2. Dominoes are a game tool, a set consists of 28 pieces, each piece is divided into upper and lower sections by a straight line, and each section is marked with a number of dots. The 28 pieces of dominoes are numbered as follows: $6-6, 6-5, 6-4, 6-3, 6-2, 6-1, 6-0, 5-5, 5-4, 5-3, 5-2, 5-1, 5-0, 4-4, 4-3, 4-2, 4-1, 4-0, 3-3, 3-2, 3-1, 3-0, 2-2, 2-1, 2-0, 1-1, 1-0,$ and $0-0$. Two players, A and B, play a game using the 28 domino pieces according to the following rules: First, A selects a domino piece and writes the numbers in the upper and lower sections on the blackboard; then, B selects a piece from the remaining dominoes and writes the numbers in the upper and lower sections on the blackboard; ... and so on, taking turns. The rule is: if all the numbers from $0$ to $6$ are written on the blackboard, the game ends and the last person to write a number wins. The question is: who has a winning strategy, A or B?
2. Player B has a winning strategy.

Considering that there are seven different numbers from $0 \sim 6$, and for any four of these numbers, there are 10 dominoes that can be formed. Thus, no matter how Player A chooses the dominoes, Player B can reasonably choose such that the different numbers on the dominoes chosen by both players do not exceed four. As a result, after a maximum of 10 moves, all dominoes with these four numbers will be taken. At this point, no matter which domino Player A picks next, there will be at most two different numbers from $0 \sim 6$ left on the board. Player B can then pick the corresponding domino to win.