# Combinatorics 3 poker hands and Some general probability

Save this PDF as:

Size: px
Start display at page:

## Transcription

1

2 Combinatorics 3 poker hands and Some general probability

3 Play cards 13 ranks Heart 4 Suits Spade Diamond Club Total: 4X13=52 cards

4 You pick one card from a shuffled deck. What is the probability that it is the Ace of Spades? 1/52 You pick one card from a shuffled deck. What is the probability that it is a spade or a diamond? 2/4 = 1/2 You pick one card from a shuffled deck. What is the probability that it's rank is higher than 5? Assuming that Ace is the highest we get 9/13

5 Basic Poker Rules 1. Each player has two private cards 2. There are 5 shared cards 3. A hand is 5 cards 4. Hand with highest rank wins High Rank = Low Probability

6 The rank of hands in poker

7 The basic rules of texas hold'm poker 1. Each player is dealt 2 cards (the hole) 2. A round of betting 3. Three cards are revealed (the flop) 4. A round of betting 5. Fourth card is revealed (the turn) 6. A round of betting 7. Fifth card is revealed (the river) 8. Final round of betting

8 Betting rounds 1. Proceed clockwise. 2. Bets start with a minimal amount and can only increase 3. Each person has to either: - Check: Match the current bet. - Raise: bet a larger amount - fold: quit the game (losing the money already put in) 4. A round of betting repeats circling until a round where all players either checked or folded = a round in which the bet has not increased. 5. In the final round: - if only one player remains, they win all of the bets (the pot). - if more than one player is checked, there is a "showdown", the checked players show their cards and the one with the stronger hand wins.

9

10 Poker is a game of talent, not of chance Each player tries to estimate the chances that theirs is a winning hand from the revealed cards and from the betting actions of the others. At the high levels of the game, familiarity with the betting styles of other players is critical. Winning or losing a single game is of little importance, it is the long term average that matters. Curious? Check out program about Annie Duke: Radiolab/Dealing with doubt At a minimum, a player has to have an intuitive knowledge of the probabilities of different hands. Which is what we will now do.

11 Calculating the probabilities of different hands What is the sample space? The sets of 5 cards out of 52. Order does not matter C(52,5) = 2,598,960

12 1 choice for the card ranks 4 choices for the suit Prob = 4/C(52,5)

13 How many choices for the ranks? the Ace can be added on either side 9 choices for the card ranks (can't be royal) 4 choices for the suit Prob = 4*9/C(52,5)=36/C(52,5)

14 Number of choices for the rank of the 4 cards? 13 choices for the rank of the single? 12 choices for the suit of the single? 4 Prob = (13*12*4)/C(52,5)=624/C(52,5)

15 Number of choices for the rank of the triple: 13 Number of choices for the rank of the pair: 12 Number of choices for the suits of the triple: C(4,3)=4 Number of choices for the suits of the pair : C(4,2) Prob = (13*12*C(4,3)*C(4,2))/C(52,5) = 3744/C(52,5)

16 Number of choices for the ranks of the cards? C(13,5) choices for the suit of the cards? 4 Prob = (C(13,5)*4)/C(52,5)=5148/C(52,5)

17 Number of choices for the ranks of the cards? (excluding straight flush and royal flush) C(13,5)-10 choices for the suit of the cards? 4 Prob = (C(13,5)*4)/C(52,5)=5148/C(52,5)

18 How many choices for the card ranks? 10 How many choices for the card suits (cannot be royal flush or straight flush)? 4^5-4 Prob = 10*(4^5-4)/C(52,5)=10,200/C(52,5)

19 Number of choices for the rank of the triple: 13 Number of choices for the suits of the triple: C(4,3)=4 Number of choices for the ranks of the other 2 cards: C(12,2) Number of choices for the suits of the other 2 cards: 4*4 Prob = (13*4*C(12,2)*4*4)/C(52,5) = 54,912/C(52,5)

20 Unlike full house (2,3) the two pairs are indistinguishable Number of choices for the ranks of the pairs? C(13,2) Number of choices for the rank of the single: 11 Number of choices for the suits of the pairs: C(4,2)^2 Number of choices for the suit of the single: 4 Prob = (C(13,2)*11*(C(4,2)^2)*4)/C(52,5) = 123,552/C(52,5)

21 The lowest ranked hand = The hand with highest probability Number of choices for the pair: 13*C(4,2) The other 3 cards must not form a pair, else the hand will be two pairs or full house. Number of possible ranks for the 3 cards: C(12,3) Number of possible suites for the 3 cards: 4**3 Prob= (13*C(4,2)*C(12,3)*4**3)/C(52,5) = 1,098,240/C(52,5)

22

23 Counting probability distributions Until now, we considered finite outcome spaces where all outcomes the same probability. All events have rational probabilities: n/m In general, probabilities can be irrational.

24 Properties of general probability distributions every event has probability between 0 and 1. The outcome space has probability 1. The probability of a union is at most the sum of the probabilities The probability of a union of disjoint sets is equal to the sum of the probabilities Disjoint sets The total probability equation

25 Partitioning a union

26

27 A few simple questions:

28 B General Formula: How about: A A B C

29 For Tue. 1. Finish Week2 homework. 2. Read class notes: - Section 4.5 (Poker) - Chapter 5

30 The total probability equation for (countably) infinite sets Consider the natural numbers: 1,2,3,... Is it possible to define a uniform distribution over them? 1st possibility: 0=P(1)=P(2)=... 2nd possibility: 0<P(1)=P(2)=...

### Texas Hold em. From highest to lowest, the possible five card hands in poker are ranked as follows:

Texas Hold em Poker is one of the most popular card games, especially among betting games. While poker is played in a multitude of variations, Texas Hold em is the version played most often at casinos

### RULES FOR TEXAS HOLD EM POKER

RULES FOR TEXAS HOLD EM POKER DEFINITIONS In these rules Action means a player acting in turn All-in means a player has invested all of his/her remaining chips in the outcome of a hand. His/her wager cannot

### UNDERGROUND TONK LEAGUE

UNDERGROUND TONK LEAGUE WWW.TONKOUT.COM RULES Players are dealt (5) five cards to start. Player to left of dealer has first play. Player must draw a card from the deck or Go For Low. If a player draws

### Ultimate Texas Hold'em features head-to-head play against the player/dealer and an optional bonus bet.

*Uultimate Texas Hold'em is owned, patented and/or copyrighted by ShuffleMaster Inc. Please submit your agreement with Owner authorizing play of Game in your gambling establishment together with any request

### Object of the Game The object of the game is for each player to form a five-card hand that ranks higher than the player-dealer s hand.

*Ultimate Texas Hold em is owned, patented and/or copyrighted by Bally Technologies, Inc. Please note that the Bureau is making the details of this game available to the public as required by subdivision

### Example Hand Say you are dealt the following cards: Suits Suits are ranked in the following order.

Chinese Poker or 13 Card Poker This game is played with 4 players. Each player is dealt 13 cards. The object is to arrange them into 3 groups: one consisting of 3 cards (front hand), and two consisting

### Poker. 10,Jack,Queen,King,Ace. 10, Jack, Queen, King, Ace of the same suit Five consecutive ranks of the same suit that is not a 5,6,7,8,9

Poker Poker is an ideal setting to study probabilities. Computing the probabilities of different will require a variety of approaches. We will not concern ourselves with betting strategies, however. Our

### Champion Poker Texas Hold em

Champion Poker Texas Hold em Procedures & Training For the State of Washington 4054 Dean Martin Drive, Las Vegas, Nevada 89103 1 Procedures & Training Guidelines for Champion Poker PLAYING THE GAME Champion

### The cloth covering a Three Card Poker 6 Card Bonus table (the layout) shall have wagering areas for eight players.

*Three Card Poker 6 Card Bonus is owned, patented and/or copyrighted by SHFL Entertainment, Inc. Please submit your agreement with Owner authorizing play of Game in your gambling establishment together

### Probabilities of Poker Hands with Variations

Probabilities of Poker Hands with Variations Jeff Duda Acknowledgements: Brian Alspach and Yiu Poon for providing a means to check my numbers Poker is one of the many games involving the use of a 52-card

### Example Hand. Suits Suits are ranked in the following order. Suits Spade (highest rank)

Chinese Poker or 13 Card Poker There are 3 or 4 players (3 in Double Combo variation, 4 in all other variations). Each player is dealt 13 cards. The object is to arrange them into 3 groups: one consisting

### 1 Bet Threat Texas Hold Em Gaming Equipment Rules of the Games Temporary Amendments: N.J.A.C. 19:40-1.2; and 19:46-1.17, 1.18 and 1.

1 Bet Threat Texas Hold Em Gaming Equipment Rules of the Games Temporary Amendments: N.J.A.C. 19:40-1.2; and 19:46-1.17, 1.18 and 1.19 Temporary New Rules: N.J.A.C. 19:46-1.13X and 19:47-35 Authority:

### Slots... 1. seven card stud...22

GAMING GUIDE table of contents Slots... 1 Blackjack...3 Lucky Ladies...5 Craps...7 Roulette... 13 Three Card Poker... 15 Four Card Poker... 17 Texas Hold em Bonus Poker... 18 omaha Poker... 21 seven card

### BAD BEAT. Bad Beat will reset at \$10,000 with a qualifier of four deuces beaten. Every Monday at 6:00 AM the Bad Beat will increase by \$10,000.

BAD BEAT Bad Beat will reset at \$10,000 with a qualifier of four deuces beaten. Every Monday at 6:00 AM the Bad Beat will increase by \$10,000. OFFICIAL RULES Horseshoe may change or cancel this promotion

### on a table having positions for six players on one side of the table 1. A true to scale rendering and a color photograph of the

Full text of the proposal follows (additions indicated in boldface thus; deletions indicated in brackets [thus]): 13:69E 1.13M Boston 5 stud poker table; boston 7 stud poker table; physical characteristics

### 2016 POKER TOURNAMENT CONTEST RULES

2016 POKER TOURNAMENT CONTEST RULES SECTION 1 Code of Conduct: Temple Etz Chaim will attempt to maintain a pleasant environment for all players, staff and volunteers, but is not responsible for the conduct

### Casino Control (3 Card Poker) Approval 2006 (No 1)

Australian Capital Territory Casino Control (3 Card Poker) Approval 2006 (No 1) Notifiable Instrument NI2006 481 made under the Casino Control Act 2006, section 96 (Rules for Authorised Games). 1 Name

### How to Play Blackjack Alex Powell, Jayden Dodson, Triston Williams, Michael DuVall University of North Texas TECM 1700 10/27/2014

How to Play Blackjack Alex Powell, Jayden Dodson, Triston Williams, Michael DuVall University of North Texas TECM 1700 10/27/2014 Blackjack Blackjack is a fun game that can be played either for money at

### THREE CARD BRAG (FLASH)

THREE CARD BRAG (FLASH) Introduction Three Card Brag is a gambling game played with a standard 52 card pack without jokers. The cards in each suit rank in the usual order from high to low: A-K-Q-J-10-9-8-7-6-5-4-3-2.

### GAME DESCRIPTION AND RULES HOLD'EM

GAME DESCRIPTION AND RULES HOLD'EM Hold'Em uses a flat disc called a dealer button to indicate the player in the dealer position for that hand (even though the game is actually dealt by a non-playing casino

### LECTURE 3. Probability Computations

LECTURE 3 Probability Computations Pg. 67, #42 is one of the hardest problems in the course. The answer is a simple fraction there should be a simple way to do it. I don t know a simple way I used the

### Source. http://en.wikipedia.org/wiki/poker

AI of poker game 1 C H U N F U N G L E E 1 0 5 4 3 0 4 6 1 C S E 3 5 2 A R T I F I C I A L I N T E L L I G E N C E P R O. A N I T A W A S I L E W S K A Source CAWSEY, ALISON. THE ESSENCE OF ARTIFICAL INTELLIGENCE.

### How to Play. Player vs. Dealer

How to Play You receive five cards to make your best four-card poker hand. A four-card Straight is a Straight, a four-card Flush is a Flush, etc. Player vs. Dealer Make equal bets on the Ante and Super

### The game also features three optional bonus bets.

Type of Game The game of Commission Free Fortune Gow Poker utilizes a player-dealer position and is a California game. The player-dealer shall collect all losing wagers, pay all winning wagers, and may

### CS 341 Software Design Homework 5 Identifying Classes, UML Diagrams Due: Oct. 22, 11:30 PM

CS 341 Software Design Homework 5 Identifying Classes, UML Diagrams Due: Oct. 22, 11:30 PM Objectives To gain experience doing object-oriented design To gain experience developing UML diagrams A Word about

### Poker Probability from Wikipedia. Frequency of 5-card poker hands 36 0.00139% 0.00154% 72,192.33 : 1

Poker Probability from Wikipedia Frequency of 5-card poker hands The following enumerates the frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement.

### Mathematical Analysis Of Packs Poker. September 22, 2014. Prepared For John Feola New Vision Gaming 5 Samuel Phelps Way North Reading, MA 01864

Mathematical Analysis Of Packs Poker September 22, 2014 Prepared For John Feola New Vision Gaming 5 Samuel Phelps Way North Reading, MA 01864 Office: 978 664-1515 Fax: 978-664 - 5117 www.newvisiongaming.com

Baccarat Gold 1 Copyright 2007 Dolchee, LLC. All rights reserved. SUMMARY OF GAME The object of the game is to assemble two hands of two or three cards with a point value as close to nine as possible.

### Know it all. Table Gaming Guide

Know it all. Table Gaming Guide Winners wanted. Have fun winning at all of your favorite games: Blackjack, Craps, Mini Baccarat, Roulette and the newest slots. Add in seven mouthwatering dining options

### Training Manual. Shuffle Master Gaming Three Card Poker Training Manual R20020325

Training Manual 2001 Shuffle Master, Inc. First Printing All Rights Reserved Printed in the United States of America No part of this publication may be reproduced or distributed in any form or by any means,

### Terms and Conditions for Charitable Texas Hold em Poker Tournaments

Terms and Conditions for Tournaments Under subsection 34(2) of the Gaming Control Act, a license is subject to terms and conditions as may be imposed by the Registrar. These are the terms and conditions

### RULES FOR PLAY TEXAS HOLD EM

RULES FOR PLAY TEXAS HOLD EM The player to the left of the dealer s button places the small blind which will be a stipulated amount. The player seated second from the dealer s left places the big blind

### Introduction to Discrete Probability. Terminology. Probability definition. 22c:19, section 6.x Hantao Zhang

Introduction to Discrete Probability 22c:19, section 6.x Hantao Zhang 1 Terminology Experiment A repeatable procedure that yields one of a given set of outcomes Rolling a die, for example Sample space

### In this variation of Poker, a player s cards are hidden until showdown. Prior to receiving cards, you must place an initial wager known as an ante.

1 POKER Poker is one of the most skilful and fascinating games ever devised, offering players a chance to test their skills against other players rather than the house (casino). Poker is as much a game

### Artificial Intelligence Beating Human Opponents in Poker

Artificial Intelligence Beating Human Opponents in Poker Stephen Bozak University of Rochester Independent Research Project May 8, 26 Abstract In the popular Poker game, Texas Hold Em, there are never

### 1. Shuffling Machine: Cards used to play Casino War shall be dealt from an automatic card shuffling device ( shuffler ).

*Casino War is owned, patented and/or copyrighted by SHFL Entertainment, Inc. Please submit your agreement with Owner authorizing play of Game in your gambling establishment together with any request for

### FOUR CARD POKER EXPERIENCEEVERYTHING. 24/7 ACTION SilverReefCasino.com (866) 383-0777

FOUR CARD POKER Four Card Poker is a game that rewards skill, patience and nerve. It is similar to Three Card poker but with one major difference. In Three Card Poker, the play wager must equal the ante;

### SPANISH 21. 3. Player blackjack always beats a dealer blackjack and is paid 3 to 2.

SPANISH 21 Spanish 21 is standard blackjack with optional bonus wagers. All rules pertaining to blackjack as posted on the WSGC website will remain the same and are not altered in this game except as noted

### PLACE BETS (E) win each time a number is thrown and lose if the dice ODDS AND LAYS HARDWAYS (F) BUY & LAY BETS (G&H)

craps PASS LINE BET (A) must be rolled again before a 7 to win. If the Point is and the shooter continues to throw the dice until a Point is established and a 7 is rolled before the Point. DON T PASS LINE

### POKER LOTTO LOTTERY GAME CONDITIONS These Game Conditions apply, until amended or revised, to the POKER LOTTO lottery game.

POKER LOTTO LOTTERY GAME CONDITIONS These Game Conditions apply, until amended or revised, to the POKER LOTTO lottery game. 1.0 Rules 1.1 POKER LOTTO is governed by the Rules Respecting Lottery Games of

### Crown Casino. PokerPro Rules

Crown Casino PokerPro Rules RULES OF THE GAME POKERPRO PAGE NO 1 DEFINITIONS...2 2 EQUIPMENT...10 3 THE CARDS...10 4 THE SHUFFLE...13 5 PLACEMENT OF WAGERS...13 6 PERMISSIBLE WAGERS...16 7 COMMISSION OR

### Crown Melbourne Limited ABN Whiteman Street Southbank 3006 Victoria Australia Telephone Facsimile

Crown Melbourne Limited ABN 46 006 973 262 8 Whiteman Street Southbank 3006 Victoria Australia Telephone 61 3 9292 8888 Facsimile 61 3 9292 6874 email: poker@crowncasino.com.au crownpoker.com.au Poker

### Optional 6 Card Bonus Wager In Three Card Poker Gaming Equipment Rules of the Games Proposed Amendments: N.J.A.C. 19:46-1.10A; 19:47-20.1, 20.

Optional 6 Card Bonus Wager In Three Card Poker Gaming Equipment Rules of the Games Proposed Amendments: N.J.A.C. 19:46-1.10A; 19:47-20.1, 20.6, 20.10 and 20.11 Proposed New Rule: N.J.A.C. 19:47-20.12A

### THE 101 CASINO BLACKJACK X with BUSTER BLACKJACK BONUS BET v1.2

THE 101 CASINO BLACKJACK X with BUSTER BLACKJACK BONUS BET v1.2 The 101 Casino 1 Type of Game The game of Blackjack X with Buster Blackjack Bonus Bet v1.2 utilizes a player-dealer position and is a California

### k o G ob in d m n a a G H

Gaming Handbook Welcome to a world of excitement This MGM Grand Detroit Gaming Guide is designed to enhance your gaming fun and total casino experience. The guide provides you with concise, easy-to-understand

### Training Manual. SHFL entertainment Three Card Poker Training Manual 2013.04.10

Training Manual SHFL entertainment Three Card Poker Training Manual 2013.04.10 2001 SHFL entertainment First Printing All Rights Reserved Printed in the United States of America No part of this publication

### Fighting an Almost Perfect Crime

Fighting an Almost Perfect Crime Online Poker Fraud Detection Philipp Schosteritsch, MSc Consultant for Software Development and Technical Advisor on Cyber Security & Privacy Foundation Graz, 2014 Contents

### Casino Gaming Rule 2010

Queensland Office of Liquor and Gaming Regulation Casino Gaming Rule 2010 This Rule is prepared by the Queensland Office of Liquor and Gaming Regulation 2010 V6 1 Queensland Contents Part 1 Preliminary...

### TEXAS HOLD EM POKER FOR SIGHT

Lions Club TEXAS HOLD EM POKER FOR SIGHT Official Rules (April 2016) Buy-in/Rebuy/Add-on: The dollar amount of the initial buy-in shall be posted in plain view of the playing table(s). The buy-in (\$135)

### Playing around with Risks

Playing around with Risks Jurgen Cleuren April 19th 2012 2011 CTG, Inc. Introduction Projects are done in a probabilistic environment Incomplete information Parameters change over time What is true in

### Basic Probability. Probability: The part of Mathematics devoted to quantify uncertainty

AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.

### Lake Elsinore Hotel & Casino 20930 Malaga Road Lake Elsinore, CA 92530

Lake Elsinore Hotel & Casino 20930 Malaga Road Lake Elsinore, CA 92530 HOLD'EM In Hold'em, all players receive two downcards as their personal hand, afler which there is a round of betting. Three boardcards

### During the last several years, poker has grown in popularity. Best Hand Wins: How Poker Is Governed by Chance. Method

Best Hand Wins: How Poker Is Governed by Chance Vincent Berthet During the last several years, poker has grown in popularity so much that some might even say it s become a social phenomenon. Whereas poker

### L TABLE GAMES OPERATIONS PLAN APPENDIX A

L TABLE GAMES OPERATIONS PLAN APPENDIX A 1 Table of Contents Sec Title Page # 1. General...4 2. Black Jack...5 3. Craps...12 4. Roulette...20 5. Poker...26 6. 3-Card Poker with Progressive Jackpot...37

### Quick gaming Guide 1

Quick gaming Guide 1 A quick and easy way to start gaming at any of our tables. For more information visit our websites: www.casino-barcelona.com www.casino-peralada.com www.casino-tarragona.com The information

### Standards of play: Type of gaming table utilized for this game:

*Let It Ride Bonus is owned, patented and/or copyrighted by SHFL Entertainment, Inc. Please submit your agreement with Owner authorizing play of Game in your gambling establishment together with any request

### PENNSYLVANIA GAMING CONTROL BOARD REMAINING TEMPORARY TABLE GAMES REGULATIONS TITLE 58. RECREATION CHAPTERS: 581, 583, 585, 587, 588, 589,

PENNSYLVANIA GAMING CONTROL BOARD REMAINING TEMPORARY TABLE GAMES REGULATIONS TITLE 58. RECREATION CHAPTERS: 581, 583, 585, 587, 588, 589, 590, 591, 592 & 593 THIS DOCUMENT CONTAINS THE REMAINING TEMPORARY

### Mus is the most popular Spanish game, due to its attractiveness and characteristics. This game was born in Basque Country

Mus is the most popular Spanish game, due to its attractiveness and characteristics. This game was born in Basque Country Object of the game The winner of the game is the team who wins three sets. The

### 1. General...3. 2. Black Jack...5. 3. Double Deck Black Jack...13. 4. Free Bet Black Jack...20. 5. Craps...28. 6. Craps Free Craps...

Table of Contents Sec Title Page # 1. General...3 2. Black Jack...5 3. Double Deck Black Jack...13 4. Free Bet Black Jack...20 5. Craps...28 6. Craps Free Craps...36 7. Roulette...43 8. Poker...49 9. 3-Card

### players on one side of the table and a place for the dealer on the opposite side.

13:69E-1.10D Switch Hands table; physical characteristics (a) Switch Hands shall be played at a table having betting positions for no more than six players on one side of the table and a place for the

### The dealer starts the game. Every player gets two cards, faceup.

BLACKJACK Here s a card game where the object is for you to draw cards that total 21 or come closer to 21 than the dealer. All cards count at face value, except for the King, Queen and Jack which count

### Laboratory work in AI: First steps in Poker Playing Agents and Opponent Modeling

Laboratory work in AI: First steps in Poker Playing Agents and Opponent Modeling Avram Golbert 01574669 agolbert@gmail.com Abstract: While Artificial Intelligence research has shown great success in deterministic

### Math 2001 Homework #10 Solutions

Math 00 Homework #0 Solutions. Section.: ab. For each map below, determine the number of southerly paths from point to point. Solution: We just have to use the same process as we did in building Pascal

### cachecreek.com 14455 Highway 16 Brooks, CA 95606 888-77-CACHE

Baccarat was made famous in the United States when a tuxedoed Agent 007 played at the same tables with his arch rivals in many James Bond films. You don t have to wear a tux or worry about spies when playing

### The temporary new rules and amendments authorize casino licensees to. offer a supplemental wager in the game of three card poker known as the three

Progressive Wager and Envy Bonus In Three Card Poker Accounting And Internal Controls Gaming Equipment Rules Of The Game Temporary Amendments: N.J.A.C. 19:45-1.20; 19:46-1.10A; and 19:47-20.1, 20.6, 20.10

### 2013 World Series of Poker Official Dealer Guide. Rio All- Suite Hotel & Casino, Las Vegas, Nevada

2013 World Series of Poker Official Dealer Guide Rio All- Suite Hotel & Casino, Las Vegas, Nevada TABLE OF CONTENTS: GENERAL DEALING PROCEDURES MULTI- TABLE TOURNAMENT PROCEDURES SINGLE TABLE SATELLITE

### Blackjack...5. Craps...8. Roulette... 10. Mini/Midi-Baccarat...11. Pai Gow Poker... 12. Pai Gow... 14. Let It Ride... 16. Three Card Poker...

GAMING GUIDE 2 3 W E L C O M E Blackjack...5 Craps...8 Roulette... 10 Mini/Midi-Baccarat...11 Pai Gow Poker... 12 Pai Gow... 14 Let It Ride... 16 Three Card Poker... 18 Spanish 21...20 Big Six Wheel...22

### MATHEMATICS 154, SPRING 2010 PROBABILITY THEORY Outline #3 (Combinatorics, bridge, poker)

Last modified: February, 00 References: MATHEMATICS 5, SPRING 00 PROBABILITY THEORY Outline # (Combinatorics, bridge, poker) PRP(Probability and Random Processes, by Grimmett and Stirzaker), Section.7.

### The New Mexico Lottery

The New Mexico Lottery 26 February 2014 Lotteries 26 February 2014 1/27 Today we will discuss the various New Mexico Lottery games and look at odds of winning and the expected value of playing the various

### Homework 6 (due November 4, 2009)

Homework 6 (due November 4, 2009 Problem 1. On average, how many independent games of poker are required until a preassigned player is dealt a straight? Here we define a straight to be cards of consecutive

### Progressive Payout Wager In Texas Hold Em Bonus Poker; Link To Caribbean Stud Poker Gaming Equipment Rules of the Games Temporary Amendments:

Progressive Payout Wager In Texas Hold Em Bonus Poker; Link To Caribbean Stud Poker Gaming Equipment Rules of the Games Temporary Amendments: N.J.A.C. 19:45-1.20 and 1.39B; 19:46-1.13G and 1.13Q; and 19:47-16.12,

### 2urbo Blackjack 21.99. 2 9 Hold their face value

2urbo Blackjack Type of Game The game of 2urbo Blackjack utilizes a player-dealer position and is a California game. The player-dealer shall collect all losing wagers, pay all winning wagers, and may not

### Poker Strategies. Joe Pasquale CSE87: UCSD Freshman Seminar on The Science of Casino Games: Theory of Poker Spring 2006

Poker Strategies Joe Pasquale CSE87: UCSD Freshman Seminar on The Science of Casino Games: Theory of Poker Spring 2006 References Getting Started in Hold em, E. Miller excellent beginner book Winning Low

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

STUDENT MODULE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Simone, Paula, and Randy meet in the library every

### Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded

Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded If 5 sprinters compete in a race and the fastest 3 qualify for the relay

TABLE OF CONTENTS poker rule book General Rules 1 Poker Etiquette 1-2 House Policies 2-3 Operating Procedures 4-5 The Buy-In/All-In/Table Stakes 5 Exposed Cards 5-6 Boxed Cards 6 Misdeals 6-7 Uncalled

### Government of Nunavut. Community and Government Services. Consumer Affairs Division

Government of Nunavut Community and Government Services Consumer Affairs Division Terms and Conditions for Texas Hold em Poker Tournaments in Nunavut Table of Contents 1. General Provisions.3 2. Penalties...3

### Bayesian Tutorial (Sheet Updated 20 March)

Bayesian Tutorial (Sheet Updated 20 March) Practice Questions (for discussing in Class) Week starting 21 March 2016 1. What is the probability that the total of two dice will be greater than 8, given that

### The game of roulette is played by throwing a small ball onto a rotating wheel with thirty seven numbered sectors.

LIVE ROULETTE The game of roulette is played by throwing a small ball onto a rotating wheel with thirty seven numbered sectors. The ball stops on one of these sectors. The aim of roulette is to predict

by Teresa Evans Copyright 2005 Teresa Evans. All rights reserved. Permission is given for the making of copies for use in the home or classroom of the purchaser only. SAMPLE PAGES Please enjoy using these

### TEXAS HOLD'EM TEXAS HOLD'EM RULES

TEXAS HOLD'EM In Texas Hold'Em each player receives two uninterruptedcards singly dealt face down as their initial hand. There is a round of betting after these cards have been delivered. Three board cards

### Approved:)12/5/13) Gambling Problem? Call 1-800-GAMBLER

) ) ) Welcome to the Fun! Use this as your guide to all of Mount Airy Casino Resort s gaming. Try your hand at Blackjack, Craps, Roulette, Midi and Mini Baccarat, Poker, Pai Gow Poker, Pai Gow Tiles, Let

### CaLw BLACKJACK NO BUST WITH ELECTRO-MECHANICAL SHUFFLER

CaLw L. A. ' s F R I E N D L I E S T NO BUST BLACKJACK WITH ELECTRO-MECHANICAL SHUFFLER OBJECT OF THE GAME Players compete against a rotating player-dealer to obtain the better hand. There are six player

### The following words and terms, when used in this subchapter, shall have the following meanings unless the context clearly indicates otherwise.

CHAPTER 69E GAMING EQUIPMENT 13:69E-1.10 (a) (u) No Change (v) If a casino licensee offers bet the set blackjack pursuant to N.J.A.C. 13:69F- 2.29, the layout otherwise required by this section shall also

### A UNIQUE COMBINATION OF CHANCE & SKILL

A UNIQUE COMBINATION OF CHANCE & SKILL The popularity of blackjack stems from its unique combination of chance and skill. The object of the game is to form a hand closer to 21 than the dealer without going

### SARTRE: System Overview

SARTRE: System Overview A Case-Based Agent for Two-Player Texas Hold em Jonathan Rubin and Ian Watson Department of Computer Science University of Auckland, New Zealand jrub001@aucklanduni.ac.nz, ian@cs.auckland.ac.nz

### Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19

Expected Value 24 February 2014 Expected Value 24 February 2014 1/19 This week we discuss the notion of expected value and how it applies to probability situations, including the various New Mexico Lottery

### Russell Thomas

From Actuarial Science to Poker Russell Thomas 11.14.2013 1 Agenda Playing poker vs. Being an Actuary Rules of No Limit Texas Hold em Poker skills Conclusions 2 How does Poker relate to being an Actuary?

### What is the probability of throwing a fair die and receiving a six? Introduction to Probability. Basic Concepts

Basic Concepts Introduction to Probability A probability experiment is any experiment whose outcomes relies purely on chance (e.g. throwing a die). It has several possible outcomes, collectively called

Probability Worksheet 2 NAME: Remember to leave your answers as unreduced fractions. We will work with the example of picking poker cards out of a deck. A poker deck contains four suits: diamonds, hearts,

### Conducting Probability Experiments

CHAPTE Conducting Probability Experiments oal Compare probabilities in two experiments. ame. Place a shuffled deck of cards face down.. Turn over the top card.. If the card is an ace, you get points. A

### Poker with a Three Card Deck 1

Poker with a Three Card Deck We start with a three card deck containing one Ace, one King and one Queen. Alice and Bob are each dealt one card at random. There is a pot of \$ P (and we assume P 0). Alice

### Commission-Free. Baccarat Dragon Bonus

Commission-Free Baccarat Dragon Bonus *Commission Free Baccarat is NOT owned, patented and/or copyrighted. *The Dragon Bonus is owned, patented and/or copyrighted by SHFL Entertainment, Inc. Please submit

### LIVE CASINO HOLD EM. Live Casino Hold em five-card poker, world-class quality. As real as it gets BENEFITS AT A GLANCE. www.evolutiongaming.

LIVE CASINO HOLD EM BENEFITS AT A GLANCE FOR OPERATORS: Authentic gameplay and interactive features Incremental profit and maximised player lifetime value Ability to build strong customer relationships

### \$2 4 40 + ( \$1) = 40

THE EXPECTED VALUE FOR THE SUM OF THE DRAWS In the game of Keno there are 80 balls, numbered 1 through 80. On each play, the casino chooses 20 balls at random without replacement. Suppose you bet on the

### This section of the guide describes poker rules for the following cash game types:

Poker Rules What has changed in version 1.2 of the Poker Rules: Rake on games with stakes of 0.02/0.04 was lowered from 2% to 1%. This section of the guide describes poker rules for: Cash Games Tournaments

### Analysis of poker strategies in heads-up poker

BMI paper Analysis of poker strategies in heads-up poker Author: Korik Alons Supervisor: Dr. S. Bhulai VU University Amsterdam Faculty of Sciences Study Business Mathematics and Informatics De Boelelaan

### Homework 3 (due Tuesday, October 13)

Homework (due Tuesday, October 1 Problem 1. Consider an experiment that consists of determining the type of job either blue-collar or white-collar and the political affiliation Republican, Democratic,