Combinatorial game theory


30th April 2010, 8:51:24 p.m. |

Game Chomp! has a very simple rule: Select the shapes of some certain objects. This variant is called betlová, ie a player who removes the last object wins! Variations of this game see also abacus. The game comes from David Gale (Gale, D. (1974). A Curious Nim-type game, Amer. Math. Monthly 81: 876-879.).


Generating nadreálných numbers

29th April 2010, 11:29:06 |

Table of the first 63 numbers



-1 +1


-2 -1 / 2 +1 / 2 +2


-3 -3 / 2 -3 / 4 -1 / 4 +1 / 4 +3 / 4 +3 / 2 +3


-4 -5 / 2 -7 / 4 -5 / 4 -7 / 8 -5 / 8 -3 / 8 -1 / 8 +1 / 8 +3 / 8 +5 / 8 +7 / 8 +5 / 4 +7 / 4 +5 / 2 +4


-5 -7 / 2 -11 / 4 -9 / 4 -15 / 8 -13 / 8 -11 / 8 -9 / 8 -15/16 -13/16 -11/16 -9/16 -7/16 -5/16 -3/16 -1/16 +1 / 16 +3 / 16 +5 / 16 +7 / 16 +9 / 16 +11 / 16 +13 / 16 +15 / 16 +9 / 8 +11 / 8 +13 / 8 +15 / 8 +9 / 4 +11 / 4 +7 / 2 +5


Come sir, we‘ll play> Konan

15th April 2010, 9:26:07 p.m. |

Hawaiian applet games venue.


Come sir, we‘ll play> Mancala

14th April 2010, 11:36:29 |

Mankala game (also known as Mancala) and Manbula. Trysse game is its presentation. Another option is to play the Egyptian Calah. Game Rules Warri.


Several online games

14th April 2010, 11:01:41 or



1st April 2010, 6:05:56 p.m. |

Kayles game is an example of an absolutely impartial games. A number of courses are taken one, or simultaneously by two adjacent objects. Who does not move, he lost. The game is completely solved. Even at its option betlové known strategy. It is an open question what happens if you could draw up to three subjects. Circular kayles You can also play online.Another online option: Bowling game.


Come sir, we‘ll play> Connect4, Go-moku, Mini Mancala, Nim puzzle, Othello

1st April 2010, 8:54:26 |

Games to play: Connect4, Go-moku, Mini Mancala, Nim puzzle, Othello, etc.


Come sir, we‘ll play> Wythoffův Nim

1st April 2010, 8:39:13 |

Wythoff Nim game with removal of objects, the rules allow remove any number of objects from one pile, or both simultaneously, but the same number.


Come sir, we‘ll play a> game 37

26th March 2010, 12:18:39 |

Game 37 is the type of game NIM. At each turn, players must take a maximum of 5 items. A player can not but draw the previous number of samples of stones. The player who first reaches the sum of more than 37, he lost.


Come sir, we have to play> games type NIM

23rd March 2010, 11:54:48 p.m. |

Bar game, the usual game NIM. Playing against the computer. Another nice option play him on several piles: Several other type games NIM them games. Other online games Nim. Interactive impartial games. Brief history:


Come sir, we‘ll play> Clober

22nd February 2010, 3:17:29 p.m. |

The goal is to capture the opponent‘s stones. Can take only the adjacent vertical or horizontal.In a normal variant, a player who can draw, he lost. Source applet.


Free Graph Paper Online / Grid Paper PDFs

13th February 2010, 1:16:41 p.m.

Different kinds of paper for graphs, such as Dots and Crosses hexagonal Hex Dot, and others.Eg. Simple Grid Graph Paper PDF Generator.


Playing Checkers (Draughts)

5th February 2010, 9:27:01 p.m. |

Checkers have been successfully analyzed in 2007. Chinook page discusses not only solved games, but most methods of exploration plays.


Traditional board games

3rd February 2010, 9:21:04 p.m. |

Traditional board games, history and useful information. At this link, and also includes a list of other games.


Analysis Games Dots-and-Boxes

2nd February 2010, 11:41:33

A list of links to a game Dots and Boxes, compiled by David Wilson. Game you can play online need to


Combinatorial Games at

30th January 2010, 11:34:00

Date Game (impartial game) Fraction Game (Partisan game) Grundy‘s Game (impartial game) Hex 7 Kayles (impartial game) Nim (impartial game) Nimble (impartial game) Northcott‘s Game (impartial game) One Pile (impartial game) Plainim (impartial game) Plainim Misčre (impartial game) Scoring (impartial game) Scoring Misčre (impartial game) Silver Dollar Game (impartial game) Silver Dollar Game With No Silver Dollar (impartial game) Sticks, Jess Realization of Scoring Misery Sticky Sticky Problem II Problem Subtraction Game (impartial game) TacTix Take-Away Games (impartial game) Turning Turtles (impartial game) Wythoff‘s Nim (impartial game) Wythoff‘s Nim II (impartial game)

Lessons in Play - book reviews

30th January 2010, 0:35:35

Science / Mathematics / Applied Lessons in Play: An Introduction to Combinatorial Theory Game by Michael H. Albert, Richard J. Nowakowski, David Wolfe & (AK Peters, Ltd.). It should Be noted That Children‘s games are not games Merel. One should Regard Them and Their Serious Bridge Activities. - Michel de Montaigne Eyquem Combinatorial games are games of pure strategy Involving two players, with perfect information and no element of chance. In Lessons in Play, starting from the very basics of game play and strategy, the authors cover a wide range of topics, from algebra and game surreal numbers to special classes of games.Classic techniques are introduced and applied in novel Ways to analyze Both old and new games, appearing Several For The First Time in this book. In Lessons in Play, author, mathematicians and game theorists Michael H. Albert, Richard J. Nowakowski, David Wolfe, and Their Together with many contributors, study games of pure strategy, In Which There are only two players‘ who alternate MOVES, Without using dice, cards or Other random devices and WHERE the players has perfect information about the current state of the game. Familiar games of this type include: tic tac toe, dots & boxes, checkers and chess. Obviously, card games Gin Rummy, and dry, and dice games and backgammon droughts are not of this type.The Game of Battleship h alternate play, and no chance Elements, But fails to include perfect information - in fact that‘s Rather the point of Battleship. The authors study the games has been dubbed combinatorial games that distinguish them from the games Usually found Under the heading of game theory, Which are games That Arise in Economics and biologists. According to Albert, Nowakowski and Wolf, for most of history, the study of Mathematical games consisted largely of Separate Analyses of EXTREMELY simple games. This was true up until the 1930s When The Sprague-Grundy theory Provided the Beginnings of a Mathematical foundation for a more general study of games. In the 1970s, the twin tomes On Numbers and Games by Conway and Winning Ways by Berlekamp, Conway, and Guy Established and publicized a complete and deep theory, WHICH CAN BE deployed to analyze countless games.Cornerstone One of the theory is the Notion of a Disjunctive sum of games, introduced by John Conway for normal-play games. This scheme is particularly Useful for games Naturally Into That split components. On Numbers and Games describes theses Mathematical ideas at a level Sophisticated. The AIM of Lessons in Play is less grand than option Visna of the two tomes, the authors AIM to Provide a guide to the evaluation scheme for normal-play two-player finite games. They Say They invented more games Than They solved During the Writing of Lessons in Play. While many found Their Way Into the book, most of theses games never made it to the rule sets found at the end. Exercises are sprinkled Throughout Each chapter. These Are intended to reinforce, and check the Understanding of, the preceding material. Ideally then, students should try Every Exercise as it is encountered. However one May consult the solutions to the exercises found at the back of the book. Chapter 0 introduces basic Definitions and loosely defines That Portion of game theory addressed in Lessons in Play. Chapter 1 Covers Some General Strategies for Analyzing Or playing games. Chapters 2, 4, and 5 contain the core of the General Mathematical Theory. Chapter 2 introduces the first main goal of the theory, That being of the DETERMINE and Game‘s Outcome class or Who should win from Ana position.Curiously, a great deal of the Structure of Some Games Can Be understood by looking at Solel Outcome classes. Chapter 3 motivates the theory Takes direction the next. Chapters 4, 5, and 6 Develop then this theory (ie, assigning values and the Consequences of theses values.) Chapters 7, 8 and 9 look at specific parts of the Universe of combinatorial games and as a result, These Are A Little More Challenging, But Also More concrete December They Are More Closely tied to actual games. Chapter 7 Takes an in-depth look at impartial games. The study of theses games pre-dates the full theory. The authors place Them in the new context and show Some of the new classes of games Under study. Chapter 8 addresses the hot games, games drought and Go and Amazons in Which There is a great incentive to move first. There is much research in this area and the authors of can only give An Introduction to this material. Chapter 9 looks at the analysis of all-small games. Most of the research emphasis he HAS been impartial and hot games. There has only been Recently Developments in this area and Theo Present the original and latest results in light of all the new Developments in combinatorial game theory. In Appendix A, the authors Present top-down induction, an approach That the authors use OFTEN in the text. Appendix B is a brief Introduction to CGSuite, and powerful programming toolkit Written in Java for performing algebraic manipulations on games. CGSuite is that the combinatorial game theorist Maple or Mathematica What is a mathematician and physicist or.While readers Need CGSuite not use while working through the text, the program does help to build Intuition, double-check work done by hand, Develop Hypotheses, and Handle Some of the drudgery of rote calculations. The Supporting website for Lessons in Play is located at If you Has Winning Ways, you Must have this book. - Andy Liu Lessons in Play is an enticing Introduction to the Wonderful World of combinatorial games.Using a rich collection of cleverly captivating examples and problems, the authors lead the reader through the Basic Concepts, and he‘s Innovative Several extensions. I highly Recommend this book. - Elwyn Berlekamp R. A neat machine, Converting Into enthusiastic novices Experts in modern combinatorial game theory. - Aviezri Fraenkel Combinatorial games are intriguing, Challenging, and Counter-Intuitive OFTEN, and are rapidly Being Recognized as an important Mathematical discipline. Now That We Have the Attractive and friendly text Lessons in Play in hand, WE CAN look forward to the appearance of many popular upper-division undergraduate courses, Which Encourage instructors to learn alongside Their Students.- Richard K. Guy Lessons in Play Makes an excellent guide for undergraduates or for self-study would Enterprising readers, with a generous collection of exercises and problems scattered Throughout the book. The theory is Accessible to Any student WHO HAS a smattering of general algebra and discrete math. Generally, a Third year college student, But Any good high school student should Be Able to follow the development with a little help.


Hex Games History

29th January 2010, 12:38:39 |

The history of the game Hex. Javhara page deals only with the game Hex, including generalization and history. Other pages on the game Hex.


A game of Tic Tac Toe

27th January 2010, 7:42:08 p.m. |


The University of Alberta GAMES Group

26th January 2010, 1:08:17 p.m. |

Game-playing, Analytical methods, Minimax search and Empirical Studies


List of abstract strategy games II

22nd January 2010, 8:41:56 p.m. |


The history of the game Halma

19th January 2010, 4:43:09 p.m. |


Game Lonny

15th January 2010, 10:50:55 p.m. |

Record lectures on game Loon.


Games of No Chance 3

16th December 2009, 9:01:29 p.m.

The latest anthology of work CGT vol 56, (ed. Albert, Nowakowski, 2009) Games of No Chance 3rd Readers will certainly deliver a set of open problems: Unsolved Problems in Combinatorial Games and reading list: Combinatorial Games: selected bibliography with a succinct gourmet Introduction.


Portable Suite Wazlaff_091205

4th December 2009, 3:47:07 p.m. |

Forensic Audit

Overall inspection system (software, hardware and networks) program allows the System Information for Windows (SIW). For example, detection of system passwords to email accounts using the menu allows Secrets. Filed DecrypTC allows to obtain a password from the ftp connection in Total Commander. Using a magnifying glass to reveal program ShowPassword zahvězdičkované password ... The new version contains only Portable_suite_Wazlaff_091205 new programs, but the total of 63 updates. The next version will be given alternative programs, including Microsoft distribute coffee. Version just unzip to a folder (like USB), and run the Launcher.


Six new online games in java

2nd December 2009, 7:10:36 p.m. |

For girls, boys, and passionate player‘s favorite games are six pages of Ferguson:


Fibonacci Nim.

Moore‘s Nim.

Dawson‘s Chess.

Dots and Boxes.


External links to combinatorial games in Java ( # games). For the analysis of some games may use a blank board, dominoes, or dots-and-boxes. Blind chess can be obtained at Graph Paper Generator.Other similar games site: JavaJive.html.


Come sir, we‘ll play> Dawson Chess

18th November 2009, 3:43:41 p.m. |

Dawson Chess is very similar kayles game (bowling). He plays the tape squares that are not normally occupied by the characters. Players regularly in their alternate routes, each move to place the character X has a blank box. Limitations on the move is that the player whose turn it is, not the character X to refer directly situated next to a character already.

The player who made the last move wins. (Normal variant.)



List of abstract strategy games

16th November 2009, 4:19:33 p.m. |




16th November 2009, 1:11:53 p.m. |

Turnablock applet games with rules


Online strategy games

16th November 2009, 12:28:34 |

Applets games such as Hex, Amazons, Clobbers, Gomoku, Reversi, etc.


n queens on a chessboard

13th September 2009, 9:40:45 p.m. |

Generalization of eight friendly games queens on the chessboard. Bibliography and abstracts.


Option harvesting sticks

13th September 2009, 9:32:59 p.m. |



Come, sir, we‘ll play!

9th September 2009, 9:09:09 |

Nancy Cayleová create a unique list of classical combinatorial games. This list, unfortunately, already on the internet is not available. The electronic archive, we attempted a partial reconstruction of the list (for example, commenting on the lack of the necessary images, etc.).Games are collected for historical reasons.

This page also includes games for motivation theory (mostly in Java). The date of July 23, 2008 includes interactive games:



Connect 4




miser them

These three miser

Queens v Knights

Tic Tac Toe (Game three to nine.)

3d tic tac toe



Update September 9, 2009 (


In the left menu added more online games, the right hand column are some rules of combinatorial game and at the end of the page are links to other sources of combinatorial games.


In the Utilities section, click utilities (such as date of birth).



Several open problems CGT

8th September 2009, 10:41:18 p.m. |

R. Guy and R. Nowakowski compiled a list of open problems of the theory of abstract strategy games (updated in 2002). UnsolvedCGT.pdf (in 2008)


Come sir, we‘ll play> board games

7th September 2009, 11:52:08 p.m. |



Come sir, we can play> them Fibonacci

7th September 2009, 0:36:37 |

Fibonacci him is absolutely fair game variant of the NIM. You play against the computer type is identified and taken in a normal variant. A player who removes the last object wins (end position). Players gradually taken the stones from one pile. Every move a player can take more than twice the stones that went into the previous opponent strength. The first player will never remove all the stones.


List of combinatorial games IV. (N. Caseyová)

3rd September 2009, 11:19:34 p.m. |

Classic Home combinatorial rules of other games. A collection of Nancy, we have already discussed at a local archive of games. Although quality is not good, but it is a copy of frequently mentioned site.


Come sir, we‘ll play> normal play impartial

31st , 2009, 3:10:29 |

Some interactive games, the definition (Fr.) as Nim, Grundy, Kayles, Wythoff, Fibonacci Nim, End-Nim, Nim limited, Prime-Nim, Coin-strip, Northcott, quinze, CGT-chess, ... Signpost is a link to Jean-paul.davalan. Another source of Nim games ala the Java Jive.


Wolf games tool

30th , 2009, 3:17:10 |

Instrument games next Obsequi, Gamesman, Combinatorial Game Suite, etc. belong to the analysis of combinatorial games. Now the new sites also include a description of the toolkit.Toolkit can be extended, such extensions is an example of a game Ataxx. Commercial environment Zillions of Games contains more than 1800 games (Reversi, Checkers, Chinese Chess, Blobs, Vertical Tic-Tac-Toe, Mini-Go, Mini-Shogi, ‚Losing‘ Chess, Dodge, Jungle, Fox and Gees, Senate, Tafl, Morris ,...).


Come sir, we can play> them betlový

30th , 2009, 1:38:47



Values play a blue-red hackenbush

28th , 2009, 10:42:42 p.m. |

When looking for value plays hackebushe shaped snake, visualizing, or solutions to reverse the problem, ie to find the value of the snake algorithm can be useful. It is suitable not only for finding the optimal strategy, but also to search for values (continuous) periodically dyed graphs.The algorithm uses a utility wz_jsgraphics.js.


Black and white NIM

28th , 2009, 3:49:20 p.m. |

Natural generalization of impartial games may be a variant of guerrilla games black and white NIM. Impartial games were investigated by the classical method, lead to Boutonovy and Sprague-Grundyovy sentence. Black and white it and its analysis leads to nonrecursive definition nadreálných numbers. Value of black-white-ment are only numbers (!) And therefore have the same importance as the Bi hackenbush (bars). To visualize the games can be used isomorphous play blue-red hackenbush


Come sir, we‘ll play> Hex-7 online

22nd , 2009, 10:25:46 p.m. |

Hex game was created as early as the 40th past century. For some time been on the list of popular games is very high, even among mathematicians and computer experts. The success of the game hex-7 indicates inter alia that the option has long been used in a TV contest ‚to quiz‘.Game you can play on any other board. Game can also be played on a cylinder or torus.

-------------------------------------------------- ------------------------------

Analysis of the Hex game (ie game hex ends a stalemate, there is a winning strategy for the first player, the game is complete, ...). Hex, play well on the small checkerboard 3x3, 4x4!


TeXLive 2008 portable

22nd , 2009, 6:39:28 |

From a purely sporting reasons, there is a distribution set to install TeXLive 2008 portable in its own directory. Installation and configuration using their own Perl scripts (Perl is also included in the distribution). Update packages, package management is thanks to the thick-mbr very simple. Ps viewer and pdf is psview-September 5


Conway games MathWorld (Wolfram Mathematica)

5th , 2009, 9:12:56 p.m. |

Games that we analyze are often algorithmically solvable. MathWorld site dealing only zhuštěnému description of combinatorial games, nadreálným numbers, but also include some relatively new results. Some games can motivate and analyzed using the programs listed here.You will need Wolfram Mathematica, Wolfram Mathematica, or at least the Players. Some games listed here are also a zipped notebook. Project implementation absolutely impartial games in Mathematica, including comments, please visit the Playing Games with Mathematica.


List of combinatorial games III

29th July 2009, 12:27:34 |

One aspect of the definitions of other combinatorial games.


Ten notches to the real numbers

6th July 2009, 7:59:44 |

Site includes suggestions for the history of the concept of numbers. Part of the presentation was used at the seminar Seven (Seminar history of mathematics and astronomy) in June 2009.Attention is paid mainly of half of the XIX. century to the present.



29th June 2009, 11:31:05 |

Site links were added to the current version of the bibliography, which is linked with the theory of combinatorial games. Added links to the original work Olof Hannera and PM Grundy. Was finally added to the actual copy numbers and passwords nadreálná combinatorial games from the English version of Wikipedia (in the left menu).


Poker NIM

27th June 2009, 8:27:09 |

This game is not fair and not even a combinatorial game (assuming repetition of moves), but the game can be analyzed as a NIM game, as well as Northcottova game.

When searching for patterns of neutral games (Sprague-value Grundyovy sequences) may be useful to use these two tables: winning and losing positions and the table values.



Birthday games

28th March 2009, 1:11:30 |

Age plays an important aspect of the comparison game. Allows us to use ordinal class gaming induction. Games (and therefore numbers) emerge gradually, by day, by stages. While the real numbers, the situation is clear, the game is still the old game knows an efficient algorithm. The final dyadic real numbers occur in the final day, the other real numbers rise until the day of ω.


Euclidean Game

22nd March 2009, 2:12:44 |

Next game is absolutely fair game to Euclid :-). In analyzing this game proves that it is necessary to get the sentence for the rest of the division, the theory of continued fractions, golden section, some elementary properties of the theory of inequalities, etc. And a ratio of the probability of winning is a nice geometric interpretation. Discover the strategic rules (how to play and win) are not so trivial. The game can be played among players who do not know the optimal routes. Otherwise, given that winning and losing positions change, it is possible to optimally correct their strokes.


Games and Strategy

21st March 2009, 1:39:07 p.m. |

When examining the game‘s most important to analyze the basic position and possible moves (position) of both players. Often it is possible to assign individual moves some value, and according to this value optimally move. Versatile instrument can be a game tree, ie up to isomorphism can be investigated only on this game (graph-oriented tree). JH Conway motivation for using game hackenbush. The article is devoted to the visualization of such games, as well as the associated strategies. Visualization in mathematics is irreplaceable. For example, allows to speak and prove the claim, ie, features of games. Figure 2 and 3 has one twig painted on the opposite side.


Laskerův NIM

14th March 2009, 11:59:03 p.m. |

Laskerův him is another type of game NIM. Something is not important. Mainly belong to the golden treasury of computer art, since the type of game him the best programs. At the same time pretty well completes the search for games like ment, (graduated neutral game with altered rules). Analysis of the game is simple, use the periodicity, kvaziperiodičnost, residual class, method, divide et impera, respectively. recurrence. Analysis of the game made a great mathematician and chess E. Lasker.


Come sir, we‘ll play> Reversi

2nd March 2009, 3:27:03 p.m.

Two variants of the game Reversi, the first non counters, the second with a counter.


Absolutely impartial games

1st March 2009, 1:24:43 p.m. |

Theory of impartial games is most elaborate theory of combinatorial games. Bouton was introduced (1902) and independently and Sprague Grundym in the thirties of last century.Although it is stated that the game comes from intangible antiquity, it is likely that not much older than the year 1902nd Theory contains some very nice phrases that allow a global view on the theory and method of calculating good moves.

In addition to specific algorithmic games playable from the archive, it is possible to use tools for calculations, see Utilities.


Come sir, we‘ll play a> silver dollar and heritage

27th February 2009, 7:41:56

Games for two players with full information, no chance. Players are regularly alternate routes and begin in a basic position (pre-agreed positions, configurations). A player who has released draft rules, lost. Eg. draw lots to determine who will start. A player can not give up his turn.During the game, but is allowed to change the settings of the degree of difficulty of the game (not the optimal strategy).


Come sir, we‘ll play> Hexi

14th February 2009, 1:44:12 p.m. |

Hexi obarvovací game is a game of the hexagon. On the complete graph K6 two players trying not to create a triangle of his color ... (Http://


The endless games ...

10th February 2009, 11:04:22 p.m. |

Conway lecture on endless games (video / handout) - 2000.


List of combinatorial games II

9th February 2009, 11:42:40 p.m. |

Reduced list Conwayových impartial two-player games (1 sheet).


BASIC for Palm OS

3rd February 2009, 7:22:14 p.m.

As the name already says, this page is devoted to the implementations of the programming language BASIC for the Palm OS platform, v3 +.


List of combinatorial games I

29th January 2009, 2:46:46

Eleven pages of new definitions of combinatorial games.


Favorite web links

27th January 2009, 1:57:56 |

Slightly categorized links on the Internet, focusing on the theory of combinatorial games, discrete mathematics, history and philosophy of mathematics ...


Portable Software

12th January 2009, 11:16:45 |

Portable software are programs that can run from a USB flash drive. Interfere with the majority OS, do not interfere with the system or data directories. Its functionality is different from the ‚big‘ programs. Their advantage lies in their portability, of course, including the configuration of these programs. Their disadvantage lies in the possibility neuchránit their sensitive data, loss of identity. Now added to the distribution Portable_Wazlaff.



25th December 2008, 11:48:39 p.m. |

Calculators CGT calculation of birth numbers, addition and multiplication impartial (totally unbiased) games.

Date of birth, multiplication them, sčítalka them, remarks on the binary system, the sum of them.


Records of lectures JH Conway (audio / video) 1

23rd December 2008, 11:20:18 p.m. |

Lectures 1

Calendar Conundrums

Archimedes and His World

Cantor‘s infinities

Goedel and Undecidability

Geometry, Logic and Physics

Escher and Symmetry

Finally, Fun


Records of lectures JH Conway (audio / video) 3

23rd December 2008, 7:01:20 p.m. |

Lectures 3

Conway: The Brick of Princeton

Conway: ordinals a

Conway: 1 and 2


Interview with the numbers of J. Conway (Audio) 2

23rd December 2008, 6:14:55 p.m. |

Lectures 2

Math Factor, October 2007


Combinatorial games online

7th November 2008, 4:54:05 |

A few external links on combinatorial games in Java.


Several elementary statement of evidence

18th October 2008, 12:45:26 |

Sentences in the theory of numbers nadreálných can prove in many ways. As they look through the concept of inductive evidence ‚previously developed‘ is shown in this note. Here creates a system of sets previously created nadreálných numbers, which is well ordered. Hence, we can use mathematical induction for proving theorems.

Objects create induction, ie after steps. First we put S0 = (0) and Sn +1 is the set of all numbers generated nadreálných only set of numbers Sn (all the previous, simpler, previously created). The smallest number α in which the number appears in Sα is called the day of birth. In the final days (n is a natural) arise only dyadic fractions in the basic shape m/2n. On the details link back to [OGAN], the first two chapters.


p-adic digit system

28th September 2008, 2:18:38 p.m. |

Binary numeral system (base system of two binary, dyadic) has an interesting application in the theory of combinatorial games. Than if we study the games held at nimbers, we summarize here the fundamental claim of the positional systems. Some claim they are only touched on, respectively. serves to refresh the memory (eg sentence with the rest of the division). It is for the reader to verify some claims themselves (the transfer dekadického numbers to binary using Horner‘s scheme, etc.).. Some claim it is necessary to add that „such destruction“ is unambiguous, respectively. ‚Algorithm must stop‘, etc. Then the p-adic study of the system here is systematic. Dekadického transfer, binary and hexadecimal numbers provide registration and calc in scientific mode. In Windows To do that, at the command prompt, type calc, and simultaneously pressing the ALT + ENTER. Binary system introduced by G. Leibniz. The example shows how to subtract and divide in a binary system.


Come, sir, we‘ll play!

22nd September 2008, 7:22:35 p.m. |

JavaScript Games


Virtual Exhibition of combinatorial games

13th September 2008, 4:00:32 p.m. |

A brief historical overview of a few board games in terms of school education (in German), and game rules.


Humor in mathematics

17th August 2008, 2:21:28 p.m.

I do not understand any concept? You‘re not alone! Sometimes the answer: „You will find on the internet ...“. Site are machine translation Navajo Wikipedia. Start reading some pages to detail ... Likely to find other similar sites, such


Construction numeric fields

15th August 2008, 4:26:50 p.m. |

When the same number of standard structures arise again. Definition of operations of addition and multiplication are always different, structures polookruh gain, integral domain, commutative element, arranged housing, ... Structure numbers are not only expanding, but also softens; some numbers to get iterative methods. Some properties of numbers are defined recursively.Numbers add various adjectives is marking numbers but different ... Some of the turnovers in the structures are repeated (eg, arrangement of natural numbers and real numbers). Conway calls his objects of study but simply a number.


Nadreálná real numbers

1st August 2008, 2:59:26 |

Real numbers are presented as dedekindovské cuts and Cauchy sequences of rational numbers. The reader can easily he inspects the operations and relations are the set of real numbers well defined. This page contains a very interesting sentence on the oldest element.This theorem is useful for simplification of numbers.


Definition nadreálných numbers

1st August 2008, 2:36:23 |

Nadreálná chapter focuses particularly on numbers ordinal numbers nadreálných properties. A few examples, explains the use of induction. Typical examples are reflexiveness relation ≤, the finite number of bottom, and a sentence reduction, which allows simplification of notation.Examples to explain the use of these sentences. Nadreálná numbers are arranged sessions ≤, == equality relation is equivalence. It is shown that at least one nadreálné number is infinitely small,  ie ( n N +) ε <1 / n.


Algebra nadreálných numbers

31st July 2008, 2:52:33 |

Chapter follows the chapter on the properties of ordinal numbers nadreálných. The chapter is made of so-called one-line definition of basic arithmetic operations. Class of all numbers is commutative nadreálných orderly body. Detailed evidence is given in the first two chapters of [OGAN].


Knuth‘s novella Nadreálná numbers

25th July 2008, 2:53:30 |

Knuth‘s 1974 novel is the first information on the numbers nadreálných (Surreal Numbers). It is written in very readable form, like mathematics or debate with Socrates Dialogues. On a desert island, two students were confronted with the numbers gradually explore their properties ... The book (113 pp) is complemented by unsolved examples. Here is a link to the English version of the DjVu format. The reader can compare with the amendment process:

J. Conway, their objects of study called numbers. Sign Nadreálná numbers (Surreal Numbers) introduced to D. Knuth.


Experimental version for mobile devices

27th June 2008, 5:03:01 |

Combinatorial game theory pages are optimized for the mobile devices such as Palm PDAs.


Palm OS

26th June 2008, 11:35:40 |

On these pages you can find applications for the Tungsten | E2 category of „You Must Have“ - programs, without which your PDA can not do. It is the second launch of Java (JVM) and two full version (!) Applications for the USB drive. Prepares still SuperWaba and Sun Java on OS Garnet.


Minišach (logical solution tree - tree)

7th June 2008, 11:08:10 p.m. |

It is played on a board 3 × 3 and the first (or last) series are constructed three white (or black) pieces (pawns). Stroke is the displacement of one stone of their color on a box, or taking an opponent‘s stone on the diagonal. The game ends when one player does not move.


List of literature, index, basic definitions and designations of CGT

7th June 2008, 1:13:16 p.m. |

Basic tools (reading list, index, basic definitions and designations CGT).



7th June 2008, 12:43:01 |

Utility programs include support for research. These are programs you can use to test hypotheses. Standard also contains comments and be a non-standard browsers.


Bibliography (References and Resources)

7th June 2008, 12:39:31 |

The first three publications are to understand the CGT almost mandatory! They‘re [Onaga, ger, eng], [WW, ENG] and Czech [OGAN, eng]. On the Internet there are many sources of information ... List the most important is continuously updated. Later there will extensive list of applications in economics, sociology and others.


Combinatorial game theory (Combinatorial Games Theory)

7th June 2008, 12:08:45 |

The basic idea of the CGT, ie what the game is and what their characteristics, identifies the ordinal approach in building a gaming universe. Indicate the equivalence class decomposition according == Games.


Information Security

7th June 2008, 11:31:21 |

Siemens PKI project is an example of the corporate establishment of strong encryption, secure communications, repudation, etc. In its time, was one of the largest deployment of internal PKI.As a result some 12-year-old research.


Nim Sum Calculator

7th June 2008, 0:36:03 |

Calculator called the sum of the NIM, ie the total number of bits in the XOR, registered in the binary system.


Come sir, we have to play> online Marienbad

2nd April 2008 1:11:17 |

Playing him on four piles of numbers 1, 3, 5 and 7 subjects.


Computer Painting

30th March 2008, 11:25:52 |

In search of iterations of irrational real numbers showed that the speed of convergence - that is, the delta area - can be visualized. Sample contains some results of this visualization