Find a great strategy to a pentomino type game

Question

I have a game.

Given an $8\times 8$ square and a set, which contains the pentominoes and four $1\times 1$ squares. Players alternately pick one item from the set. Then players (starting with the player who had chosen the first item) take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board.

So I need a great strategy. I am sure there doesn’t exist a winning strategy (and if so, then it is complicated), so I only need a strategy which helps to win.

Answer 1

This game is described in Golombs' Polyominoes (p. 8-9). He writes:

It is difficult to advise what strategy should be followed, but there are two valuable strategic principles:

1. Try to move in such a way that there will be room for an even number of pieces. (This applies only when there are two players.)
2. If a player cannot analyze the situation, he should do something to complicate the placement so that the next player will have even more difficulty analyzing it than he did.

Since this reference is quite old, you may be able to dig up some further work on this topic.

Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.