Wednesday, December 16, 2009

Unisystem 2d6

Eden's Unisystem, both Classic and Cinematic use a single 1d10 roll to determine all their random probabilities. It has the advantage of being simple and easy to do. But some games, a lot of games actually, roll dice instead of a die. Good examples that are close to Unisystem in terms of scope are BESM 3.0 and the Doctor Who Adventures in Time and Space which both use a 2d6 resolution.
So the question has come up what is the effect of using a 2d6 instead of a 1d10 roll. These are being discussed over on the Eden boards, and

Well for starters anytime you involve more dice, the probability curve is going to change. With a 1d10 the chances of getting a roll of 1 is the same as getting a roll of 9 or 7 or 3 or any other number. It's always 1 out of 10 (10%, or p=0.1).

When you add more dice than the number of potential rolls increases as due to the potential outcomes.

A 1d10 has 10 potential rolls and 10 potential outcomes.

A 2d6 has 36 potential rolls, but only 11 potential outcomes (2 to 12). Why the difference? Well a roll of 1 on one die and a roll of 6 on the other is 7 as is a roll of 2 and 4, and 2 and 5. So. This means some numbers will occur more often. This is obvious to anyone who has ever played any RPG really (unless the only thing you have played is Amber).

This also mean some outcomes are more likely to occur (high p) and others are less likely (low p), unlike a 1d10s flat outcomes.

This relationship is much closer to the way reality is modeled. We call this the Normal Curve. Now a 2d6 is not quite Normal, but it is much closer than the 1d10. Even better is the 3d4.

A quick look at Table 1 shows the 3 die types, their outcomes, the number of outcomes, their probability (p) and cumulative probability (cum p). I have also included the basic measures of central tendencies; mean, median and mode.

At first glance on the average, the 2d6 grants 1.5 points per roll (averaged out of course), and the 3d4 up to a 7.5 mean. There is also the nagging problem of both rolls cap out at 12 (not 10) and have no 1 rolls.

There is also a higher probability of rolling greater than a 9 in each case. I included 7 as well since you almost always add an attribute + a skill in many rolls. This results in far more success than the flat system. So how do we get the curve we want with the outcomes we need?

But This One Goes to 11
Simple, we subtract from the result. For the 2d6 we minus 1 (1 to 11 outcomes) and for the 3d4 we minus 2 (1 to 10 outcomes). So the 3d4-2 gives us the same range of outcomes, the same mean and median (flat distribution have no mode), but edges the probability down for success. The 2d6-1 gives us an extra point (an 11) and the averages are only .5 higher with comparable probable successes.

NOTE: I just noticed that these graphs are off by -1. The numbers are good, but I must have chosen the wrong range when making the graphs.

Now the question remains, why do it?

This brings a slightly grittier feel to your games. Successes now are less about blind luck and more about your skill. The outcomes are shot to the middle now (like reality) with fewer dramatic failures and successes. Want it even grittier? Take off another 1 from the rolls in every case to actually have a 0 outcome.
On the Eden Boards, we started calling these alternate dice methods "The Chicago Way" due to the number of Unisystem players we have here in the Chicago area.

Though I should point out while I really like the alternate dice methods, I still only use a d10 in my con games.

But I have also been playing the new Doctor Who game with a d12.

1 comment:

Anonymous said...

Hi guys,

Im new here im just posting to say Hello.

How is everyone?