I'm creating AI for a card game, and I run into problem calculating the probability of passing/failing the hand when AI needs to start the hand. Cards are A, K, Q, J, 10, 9, 8, 7 (with A being the strongest) and AI needs to play to not take the hand.

Assuming there are 4 cards of the suit left in the game and one is in AI's hand, I need to calculate probability that one of the other players would take the hand. Here's an example:

AI player has: J Other 2 players have: A, K, 7

If a single opponent has AK7 then AI would lose. However, if one of the players has A or K without 7, AI would survive. Now, looking at possible distribution, I have:

P1   P2   AI
---  ---  ---
AK7       loses
AK   7    survives
A7   K    survives
K7   A    survives
A    7K   survives
K    7A   survives
7    KA   survives
     AK7  loses

Looking at this, it seems that there is 75% chance of survival.

However, I skipped the permutations that mirror the ones from above. It should be the same, but somehow when I write them all down, it seems that chance is only 50%:

P1   P2   AI
---  ---  ---
AK7       loses
A7K       loses
K7A       loses
KA7       loses
7AK       loses
7KA       loses
AK   7    survives
A7   K    survives
K7   A    survives
KA   7    survives
7A   K    survives
7K   A    survives
A    K7   survives
A    7K   survives
K    7A   survives
K    A7   survives
7    AK   survives
7    KA   survives
     AK7  loses
     A7K  loses
     K7A  loses
     KA7  loses
     7AK  loses
     7KA  loses

12 loses, 12 survivals = 50% chance. Obviously, it should be the same (shouldn't it?) and I'm missing something in one of the ways to calculate.

Which one is correct?