Dice Pools in the 2d20 System

File today’s post under “Short But Labor-Intensive.” Having played a lot of Star Trek Adventures and some short games of Infinity, I’ve noticed a question come up repeatedly in the 2d20 system. How many dice is enough dice? With the criticals and the shifting Difficulties it can be hard to figure out whether you should be buying more dice. Well, I aim to settle that mathematically today.

Calculating the probable outcome of a die roll is pretty simple. You take all the results that would be successful and then divide that by the total number of possible results. Of course, given that a 2d20 roll has four hundred different possible rolls that’s a pretty tall order… There are good ways to figure out the probabilities here but I prefer the easy way: the calculator on anydice.com.

If you want to play around with this yourself the code to enter is output [count {1..X,1} in Yd20] where X is your Attribute + Discipline total and Y is the number of dice in the pool. In case you’re wondering, the extra 1 in the curly brackets is to count 1s twice. If you want to calculate with a Focus then replace that second 1 with 1..Z where Z is your Discipline rating (it counts everything between 1 and Z twice) but more on Focuses later.

To cut to the chase, my advice for dice pools in this system is that you can generally count on getting half your dice pool in successes for an Attribute + Discipline total (say 8-11) or half your dice pool plus one in successes for a high total (12 or 13). If you have a really high total (around 14-16) you can expect successes about equal to your dice pool or likely one less. If you want to see the raw numbers check out the table below.

Probability of rolls for 2d20 (no Focus).

Interestingly, having a Focus that’s applicable to the Task doesn’t change this advice for the most part. It makes it slightly more likely that you will get another success than otherwise but the averages are still what I said earlier. The exception to this is with very low pools and very high Discipline ratings: if you are rolling two or three dice and you have a Discipline rating of 4 and an applicable Focus you should expect to get successes about equal to your dice pool. That’s as it should be and also sort of a corner case…

What About Complications?

There’s one other thing to think about: when shouldn’t you add more dice to your pool? Each die you add, of course, is also a die that might come up a 20 which is an automatic Complication. To figure out the actual chances of that you can use the code output [count {20} in Yd20] where (again) Y is the number of dice you’re rolling. You can see the actual percentages of rolling a complication but a rule of thumb is that it’s 5% chance for each die in your pool. This means that unless you have way more dice in your pool than you need you aren’t shooting yourself in your foot. My advice is to aim for about one more die than you need if you’ve got the resources to spend.

The exception to this is if you have an increased Complication range (which you can calculate by using the above code and replacing “20” with Z..20 where Z is the bottom of the range). If you’re rolling with an 18-20 Complication range, for instance, then each die adds about 12% which is a whole different beast. In this case, don’t add any more dice than you have to given the advice above. If you roll 4d20, for instance, you have almost a 50% of rolling at least one Complication and more than a 10% chance of rolling multiple ones! So… don’t do that unless you need all those dice, although if things are that serious you might.

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