If you comb through poker strategy books or articles written on this website, you will repeatedly find assertions that poor poker players may win money in the short run but will lose money in the long run. The converse is true for professional and very good players. They may lose money in the short run but will generally win in the long run.
Why is this exactly? It is because of a concept known as expected value (EV). Expected value is your expected return on a wager. For example, suppose you made a bet with me on a coin flip. If it is heads, I give you $100. If it is tails, you give me $1. Should you theoretically take this bet (assuming that the coin is fair and has a fifty-fifty chance of landing on heads or tails)?
Definitely! There is a 50% chance of it landing on heads, meaning you win $100. Thus, your expected win is $50 (0.50 * $100). If it lands on tails, you lose $1. Thus, your expcted loss is $0.50 (0.50 * $1). Your expected profit is the expected win minus the expected loss. Thus, your expected profit is $49.50.
Obviously, you will not win $49.50. You will win $100 or lose $1. However, you should view the bet as "winning" $49.50. Outcomes in gambling are influenced by chance in the short run. However, in the long run, your outcomes will very closely reflect your expected value. If we did the coin flip example a million times, your final profit would be extremely close to $49.5 million.
So how does expected value play out in a poker game? The most clear manifestation of expected value is pot odds theory (pot odds, as well as implied odds, reverse implied odds, etc.). The whole idea of pot odds theory is that you should only draw to a hand when you have a positive expected value.
Other examples of expected value are demonstrated in the advanced moves below.
There are 8 players in the pot and you are the small blind (first person to bet). You check, and the player in the big blind position bets. Three players call. Should you call?
No, you should raise! Why? There is a 35% chance you will hit a flush on the turn or the river. If you hit this flush, you will more than likely scoop the pot. If you raise, 4 players will call, meaning you will only be putting in an additional 20% of the pot. Thus, if this was a $1-$2 game, you would have an expected value profit of $0.75 (0.35 x $5 - $1).
Please realize that this is an imperfect example. The expected win only considers the flush draw. You also have overcards, which means you could easily win if a ten or an Ace falls as well. However, there is also the chance that someone may hit a full house, so you'd have to decrease it by that. Someone could also reraise behind you and knock others out, which may decrease your expected value. Nonetheless, hopefully this example shows why some fancy plays are used.
Bluffing and calling bluffs depend on expected value. When you make a bluff, you should have some estimate in your head about the bluff's chance of success. This chance of success should meet with a positive expectation. For example, if the pot is $100 and I make a bluff of $50, I need at least a 33% of the bluff's working (assuming I have 0% chance of winning if I am called). This is because I need to win 1 out of 3 times in order to break even.
Expected value also helps clarify the differences between big mistakes and small mistakes. Big mistakes occur when a player makes a decision that has a very high negative expected value whereas a small mistake is when one gives up a small amount of expected value.
If you plan on playing poker a lot, you should eventually be able to know your expected value of an hour of play. In order to do this, you need to keep accurate records. You should record the amount of time you spend playing, the type of game, and the place where you played. After a while, you will be able to reasonably estimate your expected win or loss per hour of play (you need to log at least 200 hours at a given location and limit to have a decent estimate).
Expected value is another reason why you should never play in a poker game that you cannot afford. If you play with scared money, you will be reluctant to play when you have a small edge. You will give up a lot of expected value on some hands, which will probably turn you into an overall loser.
In blackjack, everyone grimaces at being dealt a sixteen. It's the worst possible hand and odds are you are going to lose your money. The hold'em equivalent to a sixteen is a 7 2, which is considered the worst possible hand. However, with a 7 2, odds are you will lose nothing (because you will fold preflop) or just your blind. In fact, I don't even mind being dealt 7 2 because I know what it's worth. I'm much more afraid of being dealt A A because that hand has the potential of costing me a lot of money. The paradox that a good hand is to be feared much more so than a bad one centers on the most important concept of poker: Relative Hand Value.
Everyone knows that to win at poker, you must maximize your wins and minimize your losses. Maximizing your wins is fairly easy. Slowplaying and trapping help accentuate these wins, but the reality is that any fool can win a decent amount when he has a good hand. What generally separates a winning poker player from a losing one is how the two players lose their hands. The winning poker player knows how to dump his second-best hand while the loser will call it down and lose at the showdown.
To me, the psychological difference is generally that the losing player must satisfy his need to know what the other guy had. The desire to be a policeman and make sure his opponent isn't bluffing and to make sure he didn't lose what he could have won causes him to call when he shouldn't. The winning poker player has overcome this innate desire and forces him/herself to play well.
Now that I have brought your attention to what the second-best hand is, how do you play them? It really depends on Limit vs. No-Limit poker.
When you play a fixed-limit game, calling with the second-best hand won't kill you quickly. You will notice your negative bank balance only in the long run because you will win sometimes in the short run. Generally, the best way to minimize your losses from second-best hands is through preflop play. Don't go in with hands without a decent kicker (i.e dump K8, A7) because those are often dominated hands. Having a dominated hand means that you're up against an opponent with a similar hand but one will almost always beat the other. Some examples are AA vs. AQ or AK vs. A9. The hand that is dominated has 3 outs or less (AQ must catch two queens without an ace hitting or a straight to win). Thus, correct preflop play can minimize second-best hands because you call less with dominated hands due to kicker.
Flop play is a bit different. Suppose:
You definitely have second-best hand potential, but how do you tell? Well, generally the best way is to bet or raise at flop and see what happens. If you encounter a lot of resistance, you're done for. Also, if there is a large multi-way pot, go ahead and fold. Someone is bound to have the Ace.
When you play no-limit hold'em, it's a totally different ball game. In a fixed-limit game, you won't lose too much on one second-best hand, but you can easily lose your whole stack at no-limit. That's why, in a no-limit game, it's best to play the nut-like hands more. In other words, pocket pairs go up in value because of their ability to hit a set and so do connecting cards because of their ability to hit straights. Ace-suited goes up in value too because of the nut flush, but people are generally very aware of the flush potential and will shut you out at the flop when you hit a flush draw.
Since these hands go up in value, what goes down? AQ, AJ, KQ, KJ, etc. These hands are the ones that can get destroyed at no-limit poker. These hands will win small pots with top pair, but will lose large ones when someone else hits a set or a straight.
The key to no-limit poker is not necessarily dumping these second-best hands preflop. It's sniffing out what other people have on the flop. Do not simply call bets with the second-best hand; you must raise to see where you are. When someone bets at you, they are threatening your whole stack (if the bet is a signicant one). You must reciprocate by threatening theirs.
In this example, you could be in a lot of trouble. Someone betting at you could have JT or TT. It's important to figure out their relative strength by raising them at the flop.
Now, many will ask, "Well, couldn't they just bluff reraise me?" Of course they could, but that will cost them a lot when you finally get the nut hand. Simply call the reraise and then zap them out of the rest of their stack on the turn and river.
I have received a lot of questions regarding this topic, so I am going to dedicate an entire article to it. Most advanced players know that Sklansky hand rankings (or my hand rankings for that matter) are not set in stone, but are rather general guidelines for ranking hands. This is because hand value fluctuates greatly depending on the number of people in the pot. Many people are not quite sure how to treat their starting hands when the game's dynamic fluctuates between loose and tight, thus affecting the number of people in the pot. The answer to this dilemma lies with what type of hand you hold, and how many players this type of hand is suitable against.
I am going to divide the types of hands into three categories:
Most of this is written assuming the game is longhand limit.
These are 'premium' hands that people hope to receive. They have a lot of value in of themselves and are not board-dependent to win. People generally raise preflop with these hands for value, but often a major reason to raise preflop is just to knock people out. For example, consider KK. Unless an Ace hits the board, KK will probably be the best hand at the flop. However, consider this situation:
Both opponents will be tempted to draw to see another card. Someone with two hearts will be drawing as well. All of a sudden, you face a situation where there are seventeen outs against you. Now, while you still have the highest chance out of anyone to win the pot, it is more likely that someone else will win the pot instead of you!
This is a common situation with large pairs, where they are the best hand at the flop but there is enough runners out there that one of them is bound to beat you at the river. Thus, the way to alleviate this situation is to knock these people out of the flop by making raises aimed at limiting the size of the pot. Reraise people after they raised you to make it expensive to see the flop and raise at the flop to knock people out.
For example, in the above situation, suppose you were in early position and there were 5 people at the flop. You should consider checking the flop hoping for a check-raise to knock the people between you and the original better out. This way, people with 5 outs or less won't be in the pot against you, and you have to worry less about longshot draws beating you.
Big cards like AK, AQ, KQ are great for shorthanded games, but often a curse in longhanded games. While big cards can at least become an overpair and win money from someone whose hand won't likely improve (such as top pair plus top kicker), these hands are the ones that make top pair + top kicker. Thus, when you hit the board with these hands, unless you are outkicking your opponent or your opponent is an idiot, he or she will generally be on a draw against you. Thus, you generally want to go ahead and take the pot down at the flop, or at least make it very expensive for your opponent to see the turn.
These hands change drastically in value depending on the situation. Assuming a non heads up situation (where small pairs do well simply due to the chance of your opponent not hitting anything), these are hands you want to play in a multi-way pot. You generally won't hit much with these hands, or you will hit a very nice hand like a three-of-a-kind, flush, or straight. The overreaching goal with these hands is to have pot odds in your favor. (Note: Ax suited plays a lot like a suited connector.)
If you have a suited connector, you are hoping there are enough callers and dead money in the pot to justify drawing to the straight or flush. Pot odds is why these hands will show a profit with four or more people in the pot, but will generally be poor against two or three opponents. In a multiway pot with a suited connector, you may have a flush or straight draw (that will win if you hit) but only must put in 1/10 of the pot to see the next card, which is very good odds.
If you have a small pair, you are hoping for the 13% chance of hitting a set on the flop. So if 7 people are in the pot, you have the exact pot odds for a set. However, for small pairs, not only are the pot odds good for a set, the implied odds once you hit your set are great. If you hit your set, chances are good that someone will have a second-best hand that has a slim-to-none chance of beating you.
There's a good chance that someone will pay you off with a King or maybe even a Jack. Small pairs really begin showing their profit potential with around 5 or more people in the pot.
A common question about the small pair strategy is "How should I evaluate the set potential of large pairs?" After all, I talk about how the implied odds once you hit a set are generally great. Unfortunately, this does not apply to large pairs.
If you hit a set with a large pair, there's a good chance it will be top set (meaning there's no cards on the board that are higher than that), so you won't get much action from anything besides draws. In this example, there's only so much action you can get from a hand like K J.
When playing poker, you will often find yourself on a draw after the flop. To decide how to play your draw, you should consider the pot odds, implied odds, reverse implied odds, and the chance of a redraw.
Pot odds means the odds you need to need to justify a call, just based on the money in the pot and assuming you will win if you hit a draw. For example, if you have a flush draw on the flop, you have 9 outs. This means you have a 19.1% chance of hitting a flush on the turn. To justify a call just based on pot odds, you assume you will win if you hit the flush, but will lose otherwise. Therefore, amount you call must be lower than 19.1% of the pot to justify a call.
Think of pot odds in this manner: Suppose you are at a raffle. The raffle is giving away $100 in cash to a lucky winner. You have a 20% chance of winning. How much would you spend to have a 20% chance to win $100? The correct answer is up to $20. Your 'expected' win is $20 (.20 * $100 = $20).
A poker pot is very similar to this raffle. However, your 'ticket' is a bet, and it also becomes part of the prize. If the pot is $100 and you must call $20, you will in fact be winning $120 if you win (the pot plus your bet). Thus, you need at least a 20 out of 120 chance to win (16.7%).
However, the problem with basing your decision solely on pot odds is that it neglects bets in future rounds. It also neglects the chance that you may already have the best hand, and it assumes that the opponent won't draw out against on you. It also does not take into account that you could be drawing dead, meaning that the hand you are trying to hit will still not beat the hand an opponent currently holds.
Implied odds are the odds that take into account future bets. For example, if you have a 19.1% chance of hitting a flush on a turn, you can theoretically afford to call up to 19.1% of the amount of money you would expect to win at the showdown. There is no way to always know exactly how much you will be able to win on future betting rounds; this is something you have to guess on your own.
Reverse implied odds and redraws involve the chance you hit your hand and lose anyway.
You have a 19.1% chance of hitting a flush, but not necessarily that high of a chance of winning. Someone may have or hit a full house. Thus, you have to consider how much you could lose if you hit your flush, but still lose the hand. Another example is if you have a straight draw, but there are two cards of the same suit on the board. Someone else might be on a flush draw. Even if you hit a straight, you may not win because that other player might hit a flush. So just because you have a 31.5% chance of hitting a straight on the turn or the river, it does not mean you have a 31.5% chance of winning. Basically, the idea behind reverse implied odds and redraws is that you do not automatically win once you hit your draw. You must consider the chance that you will lose even if you hit your draw and must guess the amount of money you will lose on future bets if that happens.
Calculating pot odds is a powerfool tool. However, don't just use the calculations to make all of your decisions. It is a helpful tool, but you should also consider implied odds and reverse implied odds. You should also factor in the chance that you may already hold the best hand, and the possibility that you face a raise from behind you.