Probability computation and algorithm for subsequences

Here is a game where cards 1-50 are distributed to two players each having 10 cards which are in random order. Ai开发者_JS百科m is to sort all the cards and whoever does it first is the winner. Every time a person can pick up the card from the deck and he has to replace an existing card. A player can't exchange his cards. i.e only he can replace his card with the card from the deck.A card discarded will go back to deck in random order. Now I need to write a program which does this efficiently.

I have thought of following solution 1) find all the subsequences which are in ascending order in a given set of cards 2) for each subsequence compute a weight based on the probability of the no of ways which can solve the problem. for ex: If I have a subsequence 48,49,50 at index 2,3,4 probability of completing the problem with this subsequnce is 0. So weight is multiplied by 0 . Similarly if I have a sequence 18,20,30 at index 3,4,5 then no of possible ways completing the game is 20 possible cards to chose for 6-10 and 17 possible cards to chose for first 2 position , 3) for each card from the deck, I'll scan through the list and recalculate the weight of the subsequnces to find a better fit.

Well, this solution may have lot of flaws but I wanted to know 1) Given a subsequence , how to find the probability of possible ways to complete the game? 2) What are the best algorithm to find all the subsequences?

So if I understand correctly, the goal is to obtain an ordered hand by exchanging as few cards as possible, right? Have you tried the following approach? It is very simplistic, yet I would guess it has a pretty good performance.

N=50
I=10
while hand is not ordered:
   get a card from the deck
   v = value of the card
   put card in position round(v/N*I)