The mathematics of gambling: What is the combin function?

If you have checked out the mathematics of gambling before, or perhaps you were just looking for different ways to find out the odds of winning at a particular game, trying to decide whether you should play and which game you should play, you may have come across what is called the “combin function” and wondered what it is. If you have not come across it before, you are probably wondering what it is right now!
The combin function is a mathematical function provided by Microsoft excel or open software alternatives to excel that offers an easy way of working out how many different possible combination’s of outcomes exist for a particular numerical scenario. For example, imagine you wanted to find out how many possible ways there are to draw a combination of four cards from a full deck of cards (52, not including jokers). You could try to work this out using a calculator, or a pen and paper, or even your head, but you would be at it for a long time. The Combin Function offers an easier solution. You could use the Combin Function and it would tell you immediately, provided you gave the correct input data, that there are a complete total of 270,725 distinct possible different combination’s of four cards that can be drawn from a deck of 52. This is a pretty big number – and it is very difficult to come up with unless you are either a mathematical whiz, or you use the Combin Function. This is a very useful tool as well, as it greatly helps in assessing odds and probabilities.

Combin Function

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How to use the Combin function
To use the Combin function in order to work out the number of ways in which you can form various combination’s, you will need either Microsoft Excel, or an open software alternative (Open Office is a good one). Open up the program you are using, select any cell and type the following:
Then press enter.
Obviously, you need to substitute the values x and y with the values you are working with. The value y represents the number of items to be selected, and the value x represents the number from which they will be selected. Therefore, for the example mentioned above, removing four cards from a deck of 52, the entry you would type into the excel cell would look like this:
It is that simple! The mathematics behind it, however, are a little more complicated. And while you do not strictly need to know them, considering that excel or your chosen program will do them for you, we believe that a clear understanding of the principles involved in the maths of gambling, in this instance the Combin Function, will greatly assist you in accurately assessing and understanding your odds of winning at your chosen game.
Naturally, there isn’t a little mathematician inside Excel’s source code working out your problems! Excel calculates the answer to whatever you input into the cell Combin function is that is uses the following mathematical formula:
combin(x,y) = x!/(y!*(x-y)!
As you can see, this formula is considerably more complex, and entering all your variables into it will take quite a bit longer to calculate your answer, even if you do understand the various mathematical principles and symbols involved. If you are interested, you can do a quick google search of your own to gain a firm grasp of these symbols and principles, but simply just recognising the formula is a good start. In the meantime however, and let’s be honest, for most of us, the Combin function offered by Excel and similar program’s will make your life much easier!