Chapter3RouletteandExpectedValue
Roulette has a wheel with 38 sectors . A wheel is spun and a ball is introduced
into the spinning wheel. After a while the ball comes to rest in one of the 38
sectors, which presumably, are all equally likely. Players make
Chapter4Dealingwithinfinity
Notice that, at least in theory, there is no limit to how many rolls can take
place. We might just keep rolling and rolling forever! What is the chance that this
will happen? What is the chance that the experiment will end with
Chapter 6 Random Walks
Here are three problems that arise when you think about gambling:
Problem 1: Suppose you have a bankroll of $100 and decide to repeatedly
play $1 on Black in Roulette until either you go broke, or are ahead $20. What
is the chance t
Chapter 5 Craps
Craps is a mainstay of most casinos. Players stand around a large table and place
bets while one of the players takes a turn throwing a pair of dice. There are a
dizzying array of possible bets suggested by the layout of the table, which i
Chapter 10 Bingo
The game of Bingo has long been used as a fund-raiser for churches and charities.
But it is also played in casinos, especially Native American casinos, as well on on
cruise ships. Each player buys one or more Bingo cards, each for the sam
Madrid 1
Gabriel Madrid
Professor Hoste
Mathematics of Gambling
April 6, 2014
MEGA Millions Paper
The California State Lottery consists of several lottery games and gambling techniques.
Mega Millions is an American multi-jurisdictional lottery game that p
Fantasy Five lottery
How does one play Fantasy Five? In this lottery game, a player chooses five
numbers out of the numbers: 1 to 39. Alternatively, there is a "quick pick" option, which
means that five numbers are randomly generated for the player. One p
Chapter 7 Permutations and Combinations
How many ways are there for 10 people to line up for a group photograph?
Let's start with the last problem which can be rephrased as, How many ways
are there to order n things?" Here, by order we mean exactly the sa
Chapter 8 Poker Hands
Suppose you are dealt five cards at random from a standard deck of 52 playing
cards. What is the chance that you will be dealt four-of-a-kind, or a full-house? We
can figure this out using the formula for n choose k that we developed
Chapter 9 Keno
Keno is a lottery game that is popular in most casinos. To play, you fill out a Keno
card where you mark anywhere from 1 to 20 numbers chosen from 80 numbers. The
cards are often available in the casino restaurants. Keno runners collect the
Chapter2OddsVersusChance
An alternative way to describe the chance that an event will occur is by
talking about the odds for or against the event. This is just an equivalent way of
describing probabilities, but one that is prevalent among gamblers. The id
Chapter 1
Flipping Coins and Rolling Dice
the fact that we will only use numbers between zero and one to represent the
chance of a random event is completely arbitrary, as is the choice that the
probability of an impossible event is zero while the probabi