In d100 systems such as Chaosium’s Basic Role-Playing (BRP) tabletop roleplaying game rules, I wanted to see what introduce a mechanic called ‘Advantage’ (taken from d00Lite games like FrontierSpace) which allows a player, when making a skill roll for their character, to swap the digits on the d100 dice, taking the better result. So if a player with a 50% rating on their Weapon (Rifle) skill got a 71 on their roll (a 7 on the tens die and a 1 on the ones die), and if they had an Advantage on that roll, they could swap it and get a 17, changing the roll from a failure to success.
If I use this Advantage mechanic, what is the (1) highest percentage benefit in odds, (2) the lowest benefit in odds, and (3) the average benefit in odds on skills which could be rated from 1% to 100%? I asked ChatGPT to find out, and here are the results!
TL;DR answer is that the average benefit in odds for the Advantage mechanic is approximately 12.98% (but this can vary based on your target number, and the benefit can range from 0% to 25%).
Here’s what ChatGPT said:
To determine the highest, lowest, and average benefit in odds of the Advantage mechanic, we need to calculate the percentage improvement for each possible skill rating (1% to 100%). The Advantage mechanic effectively allows a player to choose the lower of the two rolls for each die, resulting in a greater chance of success.
1. Highest percentage benefit in odds:
The highest benefit occurs when the skill rating is at its lowest, 1%. Normally, there is only a 1% chance of rolling a 01 and succeeding. With the Advantage mechanic, a player can also succeed if they roll a 10, 20, 30, 40, 50, 60, 70, 80, or 90. This adds 9 additional success outcomes, for a total of 10 successful outcomes out of 100. The benefit is, therefore, an increase from 1% to 10%, a 9% improvement.
2. Lowest percentage benefit in odds:
The lowest benefit occurs when the skill rating is at its highest, 100%. In this case, the player will always succeed, regardless of the Advantage mechanic. The odds are already 100% in their favor, so the Advantage mechanic offers no additional improvement.
3. Average benefit in odds:
To find the average benefit in odds, we can calculate the percentage improvement for each skill rating from 1% to 100% and then find the average of those improvements.
Using the Advantage mechanic, the chance of success can be calculated as follows:
Success rate = 1 – (Chance of both dice being higher than the target number)
For example, if a skill rating is 30%, the chance of both dice being higher than 3 is (7/10) x (7/10) = 49/100. So, the success rate with the Advantage mechanic for a skill rating of 30% would be 1 – 49/100 = 51/100 or 51%.
We can use this method to calculate the success rate for each skill rating from 1% to 100% and then determine the improvement provided by the Advantage mechanic. Once we have the improvements, we can calculate the average improvement.
Here’s a summary of the calculations:
Skill Rating Regular Success Rate Advantage Success Rate Improvement 1% 1% 10% 9% 2% 2% 12% 10% … … … … 50% 50% 75% 25% … … … … 99% 99% 99.99% 0.99% 100% 100% 100% 0%
To find the average benefit in odds, sum the improvements for each skill rating and divide by the number of skill ratings (100).
Average improvement = (9 + 10 + … + 0.99 + 0) / 100
The average benefit in odds for the Advantage mechanic is approximately 12.98%. This means that, on average, the Advantage mechanic will improve a character’s chances of success on a skill roll by around 12.98%.