Right so I've kind of run up against a block in a project I'm working on regarding risk and reward.
What I'm trying to do is describe a method to figure the chance of success on a given roll.
One method I normally use (that is less likely to require a calculator for expediency) is to subtract the bonus from the target number and multiply the result by 5. The number given represents a percentage chance to fail the roll. Then subtract this number from 100 to get the chance to succeed.
Though I'm almost positive thre's an equation or process that is much faster and more efficient.
Did I ever mention I'm terrible at math?
Nothing really more efficient. You could try calculating (20 + bonus - target) and multiplying by 5 for success chance if that's easier for you.
Example:
I have a +17 bonus and I need a 25.
(20+17-25) * 5 = (12 * 5) = 60% chance of success.
Aw. what happened to Claxon's post?
Was trying to clarify that yes I meant d20 rolls.
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Target DC - Bonus = Number You Need To Roll.
From there, I just figure the chances of rolling that or higher on a d20...that isn't usually too hard. So...DC 25-17=8. What are my chances of rolling an 8+ on a d20? 65%.
That doesn't work if you don't have a good handle on the odds of rolling various things...but I'd think most gamers would have a decent grasp of that. If it helps, remember an 11+ is a 50% chance, every number below that increases the chance by 5% and every one above it decreases it by 5%.
Target DC - Bonus = Number You Need To Roll.
From there, I just figure the chances of rolling that or higher on a d20...that isn't usually too hard. So...DC 25-17=8. What are my chances of rolling an 8+ on a d20? 65%.
That doesn't work if you don't have a good handle on the odds of rolling various things...but I'd think most gamers would have a decent grasp of that. If it helps, remember an 11+ is a 50% chance, every number below that increases the chance by 5% and every one above it decreases it by 5%.
Imagine I'm trying to describe this to a player who has only a basic grasp of the rules and needs to be able to do this on the fly like most experienced players are capable of.
For the record, yes I can figure out percentages easily. Finding an easy mathematical way to describe it is proving the challenge though.
I do this without thinking about it, but I think the formula is expressed as: (Target Number - Bonus) x 5 = % chance of failure
Aw. what happened to Claxon's post?
Was trying to clarify that yes I meant d20 rolls.
I deleted it, after I went back and realized I suggested what you were asking a better way to do.
I guess the only real advice is to just leave off the last step and not worry about success rate and just use the failure rate. It can cause some distortions just like the success rate can, but it amounts to the same thing. Most people who are bad at math are anxious about it too, and that is likely getting in the way. Experience makes you better at this, they will get the hang of it eventually.
What's the context and types of questions? Is it just "what's the chance to succeed?" or is it "which option is better?" or "what attack should I use?"
The descriptions above for just the basic percent of success is as simple as you can get. You could move away from percentages and just say "this would work half the time" or "this is only going to succeed 3 out of 20 times" if the person isn't good with percentages. You could also just try the old "maximize bonuses and minimize target number". Or if you do Target - Bonus = X, you want to make X small, even negative, as possible.
If you're going for the "best attack" (as I'm about to because I'm bored and it is a fun exercise, so you may not care but that's ok, heh) then you figure the percentages as above and multiply it by the average damage expected. This involves calculating average damage, which is ((sides on the die)/2 + 0.5)*dice + bonuses, so 2d4 + 1 averages to 2*(4/2 + 0.5) + 1 = 6. When multiplied to chance of success, you get the expected damage of the action. Granted, this does not include crits, but that would make things so much more complicated.
Example: Monster AC 22. Your greatsword: +7 attack, 2d6+6; Your longsword: +11 attack, 1d8+4. Greatsword's expected damage is 0.3 (chance to hit) * 13 damage (2*3.5 + 6) = 3.9; Longsword's expected damage is 0.5 * 7.5 = 4.25. So the longsword does more damage, on average against this monster than the greatsword, even though weapon one's damage roll is greater (then again, how it has such a larger to-hit is a mystery relegated to the realm of made up numbers for the purpose of a mathematical example).
In most situations, maximizing the bonuses is your best short hand to success.