Tunnels & Trolls task resolution benchmarking

Tunnels & Trolls has the first universal task resolution procedure in gaming. It's called the saving throw, after the D&D procedure. The Judge is expected to apply the results of this procedure to the fiction in a totally organic fashion. This is radical stuff!

The procedure is quite simple: roll 2d6+stat, against a target number of 15+(5*difficulty). A roll of doubles on the 2d6 "explodes"; add another 2d6 and repeat this step. If the total of the 2d6 roll(s) is/are 4 or less, the task fails. Succeed or fail, the player gets (roll+stat)*difficulty experience points.

I need a hard modelling surface to apply a "pick your own difficulty" procedure like this. I want to know what the odds are for a normal person to succeed at a given task. That way I can set the task's difficulty level irrespective of the player's actual stats.

To that end, I simulated 200k dice rolls and counted them up. (Credit to Vivit Elric for doing the actual programming; I handed in pseudo-code and got a csv with the values in return. Thanks, Vivit!) Now, let's check out the results.

2d6 DARO, 100k rolls
 

What an odd curve! I'm charmed by the sudden spikes throughout.

 Now let's see the actual task resolution value; if a random human being (aka one with 3d6 in a stat) attempts a task, what will they roll?

 

3d6+(2d6 DARO), 100k rolls

Now that's the sort of smooth graph I like to see!

From here it's a trivial matter to find the odds of rolling 20, 25, 30, etc. There's a small chance that a result of 20 to 22 could auto-fail because the 2d6 roll was 4 or less. I have factored that in, but it makes almost no difference to the average human.

Without further ado, here are the chances of an average human making a saving throw of X level:

Table showing an average human's chances of success at saving throws of various difficulties
 

I stopped at level 10 because nobody rolled anything higher in 100k checks!

I think the scale reasonably caps out around level 5 or 6. In play, we're not going to calculate the precise difficulty of any task, we're going to eyeball it, and I don't believe anybody can eyeball the difference between 1 in 2381 and 1 in 7143. Conceivably you could bump the throw up a level every time you add an additional obstacle. That'll only matter when we're dealing with non-human kindred, I guess.

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