Thursday, March 10, 2016

Dice, Cards, and Probability

Part 1 - Dice, Cards, and Probability - Foundation

This blog post is the first for a possible series of posts concerning dice and card probability. While I do not present any new information, I am posting this so that the basics will be covered.

I plan on looking at d20, d6, d100, and card decks in the future.

What is probability?

Probability is the chance or likelihood that an event or situation will happen or occur.

How do you simulate random occurrence in gaming?

In RPGs, probability and random occurrence is simulated through multiple means, methods, tool, or medium that a random probability is generated, called Random Number Generator (RNG) in computer science. Dice are the most commonly used tool to generate random numbers. Two other popular physical RNGs are a deck of cards and a computer program, app, or website. Coins, rock-paper-scissors, or guessing a number between _ and _ are other less popular methods.

Expressing the probability of single occurrence using notation.

In math, basic probability can be expressed in terms of "how many times occurrences" out of "how many times attempted".

let # = number
let O= # of occurrences
let T= total number of tries

successful O out of total T
"out of" keyword O out of T
Colon O:T
Division notation O/T or O÷T. It's best to simplify fractions.

Since probability can be expressed as a division, you can find a decimal between 0 and 1 by dividing the total number into the number of occurrences.

And that number can be converted into a percentage (%).

An example of expressing the probability of getting 'heads' on a coin flip.

For example: A coin flip is either heads or tails.
The chance of getting heads is one occurrence out of two: either heads or tails.
1 out of 2
To convert the chance of
1/2 or 1 ÷2 = 0.5
0.5=50% chance

Combinations Formula

! = factorial symbol
let n = number of items
let r = number of items being chosen at a time
nCr = n!/r! * (n-r)

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