Friday, December 21, 2012

The St. Petersburg paradox

In economics, the St. Petersburg paradox is a paradox related to probability theory and decision theory. It is based on a particular (theoretical) lottery game (sometimes called St. Petersburg Lottery) that leads to a random variable with infinite expected value, i.e., infinite expected payoff, but would nevertheless be considered to be worth only a very small amount of money. The St. Petersburg paradox is a classical situation where a naïve decision criterion (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take. Several resolutions are possible.

Investing: Kelly Criterion

Over the last few years - while researching trading strategies - I happened to learn about the Kelly Criterion:

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run. It was described by J. L. Kelly, Jr in 1956

Library Additions: Gambling and Mathematics

I'm interested in learning more about the fine art of becoming a better player of various games of chance (in particular, those that are popular in Las Vegas), and developing a better edge in the management of my own personal portfolio trading strategies.

I believe that developing skills in the former will aide me in my goals for the latter.

And so, I've been slowly amassing a small library of books on various topics related to gambling skills, and some directly (or indirectly) related to the mathematics of such games.

The Mathematics of Blackjack

Thus far, I've been able to assemble a small respectable library of books, sourced solely through local thrift stores, and Friends of the Library sales.  My gambling-related collection currently includes the following:

  • The Rules of Neighborhood Poker According to Hoyle, by Stewart Wolpin
  • According To Hoyle, by Richard L. Frey
  • Hold'em Wisdom for All Players, by Daniel Negreanu
  • Winning Low Limit HOLD'EM, by Lee Jones
  • Gambling Secrets of Nick The Greek, by Ted Thackrey, Jr.
  • Playing Blackjack As A Business, by Lawrence Revere
  • Total Poker, by David Spanier
  • The Complete Guide to Winning Poker, by Albert H. Morehead
  • The Official Poker Rules, 1st Edition, World Poker Tour
  • The TAO of Poker, by Larry W. Phillips
  • Secrets the PROS WOn't Tell You About Winning HOLD'EM Poker, by Lou Krieger
  • More Hold'Em Excellence, by Lou Krieger
  • Winner's Guide to Texas HOLD'EM Poker, by Ken Warren
  • Scarne's Guilde to Modern Poker, by John Scarne
  • Tournament Poker for Advanced Players, by David Sklansky
  •  The Psychology of Poker, by Alan N. Schoonmaker, Ph.D.
  • Read'Em and Reap, by Joe Navarro
  • Beyond Bluff's, by James A. McKenna
  • Online Poker in easy steps, by Stuart Yarnold
  • The Book of Solo Games, by Gyles Brandreth

Some recent additions to my mathematics shelf, include the following:

  • Digital Dice, Computational Solutions to Practical Probability Problems, byu Paul J. Nahin
  • The Mathematics of Games of Strategy, by Melvin Dresher
  • Elementary Concepts of Topology, by Paul Alexandroff
  • Mathematical Theory of Computation, by Zohar Manna
  • The Golden Ratio, by Mario Livio
  • How To Lie With Statistics, by Darrell Huff
  • Mathematical Circus, by Martin Gardner
  • The Man Who Knew Infinity, A Life of the Genius Ramanujan, by Robert Kanigel
  • e: The Story of a Number, by Eli Maor
  • Mathematical Snippets, by Theoni Pappas
  • The Magic of Mathematics, by Theoni Pappas
  • Essays on The Theory of Number, by Richard Dedekind
  • How to Solve Word Problems in Geometry, by Dawn Sova, Ph.D.
  • Mathematics for the Biological Sciences, by Jagdish C. Arya and Robin W. Lardner
  • Rapid Math Tricks and Tips, by Edward H. Julius
  • Mathematics for the Trades, by Robert A. Carman and Hal M. Saunders
  • Finite Mathematics with Business Applications, by Kemeny et. al.

Tuesday, December 18, 2012 Math Resources has an interesting series called: Math Illuminated

There are also a wide variety of other materials available, tailored to specific age groups:


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