New Dice Mechanic That I Am Working On

One of my other sites is You Meet In A Tavern which is a forum of Game Masters dedicated to helping other GMs with problems that they may encounter at the game table. One of the recent posts is “Player Decisions as part of Dice Outcomes – controlling the randomness” where the author of the original post describes his desire to give his players more control over the amount of risk that the PCs will take with their actions if the players sacrifice higher levels of effect. The author explained this as choosing accuracy over power (or vice versa).

For example, a PC in an RPG wants to fire an arrow at his opponent. If the PC wants to put the emphasis on accuracy the PC receives a bonus to hit the target, but now must limit the total amount of damage that the attack will do. If the PC wanted to sacrifice accuracy the PC would receive a penalty to hit the target, but the attack would be more powerful and would cause more damage if successful.

I suggested the following mechanic, which I expand upon here, and I would like feedback on the idea from others:

1. Challenges have a target difficulty ranging from 2 to 12.
2. Players must roll the target difficulty number or higher to succeed.
3. If the number rolled is higher than the target difficulty number the success gains the PC other bonuses (greater damage, more powerful in-game benefits, etc.).
4. Players may choose to roll 3d4, 2d6, or 1d12.
5. The average target difficulty number is 7.

This means that rolling a 1d12 would result in a success 50% of the time with a target difficulty number of 7. Rolling a 7 is the most probable result with 2d6, and with a target difficulty number of 7 that means that the PC would succeed 58.33% of the time. With 3d4 you would roll 7 or higher 68.74% of the time.

Yet every roll of the 1d12 has an 8.33% chance of rolling a result of 12, while 2d6 only has a 2.78% chance of rolling a result of 12, and 3d4 has only a 1.56% chance of rolling a result of 12. I feel that there are additional elements that need to accompany this mechanic to develop a game from it, but as a core mechanic I see a lot of potential here.

What needs to be developed is how the player is rewarded for taking a risk by rolling the 1d12 instead of the other dice. To address that I think there needs to be some relationship between the number of dice rolled and the target difficulty number. Using 1d12 for a roll with a target difficulty of 2 is going to succeed 91.67% of the time, but the player may choose to automatically succeed by using 2d6 or 3d4 since neither combination can roll a result lower than 2. If the target difficulty number is 7 rolling a d12 is very risky compared to rolling the 2d6 or 3d4. Yet if the target difficulty number is 12 rolling the 1d12 is actually less of a risk, and rolling 3d4 is less likely to succeed.

If I can figure out the risk versus reward part I think I can create a fun game from this mechanic. Right now the idea that I like the most is that the difference between the target difficulty number and the result of the dice roll becomes a form of currency to be spent in the game.

I will post updates about this as I make progress on the concept. For now I will just be working on the math.