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A Probabilistic Study of Dice Control in Craps
Golden Arm: A Probabilistic Study of Dice Control in Craps Donald R. Smith Robert Scott III Abstract This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting possible dice control, that in which the four faces on a rotating (horizontal) axis are favored. This is the model that we analyze in this paper. Keywords: craps; dice; dice control; probability Donald R. Smith Associate Professor Department of Management and Decision Sciences Monmouth University [email protected] Robert Scott III Professor Department of Economics, Finance, and Real Estate Monmouth University [email protected] UNLV Gaming Research & Review Journal t Volume 22 Issue 1 29 Wine loved I deeply, dice dearly (William Shakespeare, King Lear, Act 3, Scene 4) Introduction Craps is a unique casino game because the shooter directly affects (i.e., picks up and throws) the gambling instruments (dice). Craps players, more than other casino gamblers, may be the most susceptible to Langer’s (1975) illusion of control where they think they can control the outcome of a random game. -
The Mathematics of Poker: Basic Equity Calculations
- MATHEMATICS AND COMPUTER EDUCATION- THE MATHEMATICS OF POKER: BASIC EQUITY CALCULATIONS AND ESTIMATES Mark Farag Gildart Haase School of Computer Sciences and Engineering Fairleigh Dickinson University 1000 River Road, Mail Stop T-BE2-01 Teaneck, New Jersey 07666 [email protected] INTRODUCTION The game of poker has experienced a worldwide boom in popularity in the past decade. This can be attributed to a confiuence of events: the invention of the "lipstick" camera that allows viewing of players' "hole" (hidden) cards for television broadcasts, the growth of online poker rooms, and the increased popularity of "satellite" events that allow players to win their way into larger-money events. The largest single prize awarded in a poker tournament to date, 12 million US dollars, was won by an amateur player in 2006 [2]. Poker is a game of skill that contains an element of chance; it lies somewhere between chess (pure skill) and roulette (pure luck) in the spectrum of games. Since poker is a game of incomplete information, skilled players often use psychology to help them make correct decisions or to infiuence others to make incorrect decisions. Some situations do arise, however, in which mathematical considerations are paramount. It is the purpose of this article to discuss such situations. Since the first section covers the rules of poker in detail, the subsequent discussion should be of interest and accessible to students with only a basic knowledge of combinatorics and probability. THE RULES Modem poker is played with a standard deck of 52 cards, using cards marked with numbers 2 through 10, J (Jack), Q (Queen), K (King), and A (Ace) to indicate, in increasing order, their respective ranks. -
Poker 101 Poker Rules and Concepts for Our Annual Charity Tournament
Poker 101 Poker Rules and Concepts for our Annual Charity Tournament Adapted from MIT 15.S50 Lecture Brainteasers Problem: • (1) In Poker, what is the best hand to go up against Pocket Aces? (other than the other two Aces?) • (2) The situation: heads up on the turn, but before the river comes out you already know you are guaranteed to lose, regardless of what your opponent has. What are your hole cards, and what is on the board? Brainteaser Solution: • (1) In Poker, what is the best hand to go up against Pocket Aces? (other than the other two Aces?) • AA 77.50% 65s 22.50% • (2) The situation: heads up on the turn, but before the river comes out you already know you are guaranteed to lose, regardless of what your opponent has. What are your hole cards, and what is on the board? • Your hole cards: 22 • Board: any quads (5555) Announcements • Annual Charity Poker Tournament – Saturday, 4/15 • Pitch Perfect: A QFS-USWIB Production • Pitch Workshops: 4/11 and 4/18 at 6:30pm • Deadline: 4/18 • Competition: 4/20 • Registration: http://tinyurl.com/qfsuswib • If you are interested but don’t have a team, email us! Poker Rules Texas Hold ‘Em Overview • Texas Hold'em is a community card poker game, with game play focused as much on the betting as on the cards being played • Texas Holdem is played on a single table with 2 to 9 players • You win a pot by having the best hand, or by having all other players fold before the showdown • The structure of Texas Hold'em can be broken up into three main divisions: 1. -
Jan23-Lecture.Pdf
Introduction to the Theory & Practice of Poker Lecture #8 January 23, 2020 Last night’s tourney • 178 players entered • Lasted 3.5 hours • I did not win a single hand (had one chop) • Final table, please stand up! • Winner: Shehrya Haris • Special note: Qualified in both satellites • Freda Zhou, Sam Lebowitz, Claudia Moncaliano Meta game • Should you ever show your hand? • Simple answer is no • You might be providing more information than you think • If you show a strong hand when someone folds • You eliminate some uncertainty they had about whether you were bluffing • They may more correctly label you as TAG • If you show that you folded a strong hand • Because you are trying to prove how good a player you are • First, you shouldn’t let them know if you are a good player • Second, now you will get bullied by the good players • You don’t want anyone to know that you can make good lay downs • you want them to be afraid to bluff you because they think you’re such a moron that you might always call them. • Advanced move: • The “accidental show your cards on purpose” • Some pros make a living with meta-play • Table talk • Selectively showing to advance a particular image There are 2 rules for success in poker 1. Never reveal everything you know Physical tells • I’m not a huge fan of using tells • Too many books • Too many players fake them • Tells are specific to individuals • Bet sizing tells • Bet strong when weak, and vice versa • Some commonly known tells • Stare hard at someone when weak • Hand shakes when strong • Be sure hand doesn’t -
Clear-Sighted Statistics: Module 7: Basic Concepts of Probability
City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College 2020 Clear-Sighted Statistics: Module 7: Basic Concepts of Probability Edward Volchok CUNY Queensborough Community College How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/qb_oers/85 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Clear-Sighted Statistics: An OER Textbook Module 7: Basic Concepts of Probability “It is remarkable that a science [probability] that began by considering games of chance should itself be raised to the ranks of the most important subject of human knowledge.”1 –Pierre-Simon Laplace “The most important questions in life are, for the most part, really only problems of probability.”2 –Pierre-Simon Laplace Two seventeenth century French mathematicians, Blaise Pascal and Pierre de Fermat have been considered the founders of probability theory for over 300 years. Between July and October of 1654, Pascal and Fermat exchanged a series of letters about dice games that addressed questions raised by Antoine Gombaud, who was also known as the Chevalier de Méré. Gombaud is often depicted as the gambler in this story.3 With their letters, Pascal and Fermat established the core components of modern probability theory. While only seven of these letters have survived, some of the leading mathematicians of the time were aware of and commented on this correspondence. One was the era’s top scientist, Christiaan Huygens and teacher of the mathematician Gottfried Wilhelm Leibniz, alluded to these letters in 1657. -
Kill Everyone
Kill Everyone Advanced Strategies for No-Limit Hold ’Em Poker Tournaments and Sit-n-Go’s Lee Nelson Tysen Streib and Steven Heston Foreword by Joe Hachem Huntington Press Las Vegas, Nevada Contents Foreword.................................................................................. ix Author’s.Note.......................................................................... xi Introduction..............................................................................1 How.This.Book.Came.About...................................................5 Part One—Early-Stage Play . 1. New.School.Versus.Old.School.............................................9 . 2. Specific.Guidelines.for.Accumulating.Chips.......................53 Part Two—Endgame Strategy Introduction.........................................................................69 . 3. Basic.Endgame.Concepts....................................................71 . 4. Equilibrium.Plays................................................................89 . 5. Kill.Phil:.The.Next.Generation..........................................105 . 6. Prize.Pools.and.Equities....................................................115 . 7. Specific.Strategies.for.Different.Tournament.Types.........149 . 8. Short-Handed.and.Heads-Up.Play...................................179 . 9. Detailed.Analysis.of.a.Professional.SNG..........................205 Part Three—Other Topics .10. Adjustments.to.Recent.Changes.in.No-Limit Hold.’Em.Tournaments....................................................231 .11. Tournament.Luck..............................................................241 -
Mississippi Gaming Regulations
MISSISSIPPI GAMING REGULATIONS 2013 Edition Revised format June 2013 Table of Contents Title 13: Gaming .......................................................................................................................................... 16 Part 1: Organization and Administration ................................................................................................... 16 Part 1 Chapter 1: GENERAL PROVISIONS .................................................................................................... 16 Rule 1.1 Appointment Of Committees. ................................................................................................... 16 Rule 1.2 Definitions. ................................................................................................................................ 16 Part 1 Chapter 2: PUBLIC AND CONFIDENTIAL RECORDS .......................................................................... 16 Rule 2.1 Definitions. ................................................................................................................................ 16 Rule 2.2 Confidential Records. ................................................................................................................ 18 Rule 2.3 Sealing Of Documents. .............................................................................................................. 19 Rule 2.4 Access To Public Records. ......................................................................................................... 19 Rule 2.5 Access To -
Review of Beyond Counting
Review of Beyond Counting http://www.jetcafe.org/npc/reviews/gambling/beyond_counting.html Review of Beyond Counting Title: Beyond Counting Author: James Grosjean Publisher: RGE Publishing Date: 2000 ISBN: 0-910575-17-7 Pages: 223 Price: $39.95 Reviewed by Nick Christenson, [email protected] November 5, 2000 There are several well known ways a player can gamble in a casino with a positive expectation. Certainly, Blackjack card counting, skilled Poker play, some full pay Video Poker, and sports betting are the most familiar. Others may know about more esoteric methods like Blackjack shuffle tracking, Roulette wheel clocking, and advantageous slot play. There are even those who go further, looking for house mistakes in calculating payoffs in games like Keno or Sic Bo. In Beyond Counting , James Grosjean pursues this topic further than anyone I have yet encountered, looking for edges in such strongly negative expectation games as the Big Six Wheel and Three Card Poker, as well as classical games like Blackjack and Craps. After various introductions to the author and the book, we told about the strange hierarchy of casino advantage players. Grosjean tells us how the Blackjack basic strategy player won't understand what a card counter is doing, how a card counter won't see how a shuffle tracker is playing an advantage, and a shuffle tracker won't understand many of the actions of a hole card player. We come to understand the casino as a series of layers of potentially strange behavior. Who is doing what, and why? Grosjean then performs some interesting mathematical analysis surrounding card counting. -
Alright, Let's Talk About Some Postflop Play
MIT 15.S50 LECTURE 2 Wednesday, January 16th, 2013 OUTLINE: POSTFLOP PLAY 1st Half: Continuation Betting, Fundamental Theorem of Poker, Flop Analysis 2nd Half: Implied Odds, Set Mining, Bluffing (with draws), Bluffing Epiphany 1, Bluffing Epiphany 2 A REMINDER ABOUT ATTENDANCE... YOU are responsible for ensuring your attendance is marked down each class! Find the Attendance Person with your name either before class, during the break, or after class. I won’t set aside class time for attendance. REMINDER: LIVE TOURNAMENT TOMORROW 1PM, will end around 5PM if you make it until the very end. Baker House Dining. Baker House is an Undergrad dorm. Google Maps it. The front door is locked, but if you tell the secretary you’re here for the poker tournament, they’ll let you in.) ALRIGHT, LET’S TALK ABOUT SOME POSTFLOP PLAY. NOTE POSITION NAMES. THE RAISE SIZE IS A BIT BIGGER THAN 2.25BB, BUT THAT’S FINE SINCE WE HAVE A COMFORTABLE 40BB BOTH BLINDS CALL. SB CHECKS BB CHECKS CHECKING TO THE PREFLOP RAISER This is conventional. The SB and BB, regardless of what cards they have, will usually check to the preflop raiser. Why is this? The SB and BB cannot really threaten to ever have a big pair on this flop, because if they had AA, they would’ve re-raised preflop. On the other hand, HJ-1 could potentially have AA in this situation. So if the SB and BB bet, they leave themselves susceptible to get raised by HJ-1, and they’ll usually have to fold, since HJ-1 could have/threaten AA while they can’t. -
The Theory of Dice Control
SMARTCRAPS.rtf Smart Craps Page 24 of 163 The Theory of Dice Control This chapter is intended as a brief summary only on dice control and the physical skill of dice setting. If you want to master the physical skill of dice setting, you will want to read and consult with some of the resources in the "Resources »Page 7" section of this documentation. Unlike card counting in blackjack, dice setting is a physical skill, and cannot be mastered through reading and mental practice alone. Dice setters attempt to control the physical throw of the dice in such a way as to influence the outcome of the dice. This skill, when used consciously at different points in the game, generates a non-random distribution of outcomes, which the shooter hopes reverses the casino's edge in the game to the player's favor. To understand the physics of dice control, let's look at an actual craps table: Figure 1: Axes of rotation on a craps table With these labels, we can see that a shooter will be throwing the dice along the X axis toward the end of the table. Generally, a skilled dice setter will hold the dice together, parallel to the Z axis, as shown below: SMARTCRAPS.rtf Smart Craps Page 25 of 163 Figure 2: Throwing the dice parallel to the Z axis of the table A typical controlled shooter is attempting to cause the dice to rotate only around the Z axis. In theory, any spin in the Y or X axis can introduce unexpected bounces and a less controlled outcome. -
Super Powered Role-Playing Using Mini Six Bare Bones Edition Copyright 2013 Paul Hosek Cover Art by Paul Hosek Interior Art by Paul Hosek
Super Powered Role-Playing using Mini Six Bare Bones Edition Copyright 2013 Paul Hosek Cover Art by Paul Hosek Interior Art by Paul Hosek, Written by Paul Hosek Table of Contents What is MightySix? 4 Corrosive 55 Super Scent 78 Dice Rolling Limits 5 Create Matter 56 Super Soak 79 Complement (Skill Synergy, Dark Vision 56 Super Swing 79 Helping Others) 5 Dazzle 57 Super Taste 80 Hero Points and Character Destroy Matter 57 Super Touch 80 Points 6 Dimension Walk 57 Telekinesis 80 Emotion Control 58 Telepathy 81 Combat, Action and Empathy 58 Teleportation 81 Movement EM Vision 58 Toxic 81 Energy Blast 59 Transmute 82 Timing Initiative and ESP 60 Transform 82 Declaration 7 Far Sensing 60 Trap 83 Fast Static Combat 8 Flight 61 Wall Walking 83 Wound Levels 11 FTL 61 X-Ray Vision 83 Knockout Damage 12 Gestalt 61 Shrugging It Off 12 Glide 62 Power Themes 83 Healing 13 Insanity 62 PowerSource 83 Pace 13 Illusion 62 Invention 84 Velocity and Collision 14 Inception 63 Insubstantial 63 Powerk Complications 86 Characters Invisible 64 Character Advancement 88 Machine Control 65 Superhero Archetypes 88 Basic Character Mind Blast 65 Generation 15 Mind Control 66 Resources 91 Attributes 15 Mind Shield 66 Firearms 93 Might Skills 16 Mind Swap 66 Explosives 94 Moves Skills 20 Minion 67 Missiles 95 Mind Skills 22 Natural Weaponry 67 Melee 95 Mojo Skills 25 Negation 68 Protective Gear 96 Passive Defense 69 Vehicles 96 Perks and Complications 27 Possession 69 Perk-fessions 27 Power Mimic 69 Encumbrance and Fatigue 97 Combat Perks 32 Precognition/Postcognition 70 Physical Perks 37 Radio 71 You Against the World Mental Perks 37 Regeneration 71 Destroying Objects 98 Social Perks 40 Shape Change 71 Natural Hazards and Misc. -
1Principles of Probability
Principles of 1Probability The Principles of Probability Are the Foundations of Entropy Fluids flow, boil, freeze, and evaporate. Solids melt and deform. Oil and wa- ter don’t mix. Metals and semiconductors conduct electricity. Crystals grow. Chemicals react and rearrange, take up heat and give it off. Rubber stretches and retracts. Proteins catalyze biological reactions. What forces drive these processes? This question is addressed by statistical thermodynamics, a set of tools for modeling molecular forces and behavior, and a language for interpret- ing experiments. The challenge in understanding these behaviors is that the properties that can be measured and controlled, such as density, temperature, pressure, heat capacity, molecular radius, or equilibrium constants, do not predict the tenden- cies and equilibria of systems in a simple and direct way. To predict equilibria, we must step into a different world, where we use the language of energy, en- tropy, enthalpy, and free energy. Measuring the density of liquid water just below its boiling temperature does not hint at the surprise that just a few de- grees higher, above the boiling temperature, the density suddenly drops more than a thousandfold. To predict density changes and other measurable prop- erties, you need to know about the driving forces, the entropies and energies. We begin with entropy. Entropy is one of the most fundamental concepts in statistical thermody- namics. It describes the tendency of matter toward disorder. The concepts that 1 we introduce in this chapter, probability, multiplicity, combinatorics, averages, and distribution functions, provide a foundation for describing entropy. What Is Probability? Here are two statements of probability.