Poll of the Day > Hey math people - Reduce fail rate, or reroll failures?

(+) Yeah! (+)

Scenario: You're playing a 2d6 game where under default conditions a 7+ is a success.
Your AGI bonus adds to your roll, enemy stats reduce that roll, but basically under neutral conditions you just need a 7+ (which is about 58.3%)

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Ok, you have an option of 2 items: One cuts your enemy's bonus in half, so if the enemy was getting a +2 they only get a +1. The other just rerolls if you fail once.
Or, to be more precise, your chance to hit is "2d6+Offensive Modifier >= 7+Defensive Modifier"

But you are in a bad position: Making a ranged attack at 8AGI (+1) against a unit that is 4 tiles horizontally/5 tiles vertically (16+25)=41, sqrt(41)=6.4, 6.4/2 = 3.2, floored = 3. ... would have a bonus of +3. Your 2d6+1 would have to equal or beat 10. If you take the first item which cuts the enemy bonus in half it would get reduced to 1 since rounds are floored (1.5=1), or a reroll.

So, which is better: 2d6+1 >= 10 with reroll, or 2d6+1 >= 8

Or ONE attempt at 41.7%, or TWO attempts at 16.7%
(EDIT: I was off by 1 looking at the chart, it should be 58.3% and 27.8%)

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Under this scenario the first item is better since 41.7% is better than 30.6111% ............

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So what's the question?

When is rerolls ever better than reducing penalty? Is there an easy way to output all possible outcomes?

At a range of 1.999 or less then rerolls will probably be better since the enemy bonus would always be 0 and therefor the first item would do nothing...

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So you're asking which is bigger.
58.3% or 2x16.7%?

It's the 58%

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shadowsword87 posted...

So you're asking which is bigger.
58.3% or 2x16.7%?

It's the 58%

Well, it would be 58.3 or 2x27.8...

I did the math for 41.7 and 2x16.7 and concluded the first is better.... but what I am actually looking for is a way to produce all possible outcomes

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It's easiest to tabulate.
Single 2d6: 0%, 3%, 8%, 17%, 28%, 42%, 58%, 72%, 83%, 92%, 97%, 100%
Reroll 2d6: 0%, 5%, 16%, 30%, 48%, 65%, 82%, 92%, 97%, 99%, 99%, 100%

Using the +1 item is equivalent to moving one step to the right. Using a +2 item is equivalent to moving two steps to the right, and so on. Using the reroll item is equivalent to moving from the top row to the bottom row.

From here we can see that if your unmodified success condition is
2d6 >= 13, 12 or 11 (0%, 3% or 8% chance), it's better to take a +1 modifier than a reroll.
At 2d6 >= 10 or easier (17+% chance), it's better to take a reroll than a +1 modifier.
Until 2d6 >= 7 (58% chance), it's better to take a +2 modifier than a reroll. At 2d6 >= 6 (72% chance), they become basically equal.
At 2d6 >= 4 the +2 modifier becomes better again since it gives 100% chance. At 2d6 >= 3 the +1 modifier becomes better than the reroll since it gives 100% chance.
A +3 modifier is always superior.

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Binomial Distribution

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Reducing failure rate also becomes less valuable as the failure rate decreases. If failure is rolling 2 or below on a d20, +1 improves your success rate by a mere 5.6% (multiplicatively). If failure is rolling 19 or below, then +1 improves your success rate by 100%. Comparatively, a reroll has a 90% chance of succeeding in the former case, but only a 5% chance in the latter, making the +1 much better.

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Also if you have a crit system, re-rolls (or double rolls and you chose the highest) have a higher chance at crits.

There is also a big difference between re-rolling, and rolling twice.

The examples above with 2d6 vs 1d6 are only accurate if you roll both at the same time.

IF you have to choose to re-roll the dice if you don't like it, that changes things somewhat as you can end up with a lower roll that way (at least for crits).

In 5th edition you have something called rolling with advantage, where you get to roll twice and take the higher (with disadvantage you roll twice and take the lower). This is especially nice for crits, and for builds that have large crit ranges, as it gives you a very high chance of getting a crit hit (even if crits don't do as much as previous versions, just increasing the die rolls for damage, but not doubling strength bonuses and other sources of bonus damage (Feats, rage, magical weapons etc).

Also you need to determine if there are auto-fails (like you automatically fail on a 1, or auto succeed on a 20 etc) as that can alter which is better as well.

In the end, in.....most cases, a double roll (not a re-roll) is better than a bonus to your roll, but again, it depends a ton on the range of the dice, crit/fail factors etc.

To get to an extreme though (DDO is a good example of extremes, at least in the past (now it's been kinda WoW tuned which sucks a bit), you can stack tons of, say defensive mesures to insure enemies don't hit you.

First AC to a level that you would only normally get hit on a 20 (5%), which is the absolute max you can get from straight AC. Then you pump up fortification so you can't be crit at least (even on a 20), then you have 2 types of Dodge abilities (incorporation and flat out dodge) which don't stack but are seperate (each giving you a chance to totally avoid a hit if it actually happens). You can end up with less than a 1% chance to actually take non-AOE damage (and most AoE spells/abilities can be avoided completely with reflex saves + evasion.

Anyway things like attacking with advantage (or forcing enemies to attack with disadvantage) can be huge, especially if you already have a really high chance to hit (bonus), or high AC (so enemies can rarely hit you).

Also initially I thought this said "Hey meth people"...........and yet I still entered (no I don't do meth, but I thought it would be interesting....I am not Heisenburg (but I was a teacher).

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wolfy42 posted...

Also initially I thought this said "Hey meth people"...........and yet I still entered (no I don't do meth, but I thought it would be interesting....I am not Heisenburg (but I was a teacher).

If I did such a topic I would probably label it as "Crystal Healing"

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