Blindsided by Math

I feel like total crap.

I could blame my sleep apnea, but the truth is, someone started talking about odds of rolling dice in a game and I went against my better judgement.

The premise involved permutations and custom dice and I tried to walk away from it...

So now that all of the hubbub is over, I can edit the post that was due earlier today.

Still. D12 dicepools are still enticing...

Math Post – Odd Bell Curves

I posted the other day about a mechanic inspired by Target20, a system developed by Daniel Collins:

(d20 + d10) + level + modifiers ? 26

This system assumes the use of descending armor class per older editions of D&D when it comes to combat. So, let's take the case of a 6th level fighter attempting to hit a creature with an Armor Class 5. With this system it would be

(d20 + d10) + 6 + 5 ? 26

Or, you have to roll a 15 or better to hit. The chances of that are 57.5 percent.

In 2e, a similar scenario 6th level Fighter has a THAC0 of 15 requiring an 11 or better with a d20 to hit AC 4. The chance of success is 50 percent.

Not too bad really - I don't mind being a little more generous with combat. But how about lower levels? Let's see:

This scenario is a 2nd level fighter attempting to hit AC2, a tough challenge.

(d20 + d10) + 2 + 2 ? 26

In other words, roll a 22 or better, a 22.5 percent chance of success.

The same scenario in 2e means that the 2nd level fighter has a THAC0 of 19 meaning that he needs a 17 or better to hit. Chance of success is 20 percent.

Saving Throws

When doing saving throws, the basic formula is still the same:

(d20 + d10) + level + modifiers ? 26

This time, though, the modifiers are standard based on the type of Saving Throw: +0 for Spells, +1 for Breath Weapon, +2 for Petrification, +3 for Paralysis and +4 for Death. (At least, this works for Fighters and Clerics)

So, a 6th level Fighter needs to make a Saving Throw against a young dragon's Breath Weapon:

(d20 + d10) + 6 + 1 ? 26

In other words, he has to roll a 19 or better. This provides a 37.5 percent chance of success.

A 6th Level fighter making the same save in 2e has to roll a 13 or greater, a 40 percent chance of success.

Saves in my system are more lethal for higher level characters, but only by a slight margin.

Now because the modifiers are different by class, I would simply put the saves on the character sheet so that a player only needs that reference to roll anything.

Rogue Skills

Doing this take a change in how Rogue skills are handled. Instead of using percentages, skills would have a number that looks an awful lot like a skill rank used in 3e. In other words, Climb Walls wouldn't be listed as 80%, but as +15. Since 2e allows you to start with a base and add points where the player wishes, I'd have to recalculate all new starting points. Climb Walls would start at +11, others would start somewhere between 1 and 5. I haven't worked that out yet.

Anyway, if you have a first level thief with an 80% chance of climbing walls vs a 1st level Thief in Andras with a +15 Climb Walls score...

(d20 + d10) + 1 + 15 ? 26

In other words, he/she would have to roll a 10 or better, an 82 percent chance of success.

More Work to be Done

Still more to be done, obviously. Just a weird idea. Yes, it would be easier to stick to Dan's original idea. His is more tidy in some ways and the formulas don't have this weird 26 all over the place.

Yet, the flat curve works for me. It does some funky things at higher levels that I like. Combat is still not automatic at higher levels, neither are Saving Throws. Maybe it will turn out to be a silly idea after all. As always, we'll see.

Opposed Rolls

Before going into a post likely to be snored off, I wanted to thank Kevin Sullivan for the stats he generated on this site. The presentation of certain things are more clear there. He also provided me with a good idea on how to generate Class XP tables for Andras.

I had posted on Google Plus about a shortcut method of performing opposed rolls. The numbers do not come out the same, but I figured that they were close enough. What I discovered in studying these numbers points to effects of specific designs. In the end, I think that my design doesn't produce results that are always similar, but that produces results more in line with my design philosophy.

Specifically, the results show that:

  • Characters with equal bonuses to skill rolls under Microlite20 will have a similar, but varied chances of success under my system.
  • The Microlite20 system is affected by relative adjustments to the roll. My system is affected by the actual skill ranks and Attribute score.

Here is an example using the Microlite20 rules as written and comparing to my system.

Listen is Subterfuge + MIND.
Move Silently is Subterfuge + DEX

Aesir is attempting to sneak up on a guard. Aesir has a 16 DEX and a Subterfuge rank of 2. The Guard has a MIND of 12 and a Subterfuge rank of 4. According to the rules, the one with the highest roll wins. Each character receives a bonus to their individual rolls of Skill Rank + Attribute Bonus.

For Aesir, we get 2 (skill rank) plus 3 (Attribute Bonus in M20) to get 5.
For the guard, we get 4 (skill rank) plus 1 (Attribute Bonus in M20) to get 5.

Given these stats, Aesir will succeed 47.5% of the time. The guard will succeed 52.5% of the time because he will win all ties. By rule, ties go to the character with the highest skill rank.

Under the Microlite20 system, the chances of success will not change if the guard has a Skill Rank of 5 and a MIND of 10, a Skill Rank of 3 and a MIND of 14 or a Skill Rank of 2 and a MIND of 16. The adjustment to the roll remains +5.

In my system, success is determined by rolling-under the total of the Skill Rank and the Attribute itself. When performing an opposed roll, the Player Character has to subtract half the total of the NPC's skill rank and attribute. In this example, Aesir's Subterfuge rank plus DEX is 18. The guard's Subterfuge rank plus MIND is 16. Success is determined by Aesir rolling equal to or under 10. In other words, 18 minus 8 (half of 16). This give Aesir a 50% chance of succeeding. This is a slightly better chance of succeeding than with the Microlite20 system.

What I found surprising is that if the guard is changed as I mentioned earlier, Aesir's chances of success are affected.

sub MIND Aesir Wins
Guard 1 5 10 52.50%
Guard 2 4 12 50.00%
Guard 3 3 14 47.50%
Guard 4 2 16 45.00%

All four of these guards are identical according to the Microlite20 system, but the results are slightly different under my system. Nothing is really dramatic in the results, even with very improbable NPCs (do you hire MIND 16 guards? Would a MIND 10 guard have a 5 subterfuge skill?)

For the sake of completeness, let's say that Aesir is opposing a lower skilled guard of average intelligence. Subterfuge skill rank of 2 and a MIND of 10. Under the standard Microlite20 system, Aesir has a 62.5% chance of success. Ties no longer go to the guard, but they don't go to Aesir either because there would be a re-roll. Under my system, Aesir has a 60% chance to succeed.

Why does it give a worse chance? The amount of change is less in my system. If you compare the original example, Microlite20 provided no advantage to Aesir. He and the guard were equal. In my system Aesir had a slight advantage, thus a higher chance for success as compared to M20.

Changing to scores provided Aesir a great advantage. Instead of being even with the Guard, he now enjoys a +3 advantage. That big of an advantage yields bigger results. In my system, Aesir already had an advantage over the first guard. Changing the skill and MIND score had less effect because the amount of advantage changed comparatively less.

Somehow I'm Awake, What Does All This Mean?

Advancement in Microlite20 provides for increasing Skill Ranks and Attributes. This makes the characters very high powered around 10th level. In my variation of M20, characters cannot change Attributes except by magic or optionally by age.

I hope this means that characters can be fun to play for more than 10 levels.

This also means that using Microlite20 as a platform to develop Andras helps me get the bones of the system working well. This will be easier to playtest, especially for newer GMs. This also allows me to playtest a solo version of M2010 (my system). Maybe I have been reading too much T&T lately, but having a solo version plus the Mythic GM appeals to me.

As always, more later.