# Different way of playing poker?

**Discrete Mathematics**Level 3

In a poker game, there are 52 different cards with 13 different values. However, this time we are going to make their values more interesting. There are 4 different suits for each number, diamonds, clubs, hearts and spades. If the card is of a diamond suit, you multiply the number by 1 and that will be its new value. If it is clubs, you multiply it by 2, hearts, by 3 and spades, by 4. Now, you are required to rearrange the cards in order of their new value. Find the average of the values of the two cards in the centre.

**Example**

We have 8 cards, Ace of Diamonds, Ace of Clubs....Two of Spades. Ace of Diamond will become 1, Ace of Clubs will become 2, Ace of Hearts will become 3, Ace of Spades will become 4. Two of Diamonds will be \(2 \times 1=2\), Clubs, \(2 \times 2=4\), Hearts, \(2 \times 3=6\) and spades \(2 \times 4=8\). After rearranging them, you get \[1,2,2,3,4,4,6,8\] and the average of the values of the two cards in the centre is \(\frac{3+4}{2} = 3.5\).

**Details and Assumptions**

Jack has a value of 11, Queen 12 and King 13 while Ace has a value of 1.

Please pardon me for any Poker terms that I have gotten wrong.