Chance to hit percentages?

[Tyger]

Math is not my strong suit, so I am here asking for the mathematically inclined among you to off what help you can.

Is there a basic formula for computing an attacker's chance to hit with the attacker's AB (BAB + all bonuses) vs the defender's AC?

I was told it was (AC- (AB+20))x5, but that doesn't work out at all, as all it gives is the chance to hit if you rolled 20. At least, I think that's what it gives.

Any relatively easy formula for this?

[RebelRogue]

Lowest possible roll that hits - R - is determined by:

R + AB = AC <=> R = AC - AB

There is a (21-R)*5% chance of rolling at least R.

This does not account for 20 always hitting and 1 always missing.

[Douglas]

The percent chance to hit with attack bonus AB is (AB - AC + 21) x 5.

Attack bonus 0 vs AC 10: (0 - 10 + 21) x 5 = 11 * 5 = 55% chance to hit.
Attack bonus 9 vs AC 10: (9 - 10 + 21) x 5 = 20 * 5 = 100% chance to hit (even a 1 would hit if not for the natural 1 rule).
Attack bonus 0 vs AC 21: (0 - 21 + 21) x 5 = 0 * 5 = 0% chance to hit (a 20 only hits because of the natural 20 rule).