Final Thoughts

The key to no limit isn't always thinking on the fourth or fifth level. Usually thinking that deeply is unnecessary and only likely to lead you to absurd conclusions about what's going on. When you are short stacked, as you often are in tournaments, usually the zeroth and first level will suffice: "What do I have, what does he have, am I getting the right odds?"

You can also easily overthink bad and mediocre players. In our example, second level thinking suggested a good call against your regular Joe (first level) opponent, but left you paying off the expert (third level). If you always insist on thinking on the fourth level to thwart the expert (since he must know that I would take his big bet as weakness since I checked behind on the turn), you'll

Although as a general rule we do not advocate a strategy of being more likely to call a bigger bet on the river than a smaller one, this hand appears to be an exception.

get exploited by the amateur (I think he's weak, so maybe I'll try a bluff now).

Tailor your thinking to your situation and opponent. If you can reliably figure out how your opponents think and stay one step ahead of them, you'll make a lot of money.

Swapping Mistakes

Somewhere out there in math land, there's probably a perfect no limit hold 'em strategy. It's a strategy that never loses in the long run, no matter how your opponents play against you. If they call a lot, bet a lot, or fold a lot, the perfect strategy wins. If they are tricky or straightforward, the perfect strategy wins. In fact, the perfect strategy beats every opponent except another playing the perfect strategy.

What would this strategy look like? Well, it would exhibit many of the principles we've talked about in this book. It would be aware of implied odds, both the odds it gets and the odds it gives. It would call with draws only when it expected to make more on average than the price of the call. Likewise, with good hands it would bet enough (or refuse to pay off enough) to deny its opponents with draws a profitable call.

It would mix up its play to balance perfectly. Every check, call, bet, and raise would be made with a mix of hands sufficiently diversified to avoid divulging useful information about the nature of any specific holding.

We said that this strategy exists in math land, and, at least for now, that's the only place it exists. No limit hold 'em is complex enough that, while we can posit that such a strategy likely exists, and we can figure out what it would be in many individual cases, deriving a general solution covering every possible scenario is virtually impossible.

We can't know exactly what the strategy is, but perhaps we, as students of poker, should strive to play as closely to that strategy as we can get. If perfection is unattainable, surely near perfection must be the next best thing.

For many non-poker games, that reasoning holds true. In tic-tac-toe, the perfect strategy is fairly obvious, and if you play it, you will never lose. On the other hand, if you refuse to play the perfect strategy, you'll find yourself losing game after game to a player who does play it. Perfection is attainable, and it's virtually always the best way to go.

Chess is far more complex than tic-tac-toe, but the same reasoning likely holds. While no one currently plays perfect chess, it's likely that one could play perfect chess. And if you did, you'd never lose.31

But poker is a strange bird. If, somehow, you were blessed tomorrow with the knowledge of the perfect strategy (and stripped of all other poker knowledge), then you'd do quite well. Playing your perfect strategy, you'd be guaranteed not to be a long-term loser, and, in today's games with plenty of bad players, you'd likely win a mint.

But you wouldn't be the best player. At least you wouldn't be if you defined "best player" as the one with the highest average win rate in three- or more-handed games. You'd be a big winner, in the top few percent of all players, but a number of other players would win even more.

How can that be? How can someone play better than perfect? The trick is that we've defined the "perfect" strategy to be unbeatable. It's designed so no one can get the best of you. It is, fundamentally, a defensive strategy.

The biggest winners don't play the perfect defense. They go on the attack, even if it means exposing a few vulnerabilities along the way. They know that it's critical to understand the principles behind that unexploitable strategy, and that sometimes they'll need to fall back on it (or something close to it) when their opponents launch a counterattack. But they'll make the most money taking calculated risks to attack and exploit their opponents' errors.

31 Well, you probably would never lose. In chess, the player with the white pieces moves first, and that privilege confers an unbalanced advantage throughout the game. So it's possible that if two "perfect" players played against each other, white would win every time. But more likely, as in tic-tac-toe, they'd draw game after game.

The key to no limit hold 'em success isn't to play perfectly. It's to swap mistakes with your opponents. You trade small mistakes to your opponents if they will trade back big ones.

What does swapping mistakes mean? Say you find yourself heads-up against a particularly pleasant opponent. His "strategy," if you can call it that, is to call every bet. It doesn't matter what he holds or how much you bet. If you bet, he'll call. He'll also never run out of money (and neither will you); if you bust him, he's always got another buy-in ready.

Obviously, anyone could beat this player. But to win the maximum from him, you have to adjust your play to take advantage of his peculiar calling habit.

First, you'd purge bluffing from your strategy entirely. You shouldn't bluff if you're guaranteed to be called. You'd bet all your good hands on the river, never checking them as you occasionally would out of position against a better player. You'd even bet lots of weak hands you wouldn't dream of betting against a normal player.

Somewhat less obviously, you'd check every hand up to the river. Since you're guaranteed a call, you gain no advantage from betting before all the cards are out (though with some very good hands, you could bet earlier and not give up anything because no card could come that would cause you not to bet).32

This strange "wait until the river and bet it all" strategy is the right way to play against this opponent; it's the way that generates the maximum profit per hand. It significantly outperforms the "perfect" strategy.

Note that you gain nothing from betting early only because it's no limit and because your opponent promises to call every bet. If the game were limit or pot limit, where you couldn't necessarily bet everything on one round, the strategy would be different.

However, it doesn't resemble the perfect strategy at all. If you played that way against typical opponents, you'd get slaughtered. It's tailored to beat this specific opponent and no other.

Your opponent makes huge mistakes; he calls all bets no matter how bad his hand is. If you want to beat him for the maximum, you must be willing to make some "mistakes" of your own: never bluffing, checking good hands on the flop and turn, giving free cards, overbetting marginal hands, etc. You trade your mistakes for your opponent's mistakes, and since his mistakes are bigger than yours, you profit from the trade. If you refused to make mistakes, you'd have none to trade, and you wouldn't make the most of your opponent's willingness to make huge mistakes.33

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