Sudoku as a 2 person Game

I have made Sudoku into made into a game for 2 players. My game uses a 6 x 6 Grid ( 36 cells) with 6 rectangular blocks of 3 x 2. Almost the same rules of Sudoku prevail (i.e. each row, each column and each rectangular block can only have 6 different markers without repetition). At the start the Board is empty and there is a common pool of 36 markers ( which can be used by both players). The first player selects any 3 markers and gives it to the 2nd player to place on the board. After the 2nd player’s placement, he in turn chooses 3 markers and gives it to the 1st player to place on the board. The game proceeds in similar fashion in turns. The first player to complete any row or column or the 3x2 rectangular box wins ( he does not have to use all his 3 markers to accomplish this). A player loses if he cannot legally place all his 3 markers. The tactics lie not only in the placement but in the selection of the markers to give to the other player. I give examples of poor play when one cant place the 3 markers , and good play and a winning play.