Coin Labyrinth

Player A and B are playing a game on a circular table. In this game, each player puts a coin on the table(the radius of the coin is considerably lesser than that of the table) which is followed by the other player putting a similar coin on the table. This process continues until any player can't put another coin on the table surface (there can be no overlapping of coins). The player putting the last coin wins. If the coin is put on the edge of the table (coin is horizontal) such that a part of it lies outside the table it is considered fair. Now there can be two variations in the game- the players can't move the coins already put on the table (type 1) or they can change the configuration of coins on the table before they lay their coin(type 2) Both the types of the game are played. You are player A, then should you start the game(put the first coin) or play the second turn(putting the second coin) in each type for improving your chances of winning/ which turn(first or second) should you take in each type of the game?