

 

[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.

In today's session, the DM rolled five natural 20's in combat to our one.

 

[CharlesRyan]

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

Or that one of them might be rolled by Kate.

 

[Mustrum_Ridcully]

In today's session, the DM rolled five natural 20's in combat to our one.

Your DM is probably a demigod, son of the goddess of dice.

 

[Dedekind]

51% of rolls will be greater than or equal to 15. That's a pretty big difference from a flat +3.

 

[hvg3akaek]

51% of rolls will be greater than or equal to 15. That's a pretty big difference from a flat +3.

Not really, a flat +3 means that 45% are 15 or more (and 50% are 14 or more). I wouldn't call a relative 6% difference "pretty big".

With +3, 15% are greater than 20, whereas with (roll two), 0% are greater than 20.

With +3, 0% are 3 or less, with (roll two), 2.25% are 3 or less.

 

[Dedekind]

Not really, a flat +3 means that 45% are 15 or more (and 50% are 14 or more). I wouldn't call a relative 6% difference "pretty big".

I would call a relative 6% difference similar to an additional +1 to hit. Isn't that worth a whole feat in 4e?

Though I will grant the point that 20+ "rolls" are not in the mix. The AnyDice website demonstrates quite nicely how different the distribution of results changes with the 2d20 take highest method.

 

[Khime]

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

Yeah, the number of times the second number is higher is 190 (47.5%), the same number of times the second number is lower.

 

[hvg3akaek]

I would call a relative 6% difference similar to an additional +1 to hit. Isn't that worth a whole feat in 4e?

Precisely - it is significant, but it is only +1, so not "pretty big". +4 would be "pretty big"