In this heads-up game, the "swapping mistakes" theory doesn't quite ring true. After all, is a mistake really a mistake if no one exploits it? The mistakes you trade to your opponent are worthless to him because he doesn't do what it takes to profit from them. You capitalize on his mistakes, but he ignores yours.
That's fair enough. But if we extend our discussion to a three-handed game, you'll see that you really are swapping mistakes. Say you're playing in a game with the same "call every bet" opponent and another, sawier one. Your savvy opponent plays like a normal person. When you bet, she'll call only if she thinks she's a favorite. And she'll bet when she thinks it's the right play.
The thing is, she's underbankrolled. While you and the calling station play with $10,000 stacks, she plays with only $100 at a time. With the addition of a tough spot to your game, should you revert to a perfect strategy?
33 This is one time that we use the word "mistake" in a different way than the Fundamental Theorem of Poker way.
No, you shouldn't. You should play almost exactly as you played before; you check every hand to the river and then move in with hands favored over a random holding.
The key is that the savvy player has only $100. Your crazy strategy is full of mistakes, and she's going to exploit them for profit. When she actually bets her $100, both you and the other player will, on average, be big underdogs to her. She'll make money from both of you.
But she's chipping away at you only $100 at a time, while you're pummeling the other guy for $10,000. You're making mistakes, and someone is now exploiting them, but that doesn't matter. You're trading small, $100-sized mistakes for big, $10,000-sized mistakes.34 You're much better off doing that than making no mistakes and letting your calling station opponent keep his $10,000 too often.
In practice, your opponents won't be as dense as the "call them all" player described above. Even bad players who frequently make big mistakes will catch on sometimes if they are getting destroyed. If someone keeps calling and losing, after a while he'll start folding a few hands. And if someone folds hand after hand to your bluffs, eventually he'll decide to call.
So you will, in practice, always be swapping mistakes with your opponents. They make mistakes, and you attack them, making theoretical mistakes of your own. Sometimes your opponents will hit the spot you left open. That's fine, as long as you're trading a little for a lot.
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