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Analysis of Rummy Games: Expected Waiting Times and Optimal Strategies
ANALYSIS OF RUMMY GAMES: EXPECTED WAITING TIMES AND OPTIMAL STRATEGIES CHRISTOPHER FINKLE A SENIOR RESEARCH PAPER PRESENTED TO THE DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE OF STETSON UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE STETSON UNIVERSITY 2017 Contents 1 Introduction 2 1.1 Background and Objective . 2 1.2 Games of the Rummy Family . 3 1.3 Expected Value and Expected Time . 4 1.4 Existing Literature . 6 2 A Computational Approach 6 2.1 The Combinatorial Explosion of Rummy . 6 2.2 The Strategy of Dynamic Programming . 7 2.3 Introduction of Simplifying Assumptions . 8 2.4 The Bellman Equation . 10 2.5 Modifying the Bellman Equation to Describe Rummy . 11 2.6 Iterating Over the Set of Hands . 12 3 Three-Card Rummy 14 3.1 A Combinatorial Implosion . 14 3.2 Results . 16 3.2.1 Analysis of Results for 3-Card Rummy with Aces Low 16 3.2.2 Analysis of Results for 3-Card Rummy with Aces High or Low . 18 3.2.3 Analysis of Results for 3-Card Continuity Rummy . 19 4 Four-Card Rummy 21 4.1 Combinatorial Regrowth . 21 4.2 Analysis of Results for 4-Card Continuity Rummy . 21 5 Approximation and Least Upper Bounds 23 5.1 An Illustration of the Bounding Process . 23 5.2 Implementation of the Approximation Algorithm . 24 5.3 Approximation of 3-Card Rummy with Aces Low . 26 5.4 Approximation of 4-Card Rummy with Aces Low . 29 5.5 Approximation of 4-Card Rummy with Aces High or Low . -
The Penguin Book of Card Games
PENGUIN BOOKS The Penguin Book of Card Games A former language-teacher and technical journalist, David Parlett began freelancing in 1975 as a games inventor and author of books on games, a field in which he has built up an impressive international reputation. He is an accredited consultant on gaming terminology to the Oxford English Dictionary and regularly advises on the staging of card games in films and television productions. His many books include The Oxford History of Board Games, The Oxford History of Card Games, The Penguin Book of Word Games, The Penguin Book of Card Games and the The Penguin Book of Patience. His board game Hare and Tortoise has been in print since 1974, was the first ever winner of the prestigious German Game of the Year Award in 1979, and has recently appeared in a new edition. His website at http://www.davpar.com is a rich source of information about games and other interests. David Parlett is a native of south London, where he still resides with his wife Barbara. The Penguin Book of Card Games David Parlett PENGUIN BOOKS PENGUIN BOOKS Published by the Penguin Group Penguin Books Ltd, 80 Strand, London WC2R 0RL, England Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, Canada M4P 2Y3 (a division of Pearson Penguin Canada Inc.) Penguin Ireland, 25 St Stephen’s Green, Dublin 2, Ireland (a division of Penguin Books Ltd) Penguin Group (Australia) Ltd, 250 Camberwell Road, Camberwell, Victoria 3124, Australia -
Canasta by Meggiesoft Games
Canasta by MeggieSoft Games User Guide Copyright © MeggieSoft Games 2004 Canasta Copyright ® 2004-2005 MeggieSoft Games All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems - without the written permission of the publisher. Products that are referred to in this document may be either trademarks and/or registered trademarks of the respective owners. The publisher and the author make no claim to these trademarks. While every precaution has been taken in the preparation of this document, the publisher and the author assume no responsibility for errors or omissions, or for damages resulting from the use of information contained in this document or from the use of programs and source code that may accompany it. In no event shall the publisher and the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused directly or indirectly by this document. Printed: February 2006 Special thanks to: Publisher All the users who contributed to the development of Canasta by MeggieSoft Games making suggestions, requesting features, and pointing out errors. Contents I Table of Contents Part I Introduction 5 1 MeggieSoft.. .Games............ .Software............... .License............. ...................................................................................... 5 2 Other MeggieSoft............ ..Games........... ........................................................................................................ -
Opponent Hand Estimation in the Game of Gin Rummy
PRELIMINARY PREPRINT VERSION: DO NOT CITE The AAAI Digital Library will contain the published version some time after the conference. Opponent Hand Estimation in the Game of Gin Rummy Peter E. Francis, Hoang A. Just, Todd W. Neller Gettysburg College ffranpe02, justho01, [email protected] Abstract can make a difference in a game play strategy. We conclude In this article, we describe various approaches to oppo- with a demonstration of a simple deterministic application of nent hand estimation in the card game Gin Rummy. We our hand estimation that produces a statistically significant use an application of Bayes’ rule, as well as both sim- advantage for a player. ple and convolutional neural networks, to recognize pat- terns in simulated game play and predict the opponent’s Gin Rummy hand. We also present a new minimal-sized construction for using arrays to pre-populate hand representation im- Gin Rummy is one of the most popular 2-player card games ages. Finally, we define various metrics for evaluating played with a standard (a.k.a. French) 52-card deck. Ranks estimations, and evaluate the strengths of our different run from aces low to kings high. The object of the game is to estimations at different stages of the game. be the first player to score 100 or more points accumulated through the scoring of individual hands. Introduction The play of Gin Rummy, as with other games in the In this work, we focus on different computational strate- Rummy family, is to collect sets of cards called melds. gies to estimate the opponent’s hand in the card game Gin There are two types of melds: “sets” and “runs”. -
Gin Rummy (For 2 Players)
Gin Rummy (for 2 players) The Deck One standard deck of 52 cards is used. Cards in each suit rank, from low to high: Ace 2 3 4 5 6 7 8 9 10 Jack Queen King. The cards have values as follows: Face cards (K,Q,J) 10 points Ace 1 point Number cards are worth their spot value . The Deal The first dealer is chosen randomly by drawing cards from the shuffled pack - the player who draws the lower card deals. Subsequently, the dealer is the loser of the previous hand (but see variations). In a serious game, both players should shuffle, the non-dealer shuffling last, and the non-dealer must then cut. Each player is dealt ten cards, one at a time. The twenty-first card is turned face up to start the discard pile and the remainder of the deck is placed face down beside it to form the stock. The players look at and sort their cards. Object of the Game The object of the game is to collect a hand where most or all of the cards can be combined into sets and runs and the point value of the remaining unmatched cards is low. •a run or sequence consists of three or more cards of the same suit in consecutive order, such as 4, 5, 6 or 8, 9, 10, J. •a set or group is three or four cards of the same rank, such as 7, 7, 7. A card can belong to only one combination at a time - you cannot use the same card as part of both a set of equal cards and a sequence of consecutive cards at the same time. -
A Sampling of Card Games
A Sampling of Card Games Todd W. Neller Introduction • Classifications of Card Games • A small, diverse, simple sample of card games using the standard (“French”) 52-card deck: – Trick-Taking: Oh Hell! – Shedding: President – Collecting: Gin Rummy – Patience/Solitaire: Double Freecell Card Game Classifications • Classification of card games is difficult, but grouping by objective/mechanism clarifies similarities and differences. • Best references: – http://www.pagat.com/ by John McLeod (1800+ games) – “The Penguin Book of Card Games” by David Parlett (250+) Parlett’s Classification • Trick-Taking (or Trick-Avoiding) Games: – Plain-Trick Games: aim for maximum tricks or ≥/= bid tricks • E.g. Bridge, Whist, Solo Whist, Euchre, Hearts*, Piquet – Point-Trick Games: aim for maximum points from cards in won tricks • E.g. Pitch, Skat, Pinochle, Klabberjass, Tarot games *While hearts is more properly a point-trick game, many in its family have plain-trick scoring elements. Piquet is another fusion of scoring involving both tricks and cards. Parlett’s Classification (cont.) • Card-Taking Games – Catch-and-collect Games (e.g. GOPS), Fishing Games (e.g. Scopa) • Adding-Up Games (e.g. Cribbage) • Shedding Games – First-one-out wins (Stops (e.g. Newmarket), Eights (e.g. Crazy 8’s, Uno), Eleusis, Climbing (e.g. President), last-one-in loses (e.g. Durak) • Collecting Games – Forming sets (“melds”) for discarding/going out (e.g. Gin Rummy) or for scoring (e.g. Canasta) • Ordering Games, i.e. Competitive Patience/Solitaire – e.g. Racing Demon (a.k.a. Race/Double Canfield), Poker Squares • Vying Games – Claiming (implicitly via bets) that you have the best hand (e.g. -
Classic Party Games for Seniors
Classic Party Games for Seniors Dice Math-Salamanders.com – Free printable math games using dice. The site is intended for children; however, most of the games would work just as well with adults. The games are a fun way to improve math skills and memory. http://www.math-salamanders.com/math-games-using-dice.html Printable Paper - Free printable score sheets for Uno, dice, card, and domino games. Scroll down the page to find printable score sheets for many games you can play using the contents of this kit. http://www.printablepaper.net/category/score_sheets The history of dice, dice varients, and dice probability – a concise description of the history of dice and dice gaming. Also a short explanation of the different variations of dice used in gaming. The article briefly discusses the way dice work physically and mathematically. http://en.wikipedia.org/wiki/Dice Rules for the most popular dice games – • Bunko at http://www.worldbunco.com/rules1.html • Farkle at http://www.ehow.com/list_6936606_official-rules-playing-farkel.html • Yahtzee at http://www.hasbro.com/common/instruct/Family_Game_Night_Book_- _Sorry,_Clue,_Scrabble,_Yahtzee_Rule_Book.pdf See page 13 of the family Game Night Booklet. • List of popular dice games found on Wikipedia at http://en.wikipedia.org/wiki/Dice_games Dominoes Domino Basics - The history of domino games, basic domino rules of play, and domino factoids from http://en.wikipedia.org/wiki/Domino_games Dominoe-games.com – everything you need to know to play basic and advanced domino games. Includes information on domino game rule variations. http://www.domino-games.com/ Rules for popular domino games • Block Dominoes at http://www.domino-games.com/domino-rules/block-dominoes-rules.html • Draw Dominoes at http://www.domino-games.com/domino-rules/draw-dominoes-rules.html • Chickenfoot at http://www.domino-games.com/domino-rules/chickenfoot-rules.html Find a local or international Domino Club at http://www.domino-games.com/domino-clubs.html Cards Hoyle Gaming - Find a card game to play based on age or number of players. -
Card Game Rules 2018
Our Official Book Of Card Game Rules 2018 0 | P a g e Index of Games RUMMY 10 dime Rummy .............................................................................. 2 500 Rummy .................................................................................. 3 Arizona Rummy ................................................................................... 4 Desert Rummy ............................................................................. 5 Horseshit Rummy ................................................................................ 6 Push ................................................................................................. 7 Saskatchewan Rummy .................................................................... 8 OTHER CARD GAMES Canadian Salad (Whist) ................................................................................. 9 Euchre ............................................................................................ 10 Gin Rummy ........................................................................................ 11 Golf ..................................................................................................... 12 Hand and Foot Canasta ..................................................................... 13 Hand and Foot Canasta (game play) ................................................ 14 Hearts ............................................................................................ 15 Oh Hell! ............................................................................................. -
Official Continental Rules
Official Continental Rules Continental is a card game that is played with two (or more) English decks and in which you have to make different combinations, like in gin rummy. One continental game is made up of seven hands, were as in each hand you must make a different combination of trios and/or runs, increasing in difficulty each time. It’s unique in that each hand combination is fixed and you have a chance to pick cards 'out of turn' (means to take a card from the discard pile if no one before you wants it). Content - Game objectives - Start of the game: Distribution - The joker - Players of seats and cards - Variants to classic - Type of deck - Evolution of the game continental - Card values - Picking 'out of turn' - Specific vocabulary - Combinations: Trios and Runs - Dropped cards - Fixed combinations and cards to be dealt - End of the game Game objectives Combine cards in the fixed combinations for each hand and drop or expose them, since the ones left in your hand, combined or not, are the ones that count against you. The player that wins the game is the one with the least amount of points at the end of the game. Players From two to four players that are all individuals without partners or teams. Type of deck Continental is played with two English decks, with three jokers for each deck (although you can also play with two jokers per deck). You can also use poker Spanish decks. Card values Joker..................................................................50 points Ace.....................................................................20 points Face cards (king, queen, jack)...........................10 points Number cards (10, 9, 8, 7, 6, 5, 4, 3 y 2)..........their value Combinations: Trios and Runs The two combinations possible are trios and runs. -
Hit the Deck Card Game Instructions
Hit The Deck Card Game Instructions Obstreperous Mendie bestraddling fifthly while Srinivas always barricades his spotlights plebeianize extenuatingly, he line so declaratively. Bary is lawlessly relinquished after pipiest Patric yip his evangelisation sloppily. Coraciiform Petr leap nippingly. Assume the draw through ten is no limit to back to match, and places them face up as game the hit deck card in side Digimon Card Game Official Rule Manual. Etiquette of these will collect in hit the deck card game instructions. Deck Anglo-American Play therefore Playing time 5-15 min per game Random easy Medium Related games Conquian Tonk or tunk is a matching card offer which combines features of knock rummy and conquian. Triple Play Baseball Card Game Richard Gibson. All you heaven is a smell of cards to root these fun card games for two. WHAT'S INCLUDED IN THE remainder A programmable interval timer Each category includes 10 cards. While everybody's hung their favorite simple card running for kids from childhood. Both people overlook one card examine the remainings of three deck you can liberate any. Many Catholics have a hard but building wanted The Catholic Card Game visit a fun game that strengthens fellowship among friends and weave with laugher. We were excited for instructions on this site might not include html will ship. So I've noticed that on would of the cards some yet the crit entries say 'Crit Effect'. Properties printed in just two cards cannot use this is placed on each progressing pile and instructions on your card from there. No instructions card slot Got here for us On the forum There are 47 forum topics linked to enable game EM. -
FW1 Short-Appleton
Journal of Engineering Design This is a preprint of an article whose final and definitive form has been published in the JOURNAL OF ENGINEERING DESIGN © [2008] [copyright Taylor & Francis]; JOURNAL OF ENGINEERING DESIGN is available online at: http://journalsonline.tandf.co.uk/ New product development “according to Hoyle”: part 1 – the analogy E. A. APPLETON and T. D. SHORT* Durham University, South Road, Durham DH1 3LE, UK This paper, Part 1 of 2, introduces an analogy between the New Product Design process and a pack/game of cards. After introducing the analogy, it goes on to demonstrate that, just as Hoyle suggested rules for card games, similar analogous rules can be derived for product design, and the companies involved in such endeavours. It provides a “team- based” methodology for learning the analogy, and suggests a number of developments of the analogy that can be used for furthering the understanding of the New Product Design process. Part 2 of the paper will go on to provide some examples of the use of the analogy in practice. Keywords: New Product Development; Analogy; Hoyle; Card Game 1. Introduction This paper stems from an original idea that arose when one of the authors, Professor Appleton, was preparing teaching material for a lecture on Engineering Design. The lecture was to describe the use of idea generation processes and the organisation of those ideas by combining them to give a product concept. Initially, it was envisaged that a jigsaw puzzle analogy would be useful; that is, each individual idea was like a piece of a jigsaw puzzle and the first part of the embodiment phase of design was like selecting puzzle pieces and fitting them together to complete one of several possible puzzle solutions. -
110. Social Games
11-1 CHAPTER 110: SOCIAL GAMES Section EXCLUDED GAMES. General Provisions (A) Social games shall pertain only to card games; namely, any game or games played with cards 110.01 Title consisting of 52 pieces arranged in four suits of 13 110.02 Where social games permitted cards, each according to groups of figures printed on 110.03 Social games enumerated; excluded them. Social games that are allowed, but not games necessarily limited to, shall include the following 110.04 Charge to players prohibited; examples: draw poker, stud poker, lowball, high-low, limitation on bets high-low seven card, blackjack, three card monte, 110.05 Possession of unlawful gaming rummy, conquian, gin rummy, canasta, bridge, whist, devices; seizure euchre, hearts, pinochle, pitch, casino and cribbage. Licensing (B) Specifically excluded from social games are contests of chance such as any contest, game, gaming 110.15 Application for license; consideration scheme or gaming device in which the outcome 110.16 Issuance; contents depends in a material degree upon an element of 110.17 Transfer or alteration chance, notwithstanding that the skill of the 110.18 Duration of license; display; renewal contestants may also be a factor therein. Such 110.19 Fees and charges; disposition of funds activities excluded from social games, but not limited 110.20 Suspension or revocation thereto, shall include dice, dice games, roulette, wheel 110.99 Penalty of fortune, amusement devices (such as pinball or slot machines) which return to the operator or player thereof or anyone else anything but free additional GENERAL PROVISIONS games or plays, lottery, number schemes, or any other activity defined in ORS 167.117(1)-(4), (6)-(9) and (14).