Games have been an enjoyable pastime for many years. Families and friends have gathered to play board
games, card games and dice games like Yahtzee, Poker, and Monopoly.
The goal of this project is to analyze different classic games for the probability that occurs in them. You
may work alone or with a partner.
Your job:
1. Pick a classic game Blackjack
2. Analyze the probability of different events that can occur in the game. You need to find 5
different probabilities giving a specific example from different aspects of the game. Then
calculate the probability that this event occurs. You need to have one of each: basic probability,
addition, multiplication, permutation and combination.
For example: The game of LIFE.
Basic: We could evaluate probability with the spinner (Probability you spin a 5).
Addition: salary cards (Probability your salary is $125,000 or $250,000).
Multiplication: LIFE tiles (Probability you draw a $100,000 and a $50,000 tile).
Permutations: the number of ways to order 5 people in the car.
Combination: When we played LIFE and had to draw a card for a life event (payday, job,
house) we had a house rule of drawing 3 cards and selecting the one we wanted. How
many combinations of 3 cards can you get from the house cards?
3. Type a report with all of your findings and probability questions and answers that you have
decided to investigate.
4. Be sure to be careful with card games that have draw and discard piles. This impacts your
probabilities as cards are discarded between turns, which then limits the number of possibilities.
Also be sure you are accounting for other players in those situations.
Your project must include:
a. An introduction paragraph explaining the game/rules/cards/dice or whatever is used in the game
b. A paragraph for each probability problem. Be specific with what it is you are finding, how it is
found as well as the final answer. Please remember that a paragraph is roughly 5 sentences. You
need to explain all the numbers and work that lead to get to the answer to the question you posed
in the first sentence.
a. An example Paragraph For the game of Monopoly: What is the probability that I roll
doubles or a sum of 5 on my turn in the game of monopoly? This would be an example of
addition probability with disjoint events as neither of these outcomes can happen at the
same time. That means to find the P(doubles or sum of 5) = P(doubles)+P(sum of 5).
First to find the P(doubles) we know we can roll 1,1; 2,2; 3,3; 4,4; 5,5; or 6,6. This is 6
possibilities out of the total outcomes 36 for rolling two dice. Second to finding P(sum of
5). This can be done by rolling 1,4; 2,3; 3,2; or 4,1 which is 4 possibilities out of 36. This
means that ( doubles or sum of 5) = P(doubles)+P(sum of 5) = 6/36+4/36 = 10/36 = 5/18.
This means there is a 5/18 or about a 28% chance that I will roll doubles or a sum of 5 on
my next turn.
Answer
Black Jack Game Probability
Introduction
The blackjack game entails players trying to score as close to 21 without going over. The game is
played with a standard 52-card deck, and the goal is to beat the dealer by counting cards and
making better bets. The player must have a higher hand (a combination of cards that totals at
least 21) than the dealer to win.
Basic Probability
A basic probability in blackjack is the chance of any given event happening, such as receiving a
card. The odds of that event occurring determine the probabilities of different outcomes. For
example, the odds of receiving a blackjack (an ace and a two) is 6/21 or 3.6%. The odds of
receiving a ten is 1/21 or 0.06%. Another example is that the probability that the next card drawn
will be a ten is 10%. The probability of any other card being drawn is 1-10% (or 0.9%).
Generally, the more cards drawn, the more complex the probability calculation becomes.
Addition Probability
The addition probability is the likelihood that the next card will be of the same value as the
current card. For example, if the current card is an ace, the addition probability is 1.5, which
means that the next card will also be an ace. An example of when this occurs is if the player has a five and an ace, the addition probability would be 1.5, which would mean that the next card
will be a two or a three.
Multiplication Probability
The multiplication probability is the probability that a player will be dealt a certain number of
cards. An example of how this works in practice is as follows: Suppose that a player is dealt two
blackjack cards. The player has a 1 in 21 chance of being dealt this particular combination, and
so on. Therefore, the player is said to have "hit" on this particular hand. However, suppose the
player does not hit. In that case, the player can either keep the cards (in which case the player has
a 0.5 chance of getting another blackjack in future hands) or discard one of the cards and hope to
get a better hand (in which case the player has a 1 in 4.5 chance of getting another blackjack).
Permutations Probability
The permutation probability in a blackjack game is the probability that a certain permutation will
occur during the game. For example, the probability that the Ace of Spades will be the next card
dealt is 1/36, which means that the chance of seeing this particular permutation in a single game
is about 3.6% (1 out of 36). An example of a permutation that would be useful in understanding
the permutation probability is the order of cards dealt. The permutation probability for this
scenario is 1/36, regardless of which card is dealt first.
Combination Probability
The combination probability is the chance that two specific cards will be dealt with in
consecutive order. For example, the probability of being dealt an Ace of Spades and a King of
Clubs in a single hand is 16.6%. The probability can be calculated using the combination
formula: P combination = (16.6%) x (1 + ƒ), Where ƒ is the probability that any two cards will be dealt in consecutive order. In this case, ƒ is 1.6%. Therefore, the combined probability for this
particular pair is 18.4%. An example of the combination probability in action is as follows: A
player is dealt an Ace of Spades and two of Clubs. The combination probability for this hand is
16.6%. Therefore, the probability that one will be dealt a third card (either a two of Spades or a
three of Clubs) is 18.4% – 16.6 % = 3.2%.