mathematics of probability
reduces unknown values to known risk values, increasing the overall certainty of the game.
basic dice probability
take for example the standard equal-weighted, six-sided die. each outcome has a one-sixth chance of occurring.
qualities of basic outcomes
all basic outcomes are equally likely. the process always produces one of the basic outcomes. the probabilities of all basic outcomes add up to one.
combined outcomes
combined outcomes are a result that puts together more than one basic outcome. to determine a combined outcome, add the basic outcomes.
ex. the possibility of getting an even number on a standard die
- die = {1, 2, 3, 4, 5, 6}
- even sides only = {2, 4, 6}
- 1/6 + 1/6 + 1/6 = 3/6 = 50%
rolling two dice
with two dice, the notation for the basic outcomes is d1~d2. for example if the first dice rolled a three and the second dice rolled a four, the notation would be 3~4.
in the case of two equal-weighted, six-sided dice, there are thirty-six different possible outcomes. this number is found by multiplying the two possibilities together. the chance of any one outcome appearing is one-thirty-sixth.
ex. no. 1: the chance of rolling a five with two equal-weighted, six-sided dice.
- gather all basic outcomes:
1~4, 2~3, 3~2, 4~1 - add up their probabilities:
1/36 + 1/36 + 1/36 + 1/36 = 4/36 = 1/9 = 11.11%
ex. no. 2: the chance of rolling doubles with two equal-weighted, six-sided dice.
- gather all basic outcomes:
1~1, 2~2, 3~3, 4~4, 5~5, 6~6 - add up their probabilities:
1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 6/36 = 1/6 = 16.67%
importance of probability
when designing a game that involves random number generation, it is important to understand the basic principles of probability. math alone will not lead to meaningful play.
the game designer must design the board and the use of dice to achieve appropriate pacing of the events in the game.