5th Commander (EDH) and Probability for Deck Construction: Adding Fractions

Consider that in all the scenarios of types of cards you have, the total amount of cards should equal 1.  That is, when making a deck, the fractions of a deck’s constituents should add up to 1.  There are many ways to achieve this. 

For example,

1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 +1/10 + 1/10 + 1/10 + 1/10 = 10/10 = 1

Thus, in the above scenario, there would be 10 different kinds of scenarios.

Another way to achieve this is as follows:

Since 1/10 + 1/10 = 1/5

It is thus that:

1/5 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 +1/10 + 1/10 = 10/10 = 1

Or 9 different kinds of scenarios.

Also,

½ + 1/4 + ¼ = = 4/4 = 1

Or 3 different kinds of scenarios.

If the fraction 1/3 is used, then one thing that can be done is

1/3 + X = ½

Thus, X = ½ - 1/3 = 3/6 – 2/6 = 1/6

Thus, 1/6 + 1/3 + ¼ + ¼ = 1

Where 1/6 equals 99*(1/6) = 16.5 cards.

This allows for 4 scenarios.