Auto success and failures, rule of 19

[RobW]

Originally Posted by Skarg

Just always have 3 dice the same color, and use those dice only to determine the usual end results on 3 dice, with the other dice only mattering if you haven't rolled a 3-5 or 16-18.

But that's only good IF that is really what you want.

There's been some discussion in the main forum about critical failures. TFT LE has the new mechanic that chances of auto failure increase, quite dramatically, as you add dice to the roll for success.

The table on p9 of TFT LE tries to do two things as the number of dice increases: keep the odds of auto success about the same, and increase the odds of automatic failure

It's fine, but, I'm not wild about hunting things up in a table. And much more importantly, the 3D rolls have easily interpreted outcomes, eg auto-success, 2x and 3x damage. The larger rolls just don't have this. I instinctively know that on 3d6, 16 is bad, but 18 is really really bad. It even gives me license as GM to use my imagination when a critical comes up.

But if someone rolls a 8 against a dodging weapons master, is that really really bad, or just bad? I don't know.

So what I'm proposing is a variation of the colored dice idea above. Rolls for success always include 3 colored dice (the "critical dice") that are used to judge auto and critical success or failure. So on a difficult 5d roll, you would roll 5 dice, three of them are the "critical dice".

As normal, you add together all the dice and compare to the stat being checked. But the critical dice (only) are used to determine auto/critical success or failure.

The chances of auto and critical success never change as the dice increase, 5 on the critical dice means an auto success, regardless of the total on all dice. A 4 is success at the level of double damage; 3 is success at the level of triple damage. Same with critical failures: 17 on the critical dice is always a critical failure at the level of a dropped weapon; 18 is a critical failure at the level of broken weapon or backfired spell.

The chance of auto failure DO increase as the number of dice increases, according to the "rule of 19". If the sum of the critical dice + the total number of dice rolled >= 19, it's auto failure. For example, on an 8d roll for success, a roll of 11 on the critical dice is automatic failure (11 + 8 = 19, wahr wahr).

The next post will show how the rule of 19 compares to TFT p9

[RobW]

This compares the chance of auto failures for the Legacy Edition p9 table (LE p9), and the rule of 19 above. That is, as the number of dice being rolled increases, how do the odds of automatic failure increase? The two rules behave almost identically.

https://www.dropbox.com/s/f803a05jrh...lures.pdf?dl=0

Here just zooming in on rolls of 8 and fewer dice, ie the kinds of rolls that could reasonably occur in a game

https://www.dropbox.com/s/verkwwa3kh...ures8.pdf?dl=0

As above, the big advantage of this system in my mind is that now everyone around the table can instantly tell whether there's been a critical success or failure, and if so just HOW critical.

[RobW]

TLDR
On rolls for success, include 3 colored "critical dice". Add up all the dice and compare to the required stat as usual, but the result on the critical dice may override that.

The critical dice can be read for auto/critical success and failure just as in a 3d roll. For example, an 18 is a spell backfire, a 3 is a triple success.

The chance of automatic failure increases with the number of dice rolled according to the rule of 19, if the total on the critical dice + the number of dice rolled >= 19, automatic FAILURE

This works out virtually identical to the table on TFT p9, but it's much easier to interpret critical success and failure (and no table required).

[phiwum]

Originally Posted by RobW

This compares the chance of auto failures for the Legacy Edition p9 table (LE p9), and the rule of 19 above. That is, as the number of dice being rolled increases, how do the odds of automatic failure increase? The two rules behave almost identically.

https://www.dropbox.com/s/f803a05jrh...lures.pdf?dl=0

Here just zooming in on rolls of 8 and fewer dice, ie the kinds of rolls that could reasonably occur in a game

https://www.dropbox.com/s/verkwwa3kh...ures8.pdf?dl=0

As above, the big advantage of this system in my mind is that now everyone around the table can instantly tell whether there's been a critical success or failure, and if so just HOW critical.

I have a simple question. How did you generate that graph?

Did you come up with a smooth function that encodes the actual odds in a logical manner or did you calculate the odds for each of the seven integer values (2, 3, ..., 8) and apply a method to generate a smooth approximation?

Just curious. I assume the latter, but I'd be impressed if there's a continuous function easily expressed for the former. That is, if there's a natural (canonical) way to extend this discrete probability function to a continuous function with sensible values in between the integers.

I have to think about the numbers. The increased odds of auto-failure comes with an increased chance of critical failure. Since four dice is pretty common, this is a big change. If my off-hand calculation is correct, the new probability of critical failure on four dice is 9.2% 4.6%, using the rule that critical is one greater than auto. That's a huge large jump from 2.7% for RAW, leading to lots of dropped weapons.

(Edited above, since I made a significant error on the four dice critical roll. Using the rule of 19, an auto-failure on four dice occurs if you roll 15 or more on three dice, so a criticial requires 16 or more on three dice, hence 4.6%. The jump from 4.6% to 9.2% auto failure is larger, but applies only when adjDX -- or whatever stat -- is already 15 or more.)

[JimmyPlenty]

Just posting this link because it is helpful because you got me trying to figure this out. (and so I don't lose this reference again. :)

http://gurpsland.no-ip.org/articles/d6chance.htm

[phiwum]

The following link is useful too.

https://www.omnicalculator.com/statistics/dice

[hcobb]

Or you could just use:

https://www.hcobb.com/tft/TFT_Saving...rcentages.html

[JimmyPlenty]

or...yes that. Perfect Henry!

[Axly Suregrip]

Originally Posted by RobW

TLDR
On rolls for success, include 3 colored "critical dice". Add up all the dice and compare to the required stat as usual, but the result on the critical dice may override that.

The critical dice can be read for auto/critical success and failure just as in a 3d roll. For example, an 18 is a spell backfire, a 3 is a triple success.

The chance of automatic failure increases with the number of dice rolled according to the rule of 19, if the total on the critical dice + the number of dice rolled >= 19, automatic FAILURE

This works out virtually identical to the table on TFT p9, but it's much easier to interpret critical success and failure (and no table required).

This is brilliant. I love that there is no table to look up.

[RobW]

Originally Posted by phiwum

Since four dice is pretty common, this is a big change.

Yes, the chance of auto-failure on 4d6 is really the only visible difference between LE p9 and the Rule of 19

If that feels uncomfortable, you can limit the Rule of 19 to rolls of 5+ dice