Probability of casino games

“Vegas wasn’t built by winners”

Roulette (Number wheel) Roulette is a number wheel game where players try to predict the outcome of each trial. A number wheel is spun in one direction, while a small ivory ball is sent rolling in the opposite direction. Once the ball slows down, it will end up in one of 38 pockets.

Roulette wheel The Roulette wheel has 38 pockets with the numbers 1-36, plus 0 and 00. Not in numerical order The numbers 1-36 have either a red(18) or black(18) background 0 and 00 have a green background

Roulette table The table is where players place their bets by putting chips down on the number or spot that they predict will win There are numerous bets to choose from in Roulette

ODDs 1 38 What is the probability of 00 coming up? Meaning: in 38 spins it is expected that 00 would come up 1 time 1 38 Number of times casino pays out for this number of turns

Casino wins!! Betting $1 on 00 Winning pays out 35 to 1 (35x bet) So….38 bets of $1 should win $35 plus $1 bet Casino gains $2

Calculating odds 1 38 Player gets $36, but it costs $38 Cost to Player = number of bets x bet amount 38 x $1 = $38 Casino income Player wins = odds x bet 1 x 35 x $1 = $35 Casino pays out Player gets winning bet returned $1 Casino returns bet Player gets $36, but it costs $38

Hot Streak Roulette tables also have a screen showing the outcome of the last 10- 15 spins Allows superstitious players to pick number that haven’t come up in a while Gambler’s Fallacy

Craps (dice) Craps is a dice game where players try to predict the outcome of a roll of dice

Craps There are lots of bets possible, both single roll and multiple roll bets.

Craps Players bet on (Pass Line) or against (Don’t Pass) the come- out roll. Pass Line wins with a roll of either 7 or 11, and loses (crapping out) with 2, 3, or 12 If a 4, 5, 6, 8, 9, or 10 come up, then that becomes the “point”.

Craps If a 4, 5, 6, 8, 9, or 10 come up, then that becomes the “point”. If the point is then rolled again before a 7, the Pass Line bet wins If a 7 is rolled before the point, the Pass Line bet loses

Single Roll bets Players can make many different bets on a single roll of the dice Proposition bets

keno Keno is a number game where players try to predict numbers drawn at random Similar to the lottery 20 numbers are drawn from the numbers 1-80

keno Players can choose from 2 to 10 numbers. The number the player gets right, called a “catch”, compared to the number selected, determines the payout. Payouts vary by casino Example: If a player chooses 2 numbers and get both correct they could win 14x their bet If a player chooses 4 numbers and get all correct they could win 100x their bet

Lottery Powerball Players choose 5 numbers between 1-69, then choose a 6th number from 1-26

baccarat Baccarat is a card game where players try to predict which of 2 hands (either the “player” or banker) will have a better score.

baccarat In Baccarat, Aces count as 1, and 10’s and face cards count as 0. The player and banker hand are each dealt 2 cards. If either the player or banker hands add up to 8 or 9, the game is over Otherwise they draw a card according to specific drawing rules

baccarat When adding the card values together, the first digit of a 2-digit number is always dropped For Example: If a hand is a 6 and a 7, the sum of the hand is 13, but the 1 is dropped, leaving a score of 3

baccarat If either the player or banker hands add up to 8 or 9, the game is over. Higher score wins. If the player hand adds to 6 or 7 the player stays (doesn’t draw). If the player hand adds to 5 or less, then the player draws a card. The banker hand draws a card based on the banker hand score and what the player’s third card was.

blackjack Blackjack is a card game where players try to get their hand of cards to add up to more than the dealers hand, without going over 21 Also called 21

Blackjack Each player and the dealer are dealt 2 cards Usually all cards are face up except for one of the dealer’s cards Aces count as either 1 or 11, all face cards count as 10 Each player chooses whether they want to draw another card (hit) or not (stay) Going over 21 is called busting and is an automatic loss

Blackjack After all the players have chosen, the dealer reveals their cards and draws according to specific rules A Blackjack is a hand with an ace and 10 or face card Payout is 1.5x bet

poker Poker is a card game where players try to gain a 5-card hand with a higher rank than all the other players. Player versus Player

poker There are many variations to the game of Poker Straight Stud Player is dealt a complete hand Stud Some cards are face up and some are face down Draw Players can discard and draw more cards Community Player is dealt some cards and more are dealt face up to the table

poker Ranking of the hands Straight Flush (numeric order all in same suit) Four of a kind Full House (Three of a kind and a pair) Flush (all same suit) Straight (numeric order) Three of a Kind Two pairs One pair High card

Playing Cards