Mathematics of bookmaking

In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The term originates from the practice of recording such wagers in a hard-bound ledger (the 'book') and gives the English language the term bookmaker for the person laying the bets and thus 'making the book'.

Making a 'book' (and the notion of overround)

A bookmaker strives to accept bets on the outcome of an event in the right proportions so that he makes a profit regardless of which outcome prevails. See Dutch book and coherence (philosophical gambling strategy). This is achieved primarily by adjusting what are determined to be the true odds of the various outcomes of an event in a downward fashion (i.e. the bookmaker will pay out using his actual odds, an amount which is less than the true odds would have paid; thus ensuring a profit).

The odds quoted for a particular event may be fixed but are more likely to fluctuate in order to take account of the size of wagers placed by the bettors in the run-up to the actual event (e.g. a horse race). This article explains the mathematics of making a book in the (simpler) case of the former event. For the second method, see Parimutuel betting

Book

A book is a set of written, printed, illustrated, or blank sheets, made of ink, paper, parchment, or other materials, fastened together to hinge at one side. A single sheet within a book is a leaf, and each side of a leaf is a page. A set of text-filled or illustrated pages produced in electronic format is known as an electronic book, or e-book.

Books may also refer to works of literature, or a main division of such a work. In library and information science, a book is called a monograph, to distinguish it from serial periodicals such as magazines, journals or newspapers. The body of all written works including books is literature. In novels and sometimes other types of books (for example, biographies), a book may be divided into several large sections, also called books (Book 1, Book 2, Book 3, and so on). An avid reader of books is a bibliophile or colloquially, bookworm.

A shop where books are bought and sold is a bookshop or bookstore. Books can also be borrowed from libraries. Google has estimated that as of 2010, approximately 130,000,000 unique titles had been published. In some wealthier nations, printed books are giving way to the usage of electronic or e-books, though sales of e-books declined in the first half of 2015.

Keturi Brūkšniai

Keturi brūkšniai is a polemical book by Lithuanian historian Edvardas Gudavičius, written in the Lithuanian language. It was published in 2002 by Aidai in Vilnius (ISBN 9955-445-55-6). It does not have any proper title, but publishers and book sellers usually put four dashes (Lithuanian: Keturi brūkšniai) as the title.

References

Book (graph theory)

In graph theory, a book graph (often written  ) may be any of several kinds of graph.

One kind, which may be called a quadrilateral book, consists of p quadrilaterals sharing a common edge (known as the "spine" or "base" of the book). A book of this type is the Cartesian product of a star and K₂ .

A second type, which might be called a triangular book, is the complete tripartite graph K_1,1,p. It is a graph consisting of triangles sharing a common edge. A book of this type is a split graph. This graph has also been called a .

Given a graph , one may write for the largest book (of the kind being considered) contained within .

The term "book-graph" has been employed for other uses. Barioli used it to mean a graph composed of a number of arbitrary subgraphs having two vertices in common. (Barioli did not write for his book-graph.)

Theorems on books

Denote the Ramsey number of two (triangular) books by

If , then (proved by Rousseau and Sheehan).

There exists a constant such that whenever .