Sample Space and Gambling

The Dawn of Sample Sapce

Gerolamo Cardano was an physician, a gambler, and a mathematician. Early in his career, he discovered the concept of sample space, and tried to publish the concept in a book named “The book on Games of Chance”. The manuscript was rejected.

He did not try to published it again. Instead, he used the concept to make a fortune out of gambling. The book was published after his death in 1663. Here is the quote from the book.

“The possible outcomes of a random process can be thought of as a point in the space.”

This space of all possible outcomes is later known to as “sample space”.


Combination, Permutation, and Gambling

To see how sample space helps in gambling, let’s look at following examples:

A Game of Flipping Two Coins

Let flips two coin and bet on the number of heads. There can be no head, one head, and two head. Before the time of sample space, it was believed that each of these 3 outcomes are equally probable.

If you look closely, there is one way to get no head (tail-tail) and one way to get two heads (head-head). But there are two ways to get one head (head-tail and tail-head). If you are a time traveller, you should try to return to 15th century and bet more on one head. It is more likely to win when you bet on the one-head outcome.

A Game of Throwing Three Dice

Let throw three dices. There are 6 ways to get a total of 9, and 6 ways to get a total of 10. One might think that getting 9 and getting 10 are equally probable. But in fact, the total of 10 occurs more frequent. The reason is that the combination of 6+3+1 = 6+1+3 = ... = 10 occurs more frequent that of 3+3+3 = 9. This is what mathematician call "permutation''.

"The chance of an event depends on the number of ways in which it can occurs.''


Source: The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, Chapter 3 [Read the Book Review] [Read the Previous Part] [Read the Next Part].

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Book or Audiobooks?

Personally, I prefer audiobooks. It's fun, and I can listen when I'm doing something else. It also makes other activities (e.g., jogging) a lot more fun. For more detail about audiobooks, please read [this post].

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About the summary: It takes time to finish up a book. And, when you do, sometimes, you want to review what you learn from the book. If you do not make notes as you read, you might have to go through the book once again. This can be time-consuming when you are dealing with a book. But you can still flip through the book and locate what you are looking for

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This book summary will help solve the pain of having to go through the book all over again.

I am leaving out the details of the books. Most books have interesting examples and case studies, not included here. Reading the original book would be much more entertaining and enlightening. If you like the summary, you may want to get the original from the source below.