#### Overview of the mathematical parts

1) Mathematics in general

a. Ranking systems

There are ranking lists in many sports. The origin of these rankings and their value is examined. My own system for improving league tables is presented in detail.

b. The Goat Problem

More biographical/entertainment. But the aspects and aberrations in thinking are explored. Also fits with paradoxes (Monty Hall paradox).

c. The step-step-grandson

General public attitudes to mathematics and mathematicians’ attitudes to probability are discussed.

d. A few number games

A bit spun, off the wall, but entertaining and also interesting, what actually a big number, or even a small number, small probability can actually be.

e. The LaPlace experiment

Develops the basic understanding of probability theory. Not dry.

f. Bankruptcies

What causes players to go bankrupt? Even good players?

g. Simulations

Examines a few types of players by simulation, interesting results and derivation. Basically very suitable for creating a few prerequisites for understanding a successful player’s career.

h. Game developments

As a rule, a winner is determined in the game. Excitement arises from the fact that this winner has not yet been determined, but emerges in the course of the competition. This consideration looks at the development of the distribution of chances during the competition.

i. Swings

Essentially the conceptual definition of swing: “difference between winning and losing.” But suitable for building understanding in the player’s career. Misunderstandings can be cleared up.

j. Insurance

The day-to-day betting (on poor terms) of “security fanatics”. All illusion.

2) Betting mathematics

a. The betting market

How is betting done? Where do people bet? How is the market “formed”? What kind of bets are there?

b. The fair bet

A few basic considerations on betting, how odds are formed etc. (covered in the chapter “How do odds come into being?”).

c. Own estimates

How do you arrive at your own estimates? How are odds created on the betting market?

d. Expected value and equity

Establish a basic understanding of the gambler’s vocabulary. These terms have daily use. But there is also a mathematics to it.

e. The football programme mathematically

The system for calculating odds using my programme is explained in great detail.

f. Introduction to the problem of testing

forecast quality

There is the basic problem of how to check a forecast whether it was good or bad. In betting, of course, one has a financial result and can count money every day as long as there is some. But there is a mathematically absolutely correct method of comparing forecasts both with oneself and with two different forecasts. The reader is gently introduced to this. In mathematics itself, this method does not yet exist!

i. Introduction 3

A second attempt to explain this vividly.

g. The perfect betting game

Consequence of the above system: If two predictions can be compared with each other in a mathematically correct way, one can of course make the “perfect betting game” out of it, with many players.

h. The tennis programme

In principle, this is already covered in “Rating Systems”. However, it was the origin for the “rating system” I use today, which also does not yet exist in this form in mathematics.

i. Betting games

The quality of betting games, which almost everyone plays, is examined.

j. Turnover

General considerations about the profession of professional gambler. How much money does one have to turn over and how, with what return, in order to be able to finance one’s livelihood. Goes with “bankruptcies”.

k. Independent events

A bit more introduction to mathematics, some set theory, but easily explained.

l. How a quota is formed

Very detailed explanation of this principle. Mathematically well derived and explained in an understandable way.

m. How often does a double occur?

A few more calculation methods to learn how to deal with probabilities, also easy and detailed.

n. The connection between probability and odds

Covered by “How does an odds come about”.