Fundamental Formula of Gambling

A short explanation of the Fundamental Formula of Gambling

This is meant only to be an introduction to this subject as I’m no mathematic expert, but maths are indeed a great tool.

The first reference to this Formula is found in the bookThe Certainties of Hazard by the french matematician Marcel Boll who first talked about this formula, later Ion Saliu talks to more extent about it in his web site.

The problem to be solved by this formula is the number of trials N necessary for an event of Probability p to appear with the Degree of certainty DC.

So the formula is quite simple:

N = Log (1 - DC) / Log (1 - P)

Where N is the number of trials, DC the degree of certainty that we want and the probability P as a percentage.

Let’s take the example of a coin tossing:

If a coin is tossed then there is a 50% chance of it coming down heads and 50% chance of it coming down tails, that the probability P. Then let’s say that the thrower wants to have 75% degree of certainty that they throw at least one head.

So, the question here is: How many throws do I need to toss my coin to get heads with a 75% guarantied result?

I can call my function here:

print N(75,50);

The implementation in PHP of the function N is as follows:

function N($a,$b)
{
$DC=($a/100);
$P=($b/100);
return log(1-$DC)/log(1-$P);
}

The answer is two throws and everybody can test this with a coin, or move to more complex situations, lets say that you want to apply this to you 1/49 lotto system, in this case the probability P must be calculated very acurately, where probablility formula is:

 P=(n/N)*100

So here n is the number of times that our number has come out in a total of draws N .
For example if we say that number 1 has come out 12 times in the latest 47 draws, this will be: (12/47)*100 you will get a very long number like 25.531914893617 that in this case is the parameter P of our Formula.

The the parameter DC degree of certainty is the guarantied percentage you want, you just have to substitute all this values in the formula and you will get the number of trials necessary to get your number.

In the old times the matematicians were also philosophers as both matters were united, so dont’t forget they both need to really go together.