According to David Sklansky, you make money when opponents play differently than they would if they could see your cards. In his book, The Theory of Poker, Sklansky refers to this concept as the "Fundamental Theorem of Poker." Rather obviously, if you bluff at the pot and your opponent folds the best hand, you win. Less obviously, if you can get your opponent to call with improper odds, then you win. The object of winning poker is to make money. In the short run, all sorts of gambles may provide more money, but over the long run, making correct decisions in particular situations will make you the most money. Today I want to discuss preflop play of big hands in limit Hold'em.
Traditional limit wisdom says to raise big hands preflop. Recently, a school of thought has arisen advocating that one should check or limp one's big hands preflop for two reasons. For an example, see Byron Jacob's article on this subject over at CardPlayer. First, this provides deception to one's holding, which increases the likelihood of getting paid off by second best hands. Second, keeping the pot smaller makes it possible to induce mistakes from other players who will call with improper odds. These two are closely related, since obviously players who call your bets with the second best hand are making a mistake, but the second reason is directly concerned with pot odds. Are hands getting the correct odds to call and see the next card? If so, then you haven't induced a mistake. I want to focus on this second reason because I think it actually leads one to play less than optimal against particular opponents.
Let's begin with the reasoning behind this new approach of slow-playing. Let's say you are in the big blind with A-A. A middle position player whom we'll call Fish limps in. The cutoff player limps, a solid player on the button limps in, and the small blind completes.
In scenario #1 you raise and all three players call. The flop comes . The small blind checks and you lead out. Fish calls, the cutoff player folds, but the button raises and the small blind folds.
You think you are still in the lead, but you think Fish is unlikely to raise and so you just call, planning to lead if a safe card hits the turn. Fish calls. The turn card is , which is about as safe as they come, so you lead out and Fish and the button both call. The river is a , and you lead out again. This time Fish raises, the button folds and you fold as Fish must have a single pair beat in order to raise two players on the end.
As it turns out, Fish played much like a fish with , and caught two pair on the river.
Initially we might look at this as just another suck out; but if we look closer then we'll see that Fish had the odds to chase. When you lead the flop, the pot has 11 small bets; hence Fish is getting 11 to 1 pot odds to chase two pair or trip 9s. With five possible cards to improve, this will happen 10.64% of the time on the turn, which means that Fish's odds of doing so are about 8.4 to 1; hence Fish is actually correct to call your initial bet and certainly the button's raise. On the turn, the pot has nine big bets; thus Fish gets 9 to 1 pot odds to call your lead bet. Fish will improve 10.87% of the time on the river; thus Fish's odds to improve are 8.2 to 1, giving the correct pot odds to chase on the turn. Raising preflop, as traditional wisdom suggests, led to a situation in which Fish gets correct odds to chase with only second pair and a bad kicker.
What happens if you check your Aces in the big blind? Now when you lead the flop, Fish has only 6 to 1 odds to call, and makes a mistake in calling for an 8.4 to 1 chance. Similarly on the turn, Fish has only 6.5 to 1 odds and again makes a mistake in calling. Slow playing Aces preflop, then, creates a smaller pot and allows you to induce mistakes by Fish on both the flop and the turn. According to Sklansky's fundamental theorem of poker, you make money when opponents make mistakes; hence you make money by keeping the pot small initially.
Traditional wisdom appears to be in trouble, but I suggest we look at this hand from a different perspective. The object is to make money. As the favorite, do you make more money with bigger pots or smaller pots? The rather obvious answer is bigger pots. Even if you aren't inducing mistakes, you gain more money in the long term by raising preflop.
Let's consider the numbers. Assuming the hand plays to the turn as stated in the first scenario, then 88.13% of the time your Aces hold up, and if Fish and the button fold to your river bet, you will net eight big bets each time. And 10.87% of the time, Fish will hit the river, and in those cases you will lose four big bets. Over the long run, then, raising preflop in this situation will net 6.62 big bets played to the river. By contrast, you win only 4.47 big bets by checking preflop.
The new approach makes plenty of sense. You do indeed profit when other players make mistakes. Clearly, Fish does not err by chasing the larger pot but does with the smaller pot. I suggest, however, that the difference long term is the preflop decision. By raising, you induce a mistake from each caller preflop. This makes more money for you in the long run than does playing for a smaller pot so as to induce mistakes from a single player in later rounds. When you hold a big hand like A-A, you are the favorite preflop, and anyone who calls you is likely making a mistake. Sometimes, however, if there are enough limpers, then players will be getting correct odds to call.
For example, if the small blind in our example has 3-3, then this player has appropriate odds to both complete the small blind and call your raise. A pocket pair is 8.5 to 1 to improve to a set on the flop and the small blind would be getting 9 to 1 odds preflop after your raise, and hence would be correct to call on pot odds alone, not including implied odds.
By not raising preflop, you cost yourself money. The object of winning poker is to make the most money you can, and in this example, at least, attempting to control pot size so as to induce later mistakes from Fish is a mistake on your part. Particularly in a limit game, the biggest mistakes you can exploit are in the preflop hand selection of your opponents. Though I think checking this hand preflop is a mistake if the object is to induce a mistake, since you pass up such an opportunity by not betting now, checking the hand to provide deception is perfectly reasonable in the right situation.
Against a table full of fish, there is no reason to disguise your hand. Fish do not pay attention to the situation and rarely bother to consider what an opponent might have. Traditional wisdom is correct here as well. The best strategy against a loose, weak table is to bet your hands for value. As the level of competition increases, however, you will need to mix up your game. This will induce mistakes from better opponents who may call with a top pair and good kicker to your over pair. When you show your hand on the end, this will send a message to the rest of the observant players at the table: you are unpredictable and players better be careful when you bet post flop as you may well have limped in with a monster. This will allow you to win more pots with your weaker hands. The less predictable you are, the more difficulty good players will have in playing against you. This is all to your advantage. By contrast, fish have difficulty, no matter the opponent, because their own game is so full of holes.