06.29.08

[What Are The Odds] Outcome and Event

Posted in Game Design, Gameplay at 6:42 am by Christian

Single die rolls are quite easy to figure out. Rolling any particular number on a six-sided die has a chance of 1/6, or (rounded) 16.7%. Each number has the same chance of coming up. The same is true for any die – a D4 has a chance of 1/4 or 25% for each number, a D8 of 1/8 or 12.5%, a D10 of 1/10 or 10%, and a D20 of 1/20 or 5% for each number.

The difficult part starts when two dice are added together, or when modifiers and target numbers are brought into play. The reason for different probabilities for the result of a combined roll of multiple dice is that the result we see is the event (i.e., the sum), not the outcome (i.e., the specific combination of numbers rolled).

Outcome
An outcome is a specific possible result. For example, if you are asked to choose a number between 1 and 5, the number 3 would be a possible outcome. All possible outcomes have the exact same probability (in this case, one out of five, or 1/5, or 20%, or 0.2).

Event
An event is a type of outcome. In the same example of being asked to pick a number between 1 and 5, a possible event would be that an odd number is picked. There are three odd numbers (1, 3, 5) and two even numbers (2, 4) in this example, so the event of an odd number being picked has a higher probability than the event of an even number being chosen.

Determining the sum of two or more rolls requires us to add two or more dice together. For most numbers, there are several ways of achieving the same sum. For example, a 7 can be achieved by adding 1 and 6, 2 and 5, or 3 and 4.

What’s lying beneath the event of the sum, therefore, is a group of outcomes. The first die may show a 1, the second a 6. For our purposes here, we can express this outcome as 1+6. As I mentioned before, all possible outcomes of the combined roll have the exact same probability, so a 1+6 is as probable as a 1+1. The important part about this is realizing that 1+6 is a different outcome than 6+1, even though both show a 1 and a 6 and result in a sum of 7.

Think of yourself and a friend rolling a die each. Your goal is to come up with a sum of 7. When you roll your die, any number from 1 to 6 may come up. If it’s a 1, your friend has to roll a 6 to achieve the sum of 7. If it’s a 6, however, he has to roll a 1 for the same goal sum. Those are two different ways of achieving the same result, even though a 1 and a 6 are involved in both ways.

Next time we’ll start talking about specific ways to figure out probabilities for outcomes and events.

06.22.08

What Are the Odds?

Posted in Game Design, Gameplay at 10:19 am by Christian

I always liked looking at probabilities; they can be like a puzzle or riddle, when you’re trying to figure out how they work out in relation to a particular mechanic.  So a couple of years ago, I started writing a little book on probabilities for gamers and game designers.  I never finished everything about it that I wanted to, but I’ve got a couple of sections in there that people might find useful.

I figure I might as well post them here, with a little cleaning up.  I’ll leave out the introduction and stuff because I’ll just assume, for the sake of this blog, that I don’t need to explain things like the xDy method of writing about specific numbers and types of dice :)

So, expect a couple of little posts about probabilities in the near future. I’ll try to ease up on my academic braindamage and make them sound more approachable this time around (unlike one or two of my essays below :) .

06.18.08

[Children of Ra] Introduction

Posted in My Games at 8:23 pm by Christian

Lisa and my next joint project is Children of Ra, a dramatic storytelling game set in Mythic Ancient Egypt.  I’ve been working on the mechanics for a while now, and I’m still making significant changes to even the basic structure of the game.

It’s going to be substantially different from Beast Hunters in many ways: in the playstyle it promotes, the way the players are situated to one another, and the role of characters and story for the game.

I might start making some brainstorming posts sometime soon, more to get things out of my head than to say that this is definitely the way the game’s going to be.