Okay, so, there’s thief in your group and they want to infiltrate the tent of an officer from an opposing army. Its in the middle of the camp and you want to make it hard, but from your point of view, it would be a good thing if the thief was able to do it.
So, lets suppose the player rolls 2d6 and has to get at least 7 to succeed. They get +2 from their.. skill. Whatever. First, you want them to roll for moving into the camp. Then you want them to roll for moving through the camp. Then you want them to figure out where the tent is and roll for that as well. Then you want them to roll for entering the tent. They’re pretty good at what they do, so this should work, right?
Well, okay, the chance for a single roll to succeed is… what? How do you even figure that out? Okay, so its easier to figure out the cases where you’ll miss. In this case, you’ll miss if you roll 2, 3, 4. Okay, that’s different cases out of 11, but its not that simple. When rolling two dice, you have 36 possible combinations of numbers. Of those, only one results in 2, two result in 3 and three result in 4. So, that’s six different combinations where you fail or one out of every six times, meaning your chances of success are five out of six. For one roll. Seems pretty good, right?
Okay, so what are the chances of succeeding in four different rolls? That would be (5/6)^4 or 625/1296, meaning that the chance of success has now dropped below 50%. What was once a strong suit for the character has now become mediocre, almost a flip of the coin, because you wanted to make the player roll.
Okay, so there’s certain tension here. For dramatic purposes, you want the rolls, but if you don’t want the players to fail at everything, you don’t want to have them make too many of them. The problem is, most people, a group into which most GMs belong to, don’t get probabilities. The simple calculations I just made are beyond most people, and again, most GMs belong to this particular group.
Probabilities are difficult for people, because most of us don’t need them that much. Understanding them would definitely be beneficial to most of us in many situations, but we can get through life without. So, we don’t really ever learn them.
Some years back I stumbled into a conversation where someone brought up the statistic that 52% of men cheat on their partners at some point. This was made up to be horrible. We were portrayed as monsters, who have no soul. On the other hand, according to the same study they were quoting, 43% of women cheated as well. So, apparently women were basically saints. For some reason 50% was magical. Anything above it was certain and anything below was meaningless. On the other hand, if we have a million people, half of which are women and the other half men, that would mean 475000 of them have cheated at some point in their life. Since we don’t really know how the study was conducted, there’s a chance quite a few more would cheat at some point in their life afterwards, if they were still young.
So, if we compare the figures 520000 and 430000, the difference doesn’t seem that big anymore. Of course, to people with a basic understanding of probabilities, the magical 50% is ludicrous. How many people don’t even have that level of understanding? Quite a few.
Here’s a fun source for you: Why Do American Stink at Math. Its about Americans in particular, but here’s a quote from it:
A survey found that three-quarters of doctors inaccurately estimated the rates of death and major complications associated with common medical procedures, even in their own specialty areas.
Now, statistics are an integral part of medical school. In many cases you can’t even get in without being able to make calculations on them. Still, most doctors (in America) can’t even estimate stuff that should be a huge part of their job.
Now, you, as the GM, aren’t making decisions on the life and death of actual people, but your decision-making does have a huge role in what happens in the lives of the characters. You have to try to find a good balance to keep the drama going, but not being overly relient on forcing die rolls too often. That will just end up with the players always failing when they get closer to their targets. (Unless, that’s exactly what you are going for, you asshole.)
Am I able to give you guidelines here? Not really. Its so system dependent. However, I would suggest using systems with fail-forward, as I often do, because that at least means that you have outs. Each fail in the rolls in the first section doesn’t have to mean that the alarm was raised, but that maybe they have to talk themselves out of the situation, or maybe the “alarm level” of a guard was raised and an extra roll is required. Kind of basic stuff in many ways.
So, as an exercise, to which I’ll maybe give answer some day, if I remember, what are the chances of reaching the goal in the thief-example, if you give them a chance to reroll the first miss on every stage (and a success in the reroll means that the guard became alarmed, but has no other further consequences)?