Are there any guidelines for this switch in probability?

I'm trying to adapt a magic system that is based on roll over (mod+d20) vs DC to roll under attribute.

Here's the basis for the roll over:


Each spell cast (failed or otherwise) that day increases the DC by +2. If a d20 rolls a natural twenty, add and roll again. If further natural twenties are rolled, continue adding and rolling. Critical failures are up to the GM.

For every 5 points (or part thereof) above the DC the caster may add 1 point to damage, range, area of effect or duration. If they are unstated, then the defaults are used.


"Damage" could be positive energy to make it a healing spell instead recovering 1d6 damage per point. Transformation spells must exceed the HP of the target to be successful. Turning a 6 HP commoner into a frog for a few rounds is simple; doing the same to a dragon is considerably more difficult, and will likely take several rounds and a lot of courage!

A spell lasts as long as the caster concentrates (performing no other action) or as long as it's stated duration.

Example
Norris the Elder is a 5th Level Mage with INT 16. His Magical Attack is (INT + LVL) or +8. Norris has been captured by Gnolls and wishes to teach the leader a lesson. From within his wooden cage he throws a fireball into the center of the gnoll gathering, targeting the campfire (DC10) 20' away. He rolls 18+8 = 26. That's 4 points to put in to the fireball, so one goes into Range, two into damage and one into Area of Effect. All Gnolls within 10' of the campfire take 2d6 damage and start patting out singed fur, howling in pain. Norris chuckles. Norris is beaten badly for this stunt and is back in the cage, down to just 3hp.

He casts Heal on himself (DC0, +2 as it's his second spell that day). He rolls 10+8 = 18 which exceeds DC2 by 16 points. He allocates all four points to "damage" and heals 4d6hp. He's back to full health. Deciding it's time to make a break for freedom, Norris tries to use magical force to break the back of the cage. The bars are strong wood (DC10+4 as this is his third spell today). Norris rolls a natural 20, then a 12 for a total of (20+12+8) 40. That gives him 5 points to play with. Wanting to do it slowly so as not to attract attention, he puts one point into damage (1d6), 3 into rounds and the GM ok's 1 point being spent to keep everything silent. By the time the Gnolls notice the hole in the bars, Norris is long gone.

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So my thoughts for changing this to roll under is the following:

You have spell points equal to your INT.  Assemble a spell as per the above components and subtract the "cost" (the total number of elements) from your attribute.  To affect willing or inanimate objects you'll need a success; to affect unwilling subjects, you need to succeed by half.  Success (any degree) deducts the total spell points used; a failure deducts half.

A critical success (a 1) makes the cost free (no deduction in spell points)?  Is that too good?

Though the specific target numbers used might be different, it's fairly easy to switch between the two without changing the probability much at all. You just have to watch out for the "equal to or X" part. If it's equal to in one, it should be equal to in the other, as in "equal to or greater than" becomes "equal to or less than" in the other.

In a d20 roll over system: a target number of 11 is 50% success/fail. Each +/-1 is a 5% shift in probability. Here the modifier effects the roll, a bonus makes it easier, a penalty makes it harder. You can also modify the target number, an increase making it harder, a decrease making it easier. This is generally more intuitive and easy to handle, so you can modify either with ease.

In a d20 roll under system: a target number of 10 is 50% success/fail. Each +/-1 is a 5% shift in probability. Here the modifier effects the target number, a bonus makes it easier, a penalty makes it harder. You can also modify the die roll, a bonus would make it harder (less likely to roll under), a penalty would make it easier (more likely to roll under). This is generally less intuitive and makes it harder to handle, so you should try to restrict your modifiers to the target number.

Paranoia XP uses d20 roll under, with skills as target numbers. A higher skill means its easier to roll under it. Modifiers tend to be applied to the target number (skill rating) instead of the die roll, as above, it's just easier to handle.

But they're functionally identical. In Paranoia XP, roll under, a skill of 17 equates to a TN of 17, and gives you a success on a 1-17 roll, and a failure on a 18-20 roll. Just flip that for roll over. Instead of the highest 3 equalling failure (roll under), the lowest 3 equal failure (roll over). So 1-3 is a failure, whilst a 4-20 is a success. That 17 skill in a roll over system would just be a bonus with a TN of 21. These are mathematically identical in probability, 15% failure rate for each.

Though I'm curious, why subject yourself to all the work of converting it over if it's functionally identical? What do you hope to gain by converting it?

The rest of the system is roll under, so I don't want different mechanics.

Well, at a glance I'd look at your range of modifiers, figure out what half of that is, and center that number in such a way that you can't get 0 (if possible.) So for example, if your easiest roll is 5, and your hardest is 43 in roll over, your spread is 38 points. Half of that is 19. So a DC 43 maps to whatever base difficulty is -19. while 5 maps to whatever base difficulty is +19.

This way, since difficulty isn't static, you WILL have numbers go negative, but you can always say that's BS and make minimum difficulty 1

Strictly speaking, roll under is equivalent to roll over when you use 21 - 1d20.

So if you had a DC of 15 (need to roll 15 or more), it becomes 21 - 15 = 6 (need to roll 6 or less).

Switching that into your example, we get:

1) Campfire is DC 21 - 10 = 11 or less to affect. Add the Level + Int bonus, and you need a 19 or less for things to work.

Your original roll was 18, which becomes a 3 (a good roll in either case). You've rolled 16 under your target of 19, so you get 4 raises.

2) Cast heal on yourself, DC 21 - 0 = 21. -2 to target because it's the second spell, and so the DC is 19. Add the Level + Int bonus, and you're up to 27.

Your original roll was 10, which becomes an 11. You are again 16 under the target, so 4 raises.

3) Try to escape, and your target number is now 15 (the original 19 - 4 because it's your third spell).

Your original roll was a 20, which becomes a 1. Roll another d20 and perform a straight subtraction, for a total of 1 - 12 = -11. Your difference is 26, as before, granting 5 raises.


Note that you are directly subtracting a d20 in the case of a natural 1, not performing any particular manipulations. Also, when doing roll under, you just roll a d20 and compare - there is no need to see what the die roll 'becomes'. I used that in the examples above so you'd see the direct correspondence between the two methods.

Finally, note that you can't get a roll of exactly 20 with your method (assuming a bonus of 0), since on rolling a natural 20 you add another die, so you get at least 21! In roll under, this means you can't get a roll of exactly 1.


Your rules become:

Willing target: roll under 21.
Inanimate: roll under 11.
Unwilling target: roll under 11 - opponent's bonus

I'm not sure how you compute AC, but you get the idea.

Each new spell reduces your target number by 2 (or adds 2 to your roll).

Your Level + Int is added to your target number (so a bonus of 8 makes the numbers 29, 19, and 19 - opponent's bonus), or subtracts the bonus from the roll.

On rolling a natural 1, roll another d20 and subtract it from your total - this will give a value between -19 and 0. If you roll a natural 20 on the bonus die, roll again and subtract again - so the -19 becomes -20 to -39 (except the -39 is another natural 20, so...).

Negative values are very much allowed!

I have seen it done before but the entire system was different so I'm not sure if it applies