Critical success/failure table, p 9

[Axly Suregrip]

Originally Posted by TedT

Critical Success and Failure on 5 Dice

Have any of you a "widely-accepted" table showing Critical Success and Failure rolls on 5 dice? Somewhere from my TFT past I have a list for these steps on 4 dice, but my GM has - as of late - been throwing 5-dice variety obstacles at us. And I want to know when my to-hit roll does, say, double damage on one of his boorish thugs, in such a way as to make him accept its certified provenance.

See ITL pg 9 for this table.

[TippetsTX]

So not everyone agrees it is 'official', but the old Fantasy Master's Codex has the breakdown you are looking for. TBH, I prefer it since it reinforces the idea that as task difficulty increases (adding more dice), your odds of a critical success will go down.

On 4 dice...
4 = critical success/triple damage
5 = critical success/double damage
6 or less = auto-hit/success
20 or greater = auto-miss/failure
21-22 = critical failure/drop weapon
23-24 = critical failure/break weapon

On 5 dice...
5 = critical success/triple damage
6 = critical success/double damage
7 or less = auto-hit/success
24 or greater = auto-miss/failure
26-27 = critical failure/drop weapon
28-30 = critical failure/break weapon

On 6 dice...
6 = critical success/triple damage
7 = critical success/double damage
8 or less = auto-hit/success
28 or greater = auto-miss/failure
31-33 = critical failure/drop weapon
34-36 = critical failure/break weapon

[Axly Suregrip]

So do you (a plural you) think the chart on ITL pg 9 is in error or intentional?

As it was pointed out, on 8 dice, the automatic failure start beyond 50%. That seems intentional to me. That is, if something requires a 8 die saving roll and you had an army of apprentices boost your stat to 50, it will won't help you beyond 27. So an 8 die saving roll will never get easier than 46% success. that makes sense.

Now the auto successes going up seems wrong.

[phiwum]

Originally Posted by Axly Suregrip

So do you (a plural you) think the chart on ITL pg 9 is in error or intentional?

As it was pointed out, on 8 dice, the automatic failure start beyond 50%. That seems intentional to me. That is, if something requires a 8 die saving roll and you had an army of apprentices boost your stat to 50, it will won't help you beyond 27. So an 8 die saving roll will never get easier than 46% success. that makes sense.

Now the auto successes going up seems wrong.

Just playing with https://www.omnicalculator.com/statistics/dice, the maximum odds for critical success occurs at 7 dice, with 6.1%. I haven't bothered to really do an analysis deeper than that.

So, automatic success goes from 1/36 with two dice up to 6.1%. The 2 dice odds are kinda pathologically low, so let's figure it goes from about 5% to 6.1% and then starts going down. By the utterly silly 20 dice, it's down to 3.8%.

Just playing around, it seems that the probability of automatic failure is strictly increasing.

I'd say that a one percent fluctuation up around seven dice isn't a big deal for automatic success.

What should obviously keep us all up at night is what happens when we reach 16 dice and the automatic failure point is equal to the automatic success point (44). Because you know that the very first time we require a sixteen die roll, it's gonna come up 44.

You rescue the princess, but she has mega-herpes? You save the kingdom from the orc invasion just as the sun goes nova? You manage to climb the underside of the rock overhang, but fall into an Escher drawing?

ETA: To answer your question about intention, the text on ITL 9 says "Note that the numbers are weighted toward critical failure on extremely hard tasks!" It doesn't say that odds of automatic failure are strictly increasing, but I'd say it's intentional. The fact that auto success increases for a while is probably not intentional but not worth fixing. (I must say, I'm puzzled it increases like that. I would've guess strictly increasing or decreasing, not having a maximum at 7.)

[Axly Suregrip]

Originally Posted by phiwum

What should obviously keep us all up at night is what happens when we reach 16 dice and the automatic failure point is equal to the automatic success point (44). Because you know that the very first time we require a sixteen die roll, it's gonna come up 44.

If a 16 die save comes up, what will scare me is the GM that thinks this was needed.

I think it only makes sense that a auto fail beats a auto success. That is, if you are asking for a 16 die save, you really are saying this should be close to impossible.

[phiwum]

Originally Posted by Axly Suregrip

If a 16 die save comes up, what will scare me is the GM that thinks this was needed.

I think it only makes sense that a auto fail beats a auto success. That is, if you are asking for a 16 die save, you really are saying this should be close to impossible.

Oh, sure. I was only carrying this out to its mathematical conclusions. Obviously, you're not seriously going to roll much higher than eight dice if that.

The fact that things get honky at the unreasonable extremes doesn't really matter because they're unreasonable. Sixteen dice are close enough to impossible that I'd call it impossible before then.

Though, per the rules, there's roughly a 4% chance of success in that case, or 3% if we agree that auto fail trumps. That's significantly better odds than rolling double or triple damage on 3 dice (about 2%).

[hcobb]

Problem is that the increase of automatic success at increasing difficulty makes weapons mastery self-defeating.

[phiwum]

Originally Posted by hcobb

Problem is that the increase of automatic success at increasing difficulty makes weapons mastery self-defeating.

How so?

I'd buy that the increase of critical success might do that. On five dice, there is a 3.2% chance of critical success, which I presume is double damage unless you get the 1/6^5 roll of all ones. Six dice yields about 3.5%. So that is an increased probability of double damage.

Let's suppose your opponent has DX 12, so a probability of about 75% to hit. Let's presume his expected damage is x. I'll simplify by ignoring triple damage.

To hit a master who is defending (front hex), the roll is 10 or less on six dice. All of those hits are double damage. The expected damage then is

0.07 * x. Stupid error. See next post for correction.

To hit an expert who is defending, the roll is 11 or less on five dice, and that's double damage unless an eleven is rolled, so an expected damage of

0.032 * 2x + 0.026 * x = 0.09 * x.

To hit an average Joe who is defending, the roll is 12 on three dice and double damage on three or four. The expected damage is

0.019 * 2x + 0.72 * x = 0.76 * x

To hit an average Joe who is defending, the roll is 12 on four dice and double damage on seven or less. The expected damage is

0.027 * 2x + 0.31 * x = 0.36 * x

I don't see the problem. Oh, I suppose that defending against a low DX opponent can increase the odds of hitting, since auto success increases slightly. But a master surely isn't fighting such low DX buggers all that often, is he?

I must be missing something.

[hcobb]

To hit against a master defense you need to roll 14 or less, not 10 or less.

[phiwum]

Originally Posted by hcobb

To hit against a master defense you need to roll 14 or less, not 10 or less.

Ah, quite right. Fourteen or less is an automatic hit. Stupid error on my part.

That means that the expected damage for DX 12 (or anything less than DX 17) ends up rolling 14 or less on six dice, which yields about 6.1% chance of hitting. If a character with DX 12 or less attacks a weapons expert who is defending, he must roll 11 or less on five dice, which yields about 5.8% chance of hitting. The rules entail it's easier for a DX 12 (or lower) character to hit a master than an expert.

Expected damage is 0.09 * x when attacking the expert, as calculated before. When attacking the master, the expected damage is

0.035 * 2x + 0.024 * x = 0.094 * x.

Strictly speaking, you're right. The master does worse when defending against DX 12 or below.

At DX 13 or higher, the edge goes to the master, though that doesn't make things alright.

On the other hand, I don't think that it has much practical effect on the game. The master gets hit, what, one more time every 333 attacks than the expert? It's wrong that the numbers work out like this, but it's not too significant.

Thanks much for the correction. Stupid error on my part.