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.
Probability Using 2 DiceProbability Using 2 Dice
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.
Probability Using 2 DiceProbability Using 2 Dice
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
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Racing Game With Two Racing Game With Two DiceDice
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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
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Spinner AgainSpinner Again
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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
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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
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Crazy ChoiceCrazy Choice
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Experimental ProbabilityExperimental Probability
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Probability of Pulling Marbles Out Probability of Pulling Marbles Out of a Bagof a Bag
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Two ColorsTwo Colors
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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
Community Chest 2.3661 27
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
Community Chest 1.8849 37
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
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