probability in games

Probability in Probability in GamesGames

What is 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.

Types of Probability in Types of Probability in GamesGames

DiceDice SpinnerSpinner Number of objectsNumber of objects Size of objectsSize of objects Speed of objectsSpeed of objects

Kinds of DiceKinds of Dice

Probability Using 2 DiceProbability Using 2 Dice

FirstFirst, assume each die , assume each die is a cube with 6 equal is a cube with 6 equal sides.sides.

SecondSecond, assume each , assume each die has numbers 1-6. die has numbers 1-6. Opposite numbers on Opposite numbers on the die always equal 7.the die always equal 7.


This table shows all of the possible outcomes of rolling 2 dice. In the top

row, one die is a 1 and the other squares shows the possible outcomes of the other

die. Notice that it is possible to have squares with the same values, but in

different orders.


Next, find the sum of the two dice in each square. What we are looking for is the number of times the SUM of both dice occurs.

Probability Using 2 DiceProbability Using 2 DiceX is equal to the value in each cell of the previous table. Count is the number of occurrences (times or likelihood) of that sum. Find the sum of all the counts – which in this case is 36. In the right column is the probability of the outcome and it is calculated by dividing the individual count by the total count. For example, the likelihood of rolling two dice and getting a total of 7 is 6 times out of 36 events or 1 in 6.

Dice in RPG GamesDice in RPG Games• Dungeons & Dragons is credited with popularizing the use of dice in RPG’s. • RPG’s use dice to determine the outcome of events, such as the success or failure• This is considered a fairer decision since success or failure are decided randomly • Games typically determine success as either a total on one or more dice above or below a target number, or a certain number of rolls above a certain number. • Dice can also be used by a game master for other purposes, such as to randomly generate game content or to make arbitrary decisions. • Some games use dice to determine what attributes the player's character has when created

Dice TableDice Table

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Racing Game With One Racing Game With One DieDie


Racing Game With Two Racing Game With Two DiceDice


Spinner use in GamesSpinner use in Games

Spinners are a good choice for small Spinners are a good choice for small children. They are easy to understand. children. They are easy to understand. Dice are a choking hazard for small Dice are a choking hazard for small children who love to put things into their children who love to put things into their mouth.mouth.

Spinners are not always constructed well.Spinners are not always constructed well. Spinners do not often spin “true”.Spinners do not often spin “true”. Players can change the effort they put Players can change the effort they put

into their spin and change the outcomes.into their spin and change the outcomes.

Spinner ProbabilitySpinner Probability

The number of choices The number of choices on the wheel changes on the wheel changes the percentage of the percentage of outcomes.outcomes.

The size of individual The size of individual choices on the wheel choices on the wheel will change the will change the percentage of percentage of outcomes.outcomes.

SpinnerSpinner


Spinner AgainSpinner Again


Probability of Multiple Probability of Multiple ChoiceChoice

There was a TV There was a TV game called “Lets game called “Lets Make a Deal”.Make a Deal”.

Contestants had to Contestants had to chose between 3 chose between 3 different doors.different doors.

Behind one of the Behind one of the doors was a great doors was a great prize.prize.

Usually, there was Usually, there was a “clunker” behind a “clunker” behind one of the doors.one of the doors.

Number of DoorsNumber of Doors


Coin Toss ProbabilityCoin Toss Probability

Probability of heads or tails when Flipping 1 coin.

Probability of unordered pairs when flipping 2 coins.

Probability of ordered pairs when flipping 2 coins.

Coin Flip ProbabilityCoin Flip Probability

Coin TossCoin Toss


Crazy ChoiceCrazy Choice


Experimental ProbabilityExperimental Probability


Probability of Pulling Marbles Out Probability of Pulling Marbles Out of a Bagof a Bag


Two ColorsTwo Colors


Probability in MonopolyProbability in Monopoly

The probability of landing on a

specific property in Monopoly is a factor of the

probability of the dice, the location of the property on the

board, the randomness of

Community Chest and Chance cards,

and if players pay to get out of jail.

Name Probability Rank

In Jail 3.9499 1

Illinois Avenue 3.1858 2

Go 3.0961 3

New York Avenue 3.0852 4

B & O Railroad 3.0659 5

Reading Railroad 2.9631 6

Tennessee Avenue 2.9356 7

Pennsylvania Railroad 2.92 8

Free Parking 2.8836 9

Kentucky Avenue 2.8358 10

Water Works 2.8074 11

St. James Place 2.7924 12

Indiana Avenue 2.7357 13

Atlantic Avenue 2.7072 14

St. Charles Place 2.7017 15

Ventnor Avenue 2.6789 16

Pacific Avenue 2.6774 17

Boardwalk 2.626 18

North Carolina Avenue 2.6252 19

Electric Company 2.604 20

Community Chest 2.5945 21

Marvin Gardens 2.5861 22

Pennsylvania Avenue 2.5006 23

Virginia Avenue 2.4649 24

Short Line 2.4326 25

States Avenue 2.3721 26


Income Tax 2.3285 28

Vermont Avenue 2.321 29

Connecticut Avenue 2.3003 30

Visiting Jail 2.2695 31

Oriental Avenue 2.2621 32

Park Place 2.1864 33

Luxury Tax 2.1799 34

Baltic Avenue 2.1624 35

Mediterranean Avenue 2.1314 36


Chance 1.048 38

Chance 0.8669 39

Chance 0.865 40

Go To Jail 0 41

Players tend to pay to get out of jail early in the game when there is property to buy. This increases their

chances of purchasing property.

Players tend to stay in jail longer after much of the property has been developed to avoid landing on opponents’

property. It’s safe in jail. This changes the probability dynamics of the game.

These numbers represent the amount of money you will earn or pay out every time you roll. For example: There are 40 squares on the Monopoly board and the average amount on a typical roll of the dice is “7”. If

you divide 40 by 7 you will get about 6. Take the $200 for passing Go and divide by 6 turns and you will get $33.78 for every roll taken in the game.

Taking into account the amount you pay on taxes, you will earn $29.81 for every turn you take throughout

the game.

Conclusions on Conclusions on MonopolyMonopoly Railroads are excellent investments, particularly Railroads are excellent investments, particularly

when owned together.when owned together. The best return on investment is from putting a The best return on investment is from putting a

third house on New York Avenue. It has the third house on New York Avenue. It has the fastest payoff of any building on almost all of the fastest payoff of any building on almost all of the properties. properties.

The square most landed on other than Jail is The square most landed on other than Jail is Illinois Avenue, a hotel there will bring the most Illinois Avenue, a hotel there will bring the most income other than a hotel on Boardwalk. income other than a hotel on Boardwalk.

The worst investment is to buy Mediterranean The worst investment is to buy Mediterranean Avenue without first owning Baltic Avenue.Avenue without first owning Baltic Avenue.

The properties between the Jail square and the The properties between the Jail square and the Go To Jail square are landed on the most, because Go To Jail square are landed on the most, because of the jump caused by landing on Go To Jail. of the jump caused by landing on Go To Jail.

The Orange ones have the biggest bang for the The Orange ones have the biggest bang for the buck as far as building goes. buck as far as building goes.

Be sure to draw the right Be sure to draw the right conclusion!conclusion!

Probability of Being Dealt a Probability of Being Dealt a Poker HandPoker Hand

5 card deal5 card deal

5/52 X 4/51 X 3/50 X 2/49 X 1/48 = 1/2,598,960The first fraction is the chance of getting any one of 5 particular cards in the deck (5 in 52, since there are 52 cards in the poker deck). The second fraction is your chance of getting any one of 4 particular cards in the deck on your second card, and so on through the fifth fraction or the fifth card. By multiplying them together you find out what the chances are of coming up with any hand of unique cards. The numerator of our fraction in this case represents our royal flush in spades, while the denominator represents all the combinations possible.

Probability of Being Dealt a Probability of Being Dealt a Poker HandPoker Hand

5 card deal5 card dealPoker Hand Number of Combinations Probability--------------------------------------------------------Royal Straight Flush 4 .0000015391Other Straight Flush 36 .0000138517Four of a kind 624 .0002400960Full House 3,744 .0014405762Flush 5,108 .0019654015Straight 10,200 .0039246468Three of a kind 54,912 .0211284514Two Pairs 123,552 .0475390156One Pair 1,098,240 .4225690276High card only 1,302,540 .5011773940

Total 2,598,960 1.0000000000

5/52 X 4/51 X 3/50 X 2/49 X 1/48 = 1/2,598,960

Batting AveragesBatting AveragesYour favorite baseball player is batting 300. What does this mean?

A batting average involves calculating the probability of a player's getting a hit. The sample space is the total number of at-bats a player has had, not including walks. A hit is a favorable outcome. Thus if in 10 at-bats a player gets 3 hits, his or her batting average is 3/10 or 30%. For baseball stats we multiply all the percentages by 10, so a 30% probability translates to a 300 batting average.

Batting AveragesBatting Averages

Career Records

Career Leaders & Records for Batting Average

probability in games

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