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Tuesday, September 22, 2020

Situations: Why 1 in 3?

In Situations: The Basics, I wrote “Anything that’s roughly a 1 in 3 chance is good.” But why do I like a 1 in 3 chance?

Again, think of the three categories. Either you tell the player “No, what you are trying doesn’t work,” or you say “Yes, what you try to do works,” or you say “Let’s roll and see if it works or not.” There are two possible outcomes, so the simplest solution would be 1 in 2, a 50-50 chance. A bit dull.

1 in 3 is the next simple probability, easy to do on the most common kind of dice available. It makes the player’s choices a little more tense, and since a lot of actions are still going to fail, it means the player on average will have to try more than one thing to escape each situation.

It also leaves plenty of room for three possible outcomes, instead of only two, in cases where three outcomes make sense.

  • 1 in 3 chance the player succeeds,
  • 1 in 3 chance the player has to try something else,
  • 1 in 3 chance something goes wrong.

A 1 in 3 chance that something bad happens isn’t too punishing, but also isn’t so low that players will never see bad things happen.

I think Arneson and Gygax had this in mind when they were deciding on dice mechanics. They started with a 1 in 3 chance for any given situation and then revised the mechanic where desired to provide more details or options. Most of the incidental mechanics – chance of surprise, chance of dropping a weapon or torch when surprised, chance of falling into a pit – are 1 or 2 in 6, which fits the 1 in 3 model.

For reaction rolls, they needed three outcomes at the very least (Friendly, Neutral, Hostile,) with the option for more outcomes in some negotiations. A 2d6 roll allows room for more outcomes and only lowers the chance of a Friendly outcome a little: 9+ on 2d6 is a 27.78 % chance, not quite 1 in 3, but close.

Reaction Roll Probabilities

(Probability charts created using AnyDice)

For combat, a close to 1 in 3 chance of hitting an armored enemy seems about right, but you have options for better armor, worse armor, or no armor to cover, not to mention shields. So, they switched to a 1d20. The closes to a 1 in 3 chance (33.33 %) is 35 %, or 14+ on 1d20, which just happens to be the target number for a 1st level character to hit chain armor, the middle armor option.

Combat/Saving Throw Probabilities

At the next combat tier (4th level, for Fighters,) this just happens to be the target number to hit the next armor tier, plate armor. Also at this tier, the target number to hit an unarmored opponent is 8+, or 65 %, which is very close to 2 in 3.

Saving throws do get kind of crazy, maybe too crazy, but it still starts from the same principal. One of the Fighter saving throws (vs. being turned to stone) is 14+ on 1d20, with other saving throw categories being +/- 1 or 2 points away in most cases.

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  1. I like to see this on cumulative rolls: the common party of 3-4 pcs, all members searching for a secret door has a near "1" chance, but not really 100%.

    Also the same party has an almost 100% chance to springing a trap under the same circumstances, while keeping it random enough

    1. I'm not exactly following what you're saying. Are you saying that the probability of success should approach 1 in 3 every time a roll is repeated, or that a 1 in 3 chance should be added to the probability every time a roll is repeated?

    2. What I mean is that 1 in 3 is the sweet spot in which a single pc is very likely to walk over a trap unharmed (66%) but a whole party is very likely to trigger it.

      Equally is a sweet spot in which searching for secret doors would be tiresome for a character alone, but a party of 4 searching together and each having 1 in 3 chance to find it, is very likely to find it in one turn.

    3. AH, yeah... that makes more sense.

      The secret door issue is not an issue for me, specifically, because as mentioned in the follow-up post, I frequently use the result of a failed roll as the extra time needed to complete the task. So, if I make a secret door search in secret, I will get a rating of 1-4 for the number of turns needed to actually find the door. Since it's secret, players have to make a choice how much time they will potentially waste searching for a door.