Game Art and Design Unit 3 Lesson 4 Probability International Technology Education Association

Big Idea Knowledge of the basic skills and components of any field makes one uniquely prepared to perform at a high level in that area.

Formal Element: Probability

What is Probability? Probability is a branch of mathematics that deals with calculating the likelihood an event will occur and is usually expressed as a number between 1 and 0.

Probability in Games Game designers try to provide players with a new experience each time a game is played. Randomness is built into the mechanics of a game and varies the number and location of obstacles that a player may encounter. Randomness, probability, likelihood, and chance are all terms that describe how variety and unexpected outcomes are created in games.

Probability - Board Games Use dice, spinners, and sand timers to add randomness and conflict. When moves must be made in a limited amount of time or when a move is calculated by the roll of dice, the game experience is made unpredictable.

Probability - Board Games Game designers use probability to plan the randomness that occurs in a game. The probability of rolling any number with a pair of dice helps the game designer plan where to put large payoffs or huge danger zones. In most games, large payouts or huge dangers should occur infrequently.

Probability in Games: Types Dice Spinner Number of objects Size of objects Speed of objects Other

Probability types: DICE

Probability Types: Dice Use goes back thousands of years. Were originally made from joint bones of animals. Later were made from bone, metal, or pottery.

Probability Types: Dice In ancient times, the outcome of a dice throw was not considered luck, but believed to be controlled by the gods. For this reason, casting dice was a way of dividing inheritances. In ancient Rome, the goddess Fortuna (Lady Luck), the daughter of Zeus, was believed to determine the outcome of a throw.

Probability Types: Dice Terminology Use the lowercase “d” preceded by a die count and followed by the number of sides of the dice. For example, 6d8 means six eight-sided dice as shown.

Probability Types: Non-Cubic Dice Tetrahedron (black)- each side has three numbers Octahedron (white)- eight sides 10-sided (green)– face is triangular Multi-sided - up to 20 sides

Probability Types: Using Two Dice First, assume each die is a cube with six equal sides. Second, assume each die has numbers 1-6. Opposite numbers on the die always equal 7.

Do activity 3.31 before you look at the next few slides NO TITLE ON THIS SLIDE Do activity 3.31 before you look at the next few slides

Probability Types: Using Two Dice Table shows all possible outcomes. Notice that it is possible to have squares with the same values, but in different orders. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Probability Using Two Dice Find the sum of the two dice in each square. Look for the number of times the SUM of both dice occurs. 2 3 4 5 6 7 8 9 10 11 12

Probability Types: Using Two Dice x count P(X) 2 1 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 9 10 11 12 X is the possible totals. Count is the number of occurrences for that total. Sum of all the counts = 36. P(X) is the probability of the outcome (dividing individual count by total count). Rolling a 8 is 5 out of 36 times.

Probability Types: Using Two Dice

Probability types: Spinners

Probability Types: Spinners Design and layout of the spinner will affect the frequency of outcomes. Spinners created for small children may use pictures, colors, or symbols instead of numbers. Frequently chosen to be used in games for young children rather than dice because the dice pose a choking hazard.

Probability Types: Spinners Poor construction and the way a player spins can significantly change the outcome. The number and size of choices on the wheel changes the percentage. What is the probability of spinning red?

Probability Types: Spinners The probability of an event is the total number of ways an event can occur divided by the total number of outcomes. P(A) = The number of ways event can occur The total number of possible outcomes

Spinner Probability Do activity 3.32

Probability of Cards

Card Games: Randomness Occurs when players “shuffle” the cards. Affected by how many suits or number of different cards. Players use knowledge of probability to calculate the likelihood that a certain event will occur to plan the next move.

Card Games: Randomness In poker, the value of the various hands increases as the probability of the hand occurring goes down. It is very rare for a player to get a royal flush (ace, king, queen, jack, and 10 all in the same suit).

Card Games: Probability of Poker Hands (Five cards) Poker Hand      Number of Probability Combinations   -------------------------------------------------------- Royal Straight Flush                 4        .0000015391 Other Straight Flush               36         .0000138517 Four of a kind                    624        .0002400960 Full House                      3,744        .0014405762 Flush                           5,108        .0019654015 Straight                       10,200        .0039246468 Three of a kind               54,912        .0211284514 Two Pairs                     123,552         .0475390156 One Pair                    1,098,240         .4225690276 High card only           1,302,540        .5011773940 Total                        2,598,960       1.0000000000

Big Idea Knowledge of the basic skills and components of any field makes one uniquely prepared to perform at a high level in that area.

Game Art and Design Unit 3 Lesson 4 Probability Images student work, photos by Phyllis Jones, and clipart International Technology Education Association