I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.
http://en.wikipedia.org/wiki/Pie_rule
http://en.wikipedia.org/wiki/Strategy-stealing_argument
This is a good question.
You will find a detailed analysis of Nash's "strategy stealing" argument along with extensive implementation details in
Jack van Rijswijck, Set Colouring Games, Ph.D. thesis, University of Alberta, 2006:
https://webdocs.cs.ualberta.ca/~hayward/theses/jack.pdf
Stealing strategy (See Section 10.2, starting on page 104): If there were a winning strategy for the player to go second, then the first player could “steal” this strategy by making an irrelevant move, and then ignoring this move and applying the winning strategy. This strategy works because the extra piece can never be a disadvantage, a fact which itself would need to be proved.
The paths to follow for implementation of this and other strategies is given in Part II, starting on page 101.
In the Pie Rule, the second player may steal the first move and play as if they were the first player. So if the First Player had a winning strategy, then the Second player could steal it. In other words, for all combinatorial games with perfect info with the pie rule either Player Two has a winning strategy or both players have a drawing strategy.
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