Winning Strategy for a Card Game with Overlapping Cards

If $n$ is even, then the game can be split into two identical halves. Therefore, the person who moves first can always mirror the moves of the second player and win. Hence, the first player always wins if $n$ is even.

If $n$ is odd, then we can consider two cases:

Case 1: The first player removes 1 card. In this case, the second player can mirror the moves of the first player until there are only 4 cards left. At this point, the first player must remove either 1 or 3 cards, which will leave 3 or 1 cards respectively. In either case, the second player can take the remaining cards and win.

Case 2: The first player removes 2 or 3 cards. In this case, the second player can mirror the moves of the first player until there are only 5 cards left. At this point, the first player must remove either 1 or 3 cards. If the first player removes 1 card, then the second player can take the remaining 4 cards and win. If the first player removes 3 cards, then the second player can remove the remaining 2 cards and win.

Therefore, if $n$ is odd, the second player can always win by mirroring the first player's moves. Hence, the winning strategy is to play as the second player if $n$ is odd and as the first player if $n$ is even.