Probability, Decisions and Games: A Gentle Introduction Using R

Rodriguez, Abel, Mendes, Bruno

Probability, Decisions and Games: A Gentle Introduction Using R

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商品描述

INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS

Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations.

The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book:

- Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years

- Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker

- Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess, and Tic-Tac-Toe.

- Features computer simulations using R throughout in order to illustrate complex concepts and help readers verify complex calculations

- Contains exercises and approaches games and gambling at a level that is accessible for readers with minimal experience

- Adopts a unique approach by motivating complex concepts using first simple games and then moving on to more complex, well-known games that illustrate how these concepts work together

Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines.

ABEL RODR GUEZ, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory.

BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.

BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations. The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book: - Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years - Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker -

商品描述(中文翻譯)

本書介紹了概率、統計、決策理論和博弈論的基礎知識，並以有趣的機會和策略遊戲示例來激發和說明抽象數學概念。該書涵蓋了隨機和策略遊戲，並提供了各種遊戲和賭博的例子，以建立對概率、統計、決策理論和博弈論基本概念的更好理解。作者介紹了隨機變量、理性選擇理論、數學期望和變異、公平遊戲、組合計算、條件概率、貝葉斯定理、伯努利試驗、零和遊戲和納什均衡等基本概念，以及它們在輪盤、賭場、樂透、二十一點、撲克、剪刀石頭布、雞遊戲和井字遊戲等遊戲中的應用。書中使用流行的R計算環境實施的計算機模擬用於提供對關鍵概念的直觀理解和驗證複雜計算。

本書首先介紹了簡單的概念，這些概念是通過推動概率領域的發展的歷史例子來仔細解釋的，然後將這些概念應用於流行的現代遊戲。《概率、決策和遊戲：使用R進行溫和介紹》的前兩章介紹了有限和離散空間中的概率和理性選擇理論，並建立在布萊斯·帕斯卡和皮埃爾·德·費馬之間的著名通信中討論的簡單遊戲的基礎上。隨後的章節利用流行的賭場遊戲，如輪盤和二十一點，來擴展這些概念，並說明這些方法的現代應用。最後，本書通過討論一些策略遊戲來介紹博弈論。本書的特點包括：

- 介紹概率、統計、決策理論和博弈論的入門知識，並在加州大學聖塔克魯茲分校進行了六年的課堂測試。
- 通過有趣且有趣的例子，如輪盤、樂透、賭場、二十一點和撲克，說明概率的基本概念。
- 使用經典遊戲，如剪刀石頭布、國際象棋和井字遊戲，介紹博弈論的關鍵思想。
- 使用R進行計算機模擬，以說明複雜概念並幫助讀者驗證複雜計算。
- 包含練習題，以及以對初學者易於理解的方式來處理遊戲和賭博的方法。
- 通過首先使用簡單遊戲來激發複雜概念，然後轉向更複雜且著名的遊戲，以說明這些概念如何相互作用。

《概率、決策和遊戲：使用R進行溫和介紹》是一本獨特且有用的教材，適用於統計推理、概率入門、統計素養和各個學科的量化推理的本科課程的學生。作者ABEL RODR GUEZ, P.h.D是加州大學聖塔克魯茲分校應用數學和統計學系的教授，發表了40篇期刊文章，他的研究興趣包括貝葉斯非參數方法、機器學習、時空模型、網絡模型和極值理論。BRUNO MENDES, P.h.D是加州大學聖塔克魯茲分校應用數學和統計學系的講師。

作者簡介

ABEL RODRÍGUEZ, PHD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory.

BRUNO MENDES, PHD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.

作者簡介(中文翻譯)

ABEL RODRÍGUEZ, PHD, 是加州大學聖塔克魯茲分校(UCSC)應用數學與統計學系的教授。他發表了40篇期刊文章，研究興趣包括貝葉斯非參數方法、機器學習、時空模型、網絡模型和極值理論。

BRUNO MENDES, PHD, 是加州大學聖塔克魯茲分校應用數學與統計學系的講師。

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