In recent role-playing games, a popular mechanic for making task rolls easier or more difficult is the concept of “Advantage and Disadvantage“. It is also sometimes known as “Bonus Dice and Penalty Dice“.
The idea is simple. When a character tries to perform an action that, due to the prevailing circumstances, is either easier or more difficult than usual, instead of rolling a single die they instead roll multiple dice. If the task is easier, they take the best result from the dice pool. If the task is more difficult, they take the worst. In d100 systems that use this mechanic (e.g. Call of Cthulhu 7th Edition), this typically only applies to the “tens” die; the “units” die is rolled normally.
So, for example, let’s suppose a character was trying to navigate a particularly narrow ledge. The Referee calls for an Agility Task Roll. However, because it’s raining and the ledge is more slippery than usual, the Referee decides that the player must roll an additional Penalty Die.
The player rolls a 3 and a 7 on their two “tens” dice and a 2 on their “units” die. Picking the worst result (as this is a Penalty Dice situation), their final roll is 72. If the same roll was performed with a Bonus Die rather than a Penalty Die, the most advantageous “tens” dice would be selected for a result of 32.
It’s a neat mechanic and could potentially replace the existing Difficulty Modifier table in Hack100. My main reservation is the lack of transparency. If a Referee applies a Difficulty Modifier of -20% to a Task Roll, it is easily understood how much more difficult the task has become and what the new chances of success are. Conversely, whilst it’s clear that the award of a Penalty Die reduces the chance of a successful Task Roll, it’s certainly not obvious by HOW MUCH the chance of success has been reduced.
So, I thought I’d try and quantify the effects of Bonus Dice and Penalty Dice using a simple computer programme. For different numbers of Bonus Dice and Penalty Dice, the programme performed a million simulated rolls against a range of Target Percentages and tallied the number of successes. This then allowed the net effect of the Bonus Dice and Penalty Dice to be quantified.
The graph below shows the effective Difficulty Modifier for a single Bonus Die. It makes for interesting reading. What’s immediately obvious is that the effect of the Bonus Die varies with the Target Percentage. In other words, unlike a conventional Difficulty Modifier, it’s not constant. The net effect of the Bonus Die reaches a maximum of about +25% at a Target Percentage of 50% and falls to about +5% at Target Percentages of 5% and 95%. Therefore, if a character has either a very low score in a given Ability or a very high one, then the effect of a Bonus Die is going to be much less significant than if they have a mid-range value. 30% – 70% seems to be the sweet spot.
This second graph collates the same analysis for one and two Bonus Dice and Penalty Dice. It can be seen that for two Bonus or Penalty Dice the graph is asymmetric.
So, what to conclude? I don’t think replacing the Difficulty Modifier table in Hack100 with Bonus and Penalty Dice would be game-breaking. For Target Percentages in the range 20% – 80%, a single Bonus Die or Penalty Die gives a net modifier of around +/- (15% – 25%). Two Bonus Dice or Penalty Dice give a net modifier of around +/- (20% – 40%) over the same range. Overall, the effect is going to be broadly similar to the existing Difficulty Modifiers in the current Hack100 core rules. And, in keeping with the original design aims, it would remove one reference table.
On the other hand, I still feel the lack of transparency regarding the quantitative effect of Bonus and Penalty Dice remains a weakness. The approach also lacks granularity. For example, this system couldn’t capture the smaller incremental Agility penalties for wearing different types of armour.
Overall, I think I will keep the existing Difficulty Modifiers as the standard approach in Hack100 but include the option of using Bonus and Penalty Dice for those that wish to do so.
Footnote: I’m sure there must be a more elegant mathematical approach for quantifying the effect of Bonus and Penalty Dice in a d100 system than my sledgehammer computational method. If anyone has exact solutions, I’d be grateful if they could share them (if only to confirm my figures are broadly correct).