After a game session with some friends, there were some questions raised about exactly how the dice work. Given the way the rules are written (e.g. frequency of mechanics and relative cost of talents, upgrades, etc), and the way the dice are described, we expected upgrading dice to be superior to boost dice. Some quick math so seems to indicate otherwise. The arguement is built on the following demonstrable facts:

- One boost die has 2 faces with successes, each with one success, i.e. out of six outcomes (each of equal probability) there are two successes. On average (over many many rolls), we can conclude adding a boost die to a pool will add 1/3 (2/6) successes.
- One Abilitiy die has 4 faces with success, 3 with one, 1 with 2. On average, an ability die will contribute 5/8 successes to a pool.
- One Proficiency die has 8 faces with successes (or triumph, which count as one success), 2 of which have 2 successes, 1 on the other. There are 12 sides, and 10 successes amongst them, so each proficiency die will generate, on average 5/6 (10/12) successes.
- Based on this information, upgrading an ability die increases the resultant successes by 5/6 - 5/8 = 20/24 - 15/24 = 5/24 < 6/ 24 = 1/4.

By this math, the addition of one boost die seems to provide 60% more successes (over many many rolls) than upgrading an ability die (1/3 / 5/24 = 8/5 = 1.6). [Note: it is clear that the Proficiency die is superior to the Boost die, but this is not the comparison being made, because there is no way to simply add a proficiency die. This mechanisms being compared are upgrading vs addition of a boost die]

Where a Proficiency die represents an individuals expertise in a skill, further supported by his attribute, and it resides "On the top" of the spectrum of quality of the positive dice, and a Boost die represents favorable situational/environment conditions, it seems to be problematic that the "upgrading" mechanic, which is presented as being more powerful, is numerically LESS effective at producing successful results than enviromental/situational conditions.

It should be noted that, In the case of there being no ability dice to upgrade and the upgrade adds an ability die, the increase in the average success of the roll caused by the upgrade, 5/8, (1/2 probability of increasing successes rolled), the upgrading mechanic IS acutally superior to the boost die (5/8 - 1/3 = 15/24 - 8/24 = 7/24) by a substantial relative margin (5/8 / 1/3 = 15/8 = 1.875, 87.5% improvement).

This is supported in practice as well. Instead of rolling these dice over and over, I got into R and wrote some code to simulate dice rolls. I've included two typical examples of the outcomes below (all results based on 10000 simulated results, rounded to nearest 0.1%).

Ex 1. Skill rank 1, Attrib 3, average difficulty. Pool = YGGPP (1 Yellow Proficiency, 2 Green Ability, and 2 Purple Difficulty dice; I use + for boost dice, and - for setbacks)

- Base probability of success: 65.1% (90% probability interval for net success: [-2, 4])
- Probability of success following upgrade (YYGPP): 69.6% (90% probability interval for net success: [-1, 4])
- Probability of success following a boost die (YGGPP+): 71.1% (90% probability interval for net successes: [-1, 4])

Ex 2. Skill rank 0, Attrib 2, Easy difficulty. Pool = GGP

- Base probability of success: 58.0% (90% probability interval for net success: [-1, 3])
- Probability of success following upgrade (YGP): 65.5% (90% probability interval for net success: [-1, 3])
- Probability of success following a boost die (GGP+): 66.2% (90% probability interval for net successes: [-1, 3])

Ex. 3 Skill rank 3, Attrib 3, Average difficulty. Pool = YYPP

- Base probability of success: 56.3% (90% probability interval for net success: [-2, 3])
- Probability of success following upgrade (YYGPP): 70.2% (90% probability interval for net success: [-1, 4])
- Probability of success following a boost die (YYPP+): 64.9% (90% probability interval for net successes: [-1, 3])

On the surface I see two problems created by the way this mechanic is working. First, players will avoid the [typically] higher priced or more difficult to achieve talents that allow upgrading, and prefer talents that provide Boost dice. Following that, players may be more likely to argue and wheedle for boost dice based on the situation, slowing the game.

Second, players may be reluctant to improve their skills past points where the skill rank matches attribute rank for skills that are "upgraded" by other talents, since upgrading provides a larger boost at this "notches".

From a design standpoint, it seems the goal of "dice upgrade" mechanic should be to provide a very substantial benefit, which should exceed the bonus provided by a Boost die. Further, the advantage provided by an upgrade should be consistent across spectrum of pools to which it would be applied. Under the current design, these two goals are not being achieved.

I have not addressed the effect of upgrading difficulty vs the addition of Setback dice, or the effect of upgrading vs boost on advantage production. This is not due to neglect, it is due to 1) the already considerable length of this post and 2) the fact that the success of the roll does not depend on advantages produced.

Editorial: I LIKE the upgrade system, I think its clever, novel, and well implemented. There is also some psychological "wieght" that should be added when a green or purple die is upgraded following the expdenditure of a destiny point. The mechanic should be kept, but the dice need to be tweaked to allow the mechanic to live up to its potential.

-WJL