You've got a good start. Here's a few comments
1) Instead of using randsample() and then finding and removing elements from the deck, it might be much easier to simply use randperm(52) to generate a random order of the cards in the deck. You'll only need to do this once, then just grab the cards in order from the deck. e.g.
deck = DECK( randperm(52));
The deck is now shuffled, so your holes cards are just deck{1} and deck{2}. The flop is deck{3:5}, the turn is deck{6} and turn is deck{7} (assuming there is only one player and no burn cards).
Not only is this easier to program, it more closely simulates the actual game. i.e. the dealer shuffles once. dealer does not shuffle between flop and turn.
2) you said that your problem is the sorting. I think the reason why it is hard for you is that you have chosen to represent your data as a 2 character string. Although this is a human readable representation, it's not particularly easy for the computer to manipulate. You could come up with a custom sort routine that understands that 'Q' > 'J' and 'T' > '9', it would be easier to just represent the rank internally as a number between 1 and 13, and then write a small subroutine to translate the internal representation to an external representation. e.g.
if (card.rank == 13)
output = 'A';
else if (card.rank == 12)
output = 'K';
else if (card.rank == 11)
output = 'Q':
etc.
Then you can just use matlab's built-in sort routines, which already know how to sort integers just fine.
3) I alluded to this above, but it will also simplify your program if you replace the large number of individual variables with arrays of object variables. i.e. these lines here
card1_val = card1(1);
card1_suit = card1(2);
card2_val = card2(1);
card2_suit = card2(2);
you have 4 separate uniquely named variables here. it would be much better to have a card object, so you can talk about card.val and card.suit. Then card is a single object with 2 members, rather than 2 variables. Then instead of 2 separately named variables, have an array, so you have card(1).suit, card(1).val, card(2).suit, card(2).val. By having more structured data, the rest of the program should easier to write.
Hope this helps.
