Help With Trophy Dark and Trophy Dark Risk Roll Probabilities

Question

Has anyone done some basic probabilities on the Risk Roll from Trophy Dark or Trophy Gold?

This level of statistics is well beyond my knowledge.

Risk Roll

A player will build two D6 dice pools. One pool will be "light" dice and the other pool will be "dark" dice. The size of the pools can vary. Players add light dice when they have something helping them and add dark dice when there is something to harm or impede them. After the light and dark pools are determined the pools are rolled together.

The standard pool that Trophy has is 2 possible light dice and 1 possible dark dice, however I would love to see what it looks like if these pools are allowed to grow to 4 or 5 per pool.

• If a dark dice is equal or higher than the highest light dice then a player may incur a penalty to a special stat called "Ruin".
• Ruin is rated from 0 to 6. if a player incurs a ruin penalty the value of the dark dice is compared to the current ruin stat of the player. If the value is higher then the player's ruin stat increases by 1.
• The highest dice, regardless of which pool or if ruin was incurred, is then used to determine the outcome of the roll. 6 being a full success, but 5 and 4 are also successes.

Interesting Aspects and My Observations

So this one roll has 3 separate aspects being rolled.

1. Overall success based on the highest value of a rolled dice.
2. Possible ruin if the highest dice was from the dark pool.
3. Actual incurred ruin if the highest dice was also higher than the player's ruin stat.

I find this roll extremely interesting as several things can all happen with a single roll and there are even some diametrical aspects.

1. The larger both light and dark pools are, the higher the overall success at the possible cost of a higher chance of injuring ruin.
2. The ideal roll is of only light dice, but it is also possible to roll all dark dice and still succeed without injuring ruin.
3. At a certain point of ruin a player can have some ability to succeed with dark dice while not incurring additional ruin.
4. It's possible for a player to fully succeed with a 6 while also taking ruin and have a complication.

If someone can break this down to actually show what the probabilities and changing nature of possible rolls are with this system it would extremely interesting to see.

Answer 1

Here's one solution:

from icepool import d6, tupleize, highest

light = tupleize(d6, '')
dark = tupleize(d6, 'ruin')

output(highest([light] * 2 + [dark] * 1))

How it works:

• tupleize produces outcomes (1, ''), (2, ''), ..., (6, '') for light and (1, 'ruin'), (2, 'ruin'), ..., (6, 'ruin') for dark.
• highest takes the highest roll in the list. Since 'ruin' > '', dark dice are taken over light dice that rolled the same number.

Example output:

Die with denominator 216

Outcome[0]	Outcome[1]	Quantity	Probability
1	ruin	1	0.462963%
2		3	1.388889%
2	ruin	4	1.851852%
3		10	4.629630%
3	ruin	9	4.166667%
4		21	9.722222%
4	ruin	16	7.407407%
5		36	16.666667%
5	ruin	25	11.574074%
6		55	25.462963%
6	ruin	36	16.666667%

Here's an AnyDice version:

LIGHT: d{10, 20, 30, 40, 50, 60}
DARK: d{11, 21, 31, 41, 51, 61}

output [highest of [highest 1 of 2dLIGHT] and [highest 1 of 1dDARK]]

AnyDice only has integer outcomes, but we can use digits as a stand-in for tuples: here the tens digit is the top number, and the ones digit is whether there is a threat of ruin. AnyDice doesn't support pools of mixed dice, but we can get around this by taking the highest of each individual type of dice, then taking the highest among those.