Tuesday, February 04, 2014

Opposing die rolls

As players we are used to rolling to beat a target number with our dice. What I've been looking into and using in my games recently is rolling dice to beat a difference between dice. So instead of rolling 14 on a d20 or higher you need to have a difference of 5 or higher between two d20s. How does this work and how does it affect the game?

How does it work? Simply put the player rolls dice and the GM rolls dice. What matters is not the value each one rolls, but rather the difference between these rolls. To make a simple example lets play with d10s. A task has to be solved and the GM sets the difficulty at 5. To succeed the player and GM roll a d10. The difference between the rolls has to be 5 or greater to succeed.

The odds for a d10 - d10 is the following:

Since we are only concerned with the difference and not which is higher we must consider the absolute value of the die roll as show in the following graph:

Why has this caught my attention lately? Well for starters lets look at more complex dice. Look a the d20 vs d20 and 2d20 vs 2d20 below. The 2d20 vs 2d20 gives a nice flat curve towards the higher values. This means high difficulty tasks are going to be very improbable to succeed at unless the character has a lot of skill.

For example if the task requires a 32 or higher difference between the rolls the odds of success are minimal. If the character has just a +3 from skill the odds don't budge the slightest. On the other hand a character with +10 bonus would get considerable benefit, he's an expert. Yet this might not be enough to ensure an acceptable degree of success. Come in team play. Since there are a lot of values (0 to 38) it is easy to implement a mechanism for team play and group cooperation. If 4 characters all add their +4 to the task thats +16. It drops the difficulty from 32 to 16, making a task with 0.5% chance of success into one with 20% chance of success.

Finally the thing I really like, and that's because I'm a wicked GM, is that this keeps the players guessing. I don't have to reveal my roll and since there's no target value they're left guessing if they succeeded or not. Specially in the easier tasks. If the task is hard, once again taking the 32 difficulty rating as an example, it's pretty obvious from the player's roll which option is a winner and which one isn't. This is similar to real life, if the task is hard and you're not very experienced you don't raise your hopes up of having a success and you pretty much know you blew it. On the other hand if the difficulty is 10, there are a lot of values that I can roll as a GM that will give them a 10 or greater difference. The player rolls a 15, and well a 0, 1, 2, 3, 4, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 and 38 on my roll would mean failure. What did I roll? Did I roll these less probable values or the more probable ones between 5 and 25? Time to open the treasure chest and find out.

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