Some time ago, I asked myself if infinite gomoku is a first player win, which seems not proven yet, and while searching for an answer I often heard the term "strategy stealing game".
I just thought it means that the second player will always lose if both players play correctly, or always player one in some rare cases, but now I checked Wikipedia and it seems like that only means that player 2 doesn't have a guaranteed winning strategy in such a game...
And the more I think about it, the less sense it makes for me. Shoudn't it be good if the second player has no way to win for sure? I mean if he had, it would be a second player win game, just as bad as a first player win game.
For example in tic-tac-toe. Player 1 can't win if player 2 doesn't make any mistake, player 2 can't win if player 1 doesn't make any mistake. No one has a guaranteed winning strategy. Is it, or is it not a strategy stealing argument? Shouldn't it be just like that?
A strategy-stealing argument is one that includes the idea "But if player A had a winning strategy, then player B could use that strategy (or a slight modification of it) to win the game."
A classic example is the game of chomp. The game is played on an $m\times n$ grid of squares and players 1 and 2 take it in turns to eat squares. Specifically, a move consists of choosing an uneaten square $(a,b)$ and then eating all squares $(x,y)$ such that $x\geq a$ and $y\geq b$. The square $(1,1)$ is poisoned so whoever is forced to eat it loses.
Theorem. Player 1 has a winning strategy, except in the case $m=n=1$.
Proof. If $m=n=1$, player 1's only possible move is to eat the poisoned square, which loses. So, suppose that $(m,n)\neq(1,1)$ and suppose, towards a contradiction, that player 2 has a winning strategy. That means that, for any first move player 1 might make, player 2 has a reply that allows him to win the game. In particular, if player 1's first move is $(m,n)$, player 2 can force a win by playing some move $(u,v)$. Notice that the position after the moves $(m,n)$ and $(u,v)$ is identical to the position that would have arisen if player 1 had just started by playing $(u,v)$. So, instead of playing $(m,n)$, he could have played $(u,v)$ and then used player 2's supposed winning strategy to win the game. Therefore, player 1 has a winning strategy, contradicting our assumption that player 2 has one – they can't both be able to force a win!
Chomp is a two-player game of perfect information, with no ties, so one of the players must have a winning strategy. Since player 2 does not have a winning strategy, player 1 must do. $\quad\Box$
As for your question about whether this is good or bad, it doesn't really make sense. It's like asking if prime numbers are good or bad. They're neither: they just are.