Random Number Generators (RNG) Knoxville Game Design August 2019 Levi D. Smith 

Real World RNG • Dice – integer, 1 to 6 • Coin flip – boolean: heads, tails • Magic Eight Ball – boolean: yes, no (sort of) • Draw a card • Spin a wheel • Rock, Paper Scissors 

Random Number Tables • Random numbers published in books • Integers • Point at a number • Remove numbers out of range • Remove doubles 

Quick and Dirty methods • Modulo of system time or frame count for range • Add lower bound • The longer the tick, the less random the value will be • In 6502 NES games • Can increment a variable on every frame • An 8-bit integer rolls over at 256 • Frame variable can be used for a random value between 0 and 256 Random number in bash script 

Unity / C# Examples Coin Flip Rock, Paper, Scissors Dice Roll 

Unity / C# - Draw Cards from a Deck • Create List of Card objects (Suit, Rank) • Two approaches • Shuffle List of Cards • Pick card from random position 

GameMaker GML Examples Dice Roll Coin Flip Rock, Paper, Scissors 

Unreal Blueprints Examples Dice Roll Coin Flip 

Seeds • Used for generating the same set of random numbers • Good for testing • Could be used for multiplayer game • Seed is generated on the server and sent to all players • Each player gets the same series of random items 

Bag method • Seven items are randomized then dealt • After the “bag” is empty, another seven items are randomized and dealt • Prevents runs of same item occurring • Although, an item could appear twice consecutively if it was last in one bag and first in the next bag • https://tetris.fandom.com/wiki/Random_Generator 

Bag example Completely Random Using Bag Method 

Bag Method Code Each time Get Piece is clicked, a random number (0 through 6) is drawn from the bag and added to the list If the bag is empty, then it is refilled with integers (0 through 6) 

Probability • Two dice • Probability of rolling 12 • [6, 6] = 1 outcome • 36 total outcomes • 1 / (6 * 6) = 1 / 36 = 2.78% • Probability of rolling 7 • [1,6] [2,5] [3,4] [4,3] [5, 2] [6, 1] = 6 outcomes • 6 / (6 * 6) = 1 / 6 = 16.67% 

Combination • How many different combinations of an 8 card hand from a 75 card deck? (each card is unique, order in hand does not matter) • n choose k = n! / k! (n - k)! • 75 choose 8 = 16,781,053,725 • Chance of drawing a specific combination is 1 / 16,781,053,725 or 0.000000006% 

Permutations • Order does matter • P(n, k) = n! / (n – k)! • How many different sequences of first two pieces in Tetris? (bag method) • P(7, 2) = 7! / (7 – 2)! = 7! / 5! = 5040 / 120 = 42 • or 7*6*5*4*3*2*1 / 5*4*3*2*1 = 7 * 6 = 42 • no bag = 72 = 7 * 7 = 49 • How many different sequences of first five pieces in Tetris? (bag method) • P(7, 5) = 7! / (7 – 5)! = 7! / 2! = 5040 / 2 = 2520 • or 7*6*5*4*3*2*1 / 2*1 = 7 * 6 * 5 * 4 * 3 = 2,520 • no bag = 75 = 7 * 7 * 7 * 7 * 7 = 16,807