Hold'em Brain: The River

The River Paradox

On the River, you want to avoid two types of mistakes:

1. Folding with the best hand
2. Calling too often with the worst hand

These two mistakes run counter to each other, I call it the River Paradox. You do not want to make the mistake of folding a winning hand, but you also do not want to make the mistake of calling too often when you are beat. Folding on the River when you have the best hand is a costly mistake. Pots are usually of substantial size by the River. When a pot is stolen from you on the River, it is difficult to make up for the loss. These mistakes do not have to happen often for it to be costly. Calling on the River too often without the best hand does not cost as much, but it will occur more often. This is a small mistake on any individual hand and only costs one big bet. But the opportunities to make this mistake will occur frequently. When this mistake is repeatedly made, the cost adds up quickly. It is difficult to balance the play on the River to avoid both mistakes.

How does one solve the River Paradox? By figuring out the tendencies of opponents, reading hands well and being prepared for situations before they happen. This chapter will give you the tools to solve the problems on the River.

Heads-up play on the River is more interesting than when there are more players. With 3 or more players, the pot is usually large enough that manyt players will call with legitimate hands that have any chance of winning. The discussion here will start with heads-up play then go on to some interesting multiple player River situations.

Thinking on the River: Heads-up

There are four variables that you need to think about on the River when heads-up (down to just two players). These issues are reflected in the "General Table for Heads-Up River Play".

1. Are you the first to act or the last to act? (Shown in the column headings on the table)
2. You have to estimate the probability that you have the best hand. You have been thinking about this issue since the first two cards. The River is the culmination of this thought process. (Shown in the row headings in the table.)
3. You have to know how your opponent plays. Is he passive or aggressive? Will he value bet or check it down? Will he bluff or not? (Shown in the 2nd and 3rd columns)
4. Given you know the answer to the first three variables, you have to come up with the best plan to maximize profits and/or minimize losses.

General Table for Heads-Up River Play

Your chance of having the best hand	You are first to act & he is Aggressive	You are first to act & he is Passive	You are last to act against a check	You are last to act against a bet
0%	Check or Bluff	Check	Check or Bluff	Fold or Bluff
25%	Check-Call	Check-Call	Check	Call
50%	Check-Call	Bet, unless he was on a draw, then Check-call	Check	Call
75%	Check-Call / Bet if it looks like a draw made it	Bet, unless he was on a draw, then Check-call	Bet	Raise / Call
100%	Bet / Check-Raise	Bet	Bet	Raise

% of having the best hand: A Note

It is difficult to estimate your probability of having the best hand. You need to be able to think critically about the development of the hand as well as have a good idea of how your opponents play. After reading this chapter, the usefulness of being able to pinpoint your probability of winning should be clear.

You can have the same probability of having the best hand in a variety of ways. It is not as static as this table shows. You can think you have a 50% chance of winning while your opponent knows whether he has a 0% or a 100% chance of winning. This can happen if he was on a draw. For example, if there is a possible straight draw and a possible flush draw on the board, and a card comes that completes a possible straight draw, you will not know if he has a straight or a busted flush, but he will know. You can also think you have a 50% chance of winning while your opponent thinks the same. For example, you could have a split middle pair of T's with a A kicker, thinking your opponent either has top pair or middle pair with a worse kicker. Meanwhile, your opponent could have top pair with a bad kicker and think you have a top pair with a better kicker or middle pair. In that case, both of you will think you are close to having a 50% chance of winning.

Difference scenarios may provide you with the same probabilities of having the best hand. You need to act according to the situation instead of just the probability. These issues are discussed in the sections of "50% of having the best hand" and "75% of having the best hand".

0% of having the best hand: First to act

If you have no chance of winning, then your decision is whether to bluff or to fold.

Here are some ways you may be able to bluff successfully:

1. If you think your opponent is weak too, a bet may win the pot. If your late position opponent checked on the Turn after you checked, then he may be weak. It may be he is inducing a bluff, but it could be because he does not have much of a hand himself. The strength of your hand is no longer relevant, what is relevant is the probability he folds.
2. A scare card comes on the River (an overcard, especially an A, and a third flush card are the most common forms of scare cards). If it looks to your opponent like you may have been on a draw, then one of these cards may help you bluff successfully. For example, if you had AK and were drawing to a pair when the Flop came with two cards to a flush, you should consider betting on the River if the River card would complete a possible flush. Your opponent may have thought that was the reason you were calling and make the mistake of folding when you bet on the River. Of course, you will need to choose to make this bluff against an opponent that can fold. You would not want to bet into a calling station since they are unlikely to fold.

0% of having the best hand: Last to act

Aggressive players may bet on the River when they are first to act because they do not want to miss a bet if they are ahead. Against the players who may bet for value with little edge, a raise as a bluff has a greater chance of succeeding. If they bet with little edge, your raise may convince them that their original evaluation was wrong. Against passive players who are less likely to bet for value, a raise will not work as often, because they are usually in the mode of checking and calling. When passive players check they are not giving you any information about the strength of their hand. But passive players can bluff too. When they have a legitimate hand, some passive players are more likely to check with the intention of calling. They are less likely to bet for value. So when they do bet, it means either they have a great hand or they are bluffing. If you know your opponents well, then you will have a good idea of when and how often they like to bluff.

25% of having the best hand: First to act

If you only have a 25% chance of winning, you should typically check with the intention of calling. Most of the time, you will have enough pot odds to showdown your hand, so the question is to bet or check with the intention of calling.

Here are the different possibilities involving betting and checking.

1. If you bet and your opponent does have a better hand, he will call or raise and you will have lost one bet.
2. If you bet and your opponent has a worse hand, he will fold so you do not gain anything.
3. If you check and your opponent has a better hand, he will bet and you will lose one bet.
4. If you check and he has a worse hand, your check may induce him to bluff.

Here is a table assuming he always bets when you check to him (either because he has the better hand or because you induced him to bluff). The table also assumes if you bet, he will call with a better hand, but fold with a worse one.

Your Action	You have best hand	You have worst hand
Bet	0	-1
Check with intention of calling	+1	-1

Checking with the intention of calling as a strategy dominates betting in this case. If you have the best hand, then you win one big bet if you check but none if you bet. If you have the worst hand, you will lose 1 big bet either way. Against this simple opponent, you should always check with the intention to call a bet.

Here is an EV table with a more realistic passive opponent. The pot size is 6 big bets. If you bet, your opponent will always call. So if you bet and have the best hand, you will win 7 big bets. If you check, your opponent will only bet with his best hands. He will bet 25% of the time and check 75% of the time. When he bets, it is when he is absolutely sure he has the best hand (if you knew this, then you would fold, but let's assume you don't know that).

Action vs passive player	Computation	Result
EV when you bet	(25% x 7) + (75% x -1)	+1.00
EV when you check	(25% x 6) + (25% x -1) + (50% x 0)	+1.25

The table shows that you should check when you are the underdog and your opponent is passive. If you bet, you are basically betting his hand for him, even when he is too scared to bet it himself.

Let's take a bit of a tangent here and compare this scenario to the scenario when you have a 50% chance of having the best hand. It is important to discuss this now is so you can see that the choice of checking or betting against the passive player is dependent on the probability you have the best hand. You should not be checking against a passive player in all situations.

Action vs passive player when you have a 50% of having the best hand	Computation	Result
EV when you bet	(50% x 7) + (50% x -1)	+3.00
EV when you check	(50% x 6) + (25% x -1) + (25% x 0)	+2.75

When the probability of you having the best hand increases up to 50%, then you have a greater EV when you bet than when you check. The point where the EV of betting and the EV of checking (against this passive player) are equal is when you have a 37.5% chance of winning. This is the case when your opponent acts as described, and the pot size is irrelevant (you can put in 100 for the pot size and get the same difference for the EV of betting and checking). Figuring out the probability that you have the best hand is difficult. It takes skill in reading the other player's hand as well as experience in understanding different situations in Hold'em. But if you can do it well, you will have an easier time choosing whether to bet or check.

Let's go back to when you have a 25% chance of having the best hand. Let's switch the opponent to a sharp, aggressive player. Because he is sharp, he will fold when you bet the best hand, but call when you bet the worst hand. Consider two different levels of aggressive players when you check.

Those that will bet 100% of the time when you check and those that will only bet 50% of his best hands when you check (compare this to the passive player who bets 25% of his best hands when you check).

Action vs different aggressive players	Computation	Result
EV when you bet	(25% x 6) + (75% x -1)	+0.75
EV when you check and he bets 100% of the time	(25% x 7) + (75% x -1)	+1.00
EV when you check and he bets 50% of the time	(25% x 6) + (50% x -1) + (25% x 0)	+1.00

Against either player, it is also better to check with the intention of calling rather than betting. Although not listed, against the opponent who will bet with 75% of the time, your EV is the same as when you bet because he is not betting when you have the best hand, just like he was not calling when you bet and you had the best hand.

25% of having the best hand: Last to act

If you are last to act with a 25% chance of winning, you should check. A better hand will usually call when you bet, but a worse hand likely will not. This means you are not getting value when you have the best hand but are giving away value when you have the worst hand. The only advantage to betting is if you can pull off a successful bluff. But you have a hand that can win 25% of the time. That means you need to convince your opponent to fold with a relatively strong hand (which is rare), in order for a bluff to work. Remember, if he folds a worse hand, you did not gain anything by betting.

The only time you may want to bet is if your opponent is loose and aggressive. The fact that he did not bet when he is first to act may mean that he does not have a good hand. In that case he has given you new information by his actions (as opposed to the passive player who always checks so his action does not give you new information). Thus you can upgrade your opinion of your own hand, possibly to 75%. If he is loose, he will call (this is not the same as when your opponent thinks you may have made a possible draw on the River, in that case, the aggressive player's check may simply reflect his fear that you were on a draw, and you should check as well).

If he bets, you will usually have pot odds to call (just 3 big bets would do). A bluff is not a good idea for the same reason listed when your opponent has checked.

50% of having the best hand: First to act

Against passive players who were not on a draw, you should bet when you have a 50% chance of having the best hand. They will call your bet often, but if you check, they will bet only with their best hands. Let's take a look at an expected value equation for a situation like this. Your opponent is a passive player who plays straightforward. If you bet, your opponent will always call.

Since you believe you have a 50% chance of winning and he will always call, the expectancy for betting is zero. However, if you check, your opponent has the option of betting or checking. Like most passive players, he will not bet unless he is confident he has the best hand. Let's say he only bets 20% of the time, but during those times, he has an 80% chance of having the best hand. The other 80% of time that he checks, he has a 42.5% chance of having the best hand. On average, these numbers are consistent with your assumption that you have a 50% chance of winning (20% x 80% + 80% x 42.5% = 50%). Let's also assume there is already 5 big bets in the pot. This assumption is important, because if there were no bets in the pot at all, then you could simply fold once he bets since he is more likely to have you beat when he does bet.

Action vs passive	Computation	Result
EV when you bet	(50% x 6) + (50% x -1)	+2.50
EV when you check	(20% x 80% x -1) + (20% x 20% x 6) + (80% x 42.5% x 0) + (80% x 57.5% x 5)	+2.38

The EV of betting is greater than the EV of checking (2.50 vs 2.38). So you should bet against a passive player who was not on a draw.

Against passive players who may be on a draw, you will have to check and call. For example, there are both straight draws and flush draws (and you are not sure which one he was drawing to). One of the draws gets there on the end. You still do not know if you have the best hand or not, but your opponent knows. If he has a busted draw, you cannot bet since he will not call. The best plan would be to check in order to induce him to bluff. If he has made his draw, then he will call or raise when you bet.

A table previously shown when you have a 25% chance of having the best hand and are first to act applies here too.

Your Action	You have best hand	You have worst hand
Bet	0	-1
Check with intention of calling	+1	-1

Here is an example.
Your hand: A♣A♠
Board: J♥T♥2♣ [turn] 3♠ [river] 9♣

Your opponent raised you on the Flop and checked on the Turn which makes you think he is on a draw. The 9♣ could have made a straight draw, but not a flush draw. If your opponent had two hearts for a busted flush draw, then he will not call if you bet. But if he was on a straight draw with KQ, then he will raise you. If you check and he was on a busted flush draw, then he may try to bluff to win the pot. You think your chances of having the best hand is close to 50% but your opponent has more information than you, he knows if he has made his draw or not, he knows if he has a 0% a 100% chance of having the best hand. It is better for you to check and call rather than bet. In this situation, the passive player has unwittingly turned into an aggressive player due to his hand.

In this EV chart, assume the passive opponent was on a draw. You do not know if he has made it or not, as far as you know, there is a 50% he made it and a 50% he missed. But he knows whether he has made it or not. If he did not make it, he will bluff 10% of the time and give up and muck his hand 90% of the time.

Action vs when your passive opponent is on a draw	Computation	Result
EV when you bet	(50% x 6) + (50% x -1)	+2.50
EV when you check	(50% x 10% x 7) + (50% x 90% x 6) + (50% x -1)	+2.55

You do not gain that much by checking compared to calling, but you still gain. Passive opponents will not bluff that often, but given the chance, they may bluff once in a while with nothing. The key here is that if you bet, you cannot win any bets. But if you check, you will either win the same amount or more if they decide to bluff. If he will never bluff, then the EV of betting is the same as the EV of checking if you are willing to call when he bets. But if he never bluffs, then you would actually fold when he bets, so checking is still better than betting.

If you are against an aggressive player who will bluff when you check (whether or not he was on a draw), then you should check and let him bet. Here is the EV table against an aggressive opponent who will bluff 40% of the time he has the worst hand when you check.

Action vs aggressive	Computation	Result
EV when you bet	(50% x 6) + (50% x -1)	+2.50
EV when you check	(50% x 40% x 7) + (50% x 60% x 6) + (50% x -1)	+2.70

Against an aggressive opponent, you should check and call because he is willing to bet more often than he will call.

In summary, the key is the opponent and what the type of hand he is playing. You want to bet against passive opponents who are not on a draw (this is because they are likely to call you when they have a worse hand if they were not on a draw, but if they had a busted draw, they are not going to call you). You want to check with the intention of calling against aggressive opponents who are willing to bluff with hands that they may not call with if you had bet. You want to check with the intention of calling against passive opponents who were on a draw and you are not sure if they made it or not.

50% of having the best hand: Last to act

Before the early position player acted, you thought you had a 50% chance of having the best hand. Once the early position player acts, he may or may not have given you information. If the early position is a passive player, then he will usually check even if you would bet in his place. This means he has not given you any extra information when he does check. So you should lean towards checking because he may fold with his worst hands, but will always call when he has the best hand. If you bet, he may call 95% of the time. 50% of the time, he has a better hand, 45% of the time he has a worst hand and 5% of the time he will fold with the worst hand. A bet has negative value in that case.

However, against sharp and aggressive players, their check may give you useful information. Their check may signify they do not have anything (otherwise they would have bet as they are afraid to miss a bet), but it could be trying to induce you to bluff too. If you are not sure, lean towards checking as well. If you know your opponent's tendencies, then you can use that information to decide to check, bet with the intention of calling a check-raise or bet with the intention of folding to a check-raise. For example, against a loose and aggressive player who likes to bet, you should consider betting when he checks.

If the opponent bets, you should call if his bet has not changed your opinion about the probability you have the best hand.

75% of having the best hand: First to act

If you are heads-up against a passive opponent and you have a 75% chance of winning, the strategy is to bet. You cannot count on the passive player to bet if you check, so you should bet and hope he calls. But if you think your opponent may have been on a draw, you should check with the intention of calling, as discussed previously.

If your opponent is aggressive then you have more options. You can bet or you can check with the intention of calling or raising. It will depend on how loose the aggressive player is. If you are check-raising, you want a player to call with a worse hand than yours. If you think the aggressive player will bet but not call when you check-raise, then you might as well bet. Instead of taking the chance that he checks with a worse hand, you want to bet to make sure he does pay you off.

An aggressive player can turn into a passive player if he thinks you were on a draw and the draw comes on the River. In that case, you should no longer think of the player as an aggressive player if he is going to act like a passive player in this situation. You should now definitely bet because he is less likely to bet if you check. An aggressive player is more likely to check if he thought there was a chance you were on a draw and it looks like the draw made it. In that case, the aggressive player will no longer play aggressively but has turned temporarily into a passive player. For example, you have top pair with top kicker. The board contained two cards of the same suit and the River card is at third card of that suit. If you are planning to call after you have checked anyway, you might as well bet. This is because it will be hard for any hand that you can beat to bet after you have checked, even from an aggressive player. For example, the aggressive player would not bet one pair with a lower kicker if he thought there was a chance you were on a draw and the draw made it. But he may call thinking you are trying to use the scare card to bluff.

75% of having the best hand: Last to act

If it is checked to you, you should bet against any player. If a player has bet, you can consider calling or raising. If you decide to raise, you need to have a back up plan in case you get re-raised. Against certain players, a re-raise can only mean they have the nuts, so you have to be aware that you are willing to fold if you get re-raised against this player even before you raise him in the first place. Against some sharp players, they may not call with a worse hand if you raise on the River, so that means a raise has no value (against these players, you should throw in a bluff now and then). When you do have the best hand, he is not going to call, when he has the best hand, he'll call or re-raise.

100% of having the best hand: First to act

If you think you are guaranteed to have the best hand, then you have the nuts. Against passive players, you have to bet since they will not. Against aggressive players, you may decide to bet or try a check-raise. Here are the reasons to check-raise against an aggressive player.

1. You are quite sure he will bet based on the play of the hand. Check-raise to get more money into the pot (although sometimes you may want to bet and let him raise so you can re-raise - this depends on how aggressive the aggressive player is, and the texture of the board).
2. You want to check-raise for future value. You want to be able to check-raise on the River with a bluff, so if you try for a check-raise with the nuts, your opponent may remember it and fold to you in the future when you try it again.
3. You want to check-raise so that he gets the message that he should not bet for value against you. You want to convince him that a check by you in first position does not necessarily mean you are weak.

100% of having the best hand: Last to act

This is the easiest situation. Bet, raise and re-raise. Have fun!

Thinking on the River: multiple player pots
Three players or more on the River

If there are three or more players on the River, you should play straightforward. Bet if you think you have a high chance of having the best hand, check if you are not that confident. Call if you have a reasonable chance of having the best hand relative to the pot size. When you consider bluffing, you need to consider the possibility that all players will fold, not just one.

When not to raise even you have the best hand

If there are more than two players, you may not want to raise if you can make more by just calling.

There are a couple of examples.

Example: When you have the nuts

There are three players in the hand and you are second to act. You have the nuts. The second player bets. You are absolutely sure that both players will fold if you raise. But the third player may call if you just call. You do not gain anything by raising, but if you call, you may be able to get the third player's chips too.

Example: When you probably have the best hand, but not the nuts

You have a 60% chance of having the best hand, and you are the second player to act in a 4-way pot. You think the first player has 40% chance of winning. Both the third player and the fourth player are calling stations with 0% chance of having the best hand. If you raise, both calling stations will fold. If you call, there is a 50% chance that exactly one of them will call. If the first player bets, you should not raise even though you are a favorite to win the hand.

Action	Computation	Result
EV when you call	(60% x 50% x 7) + (60% x 50% x 6) + (40% x -1)	+3.50
EV when you raise	(60% x 7) + (40% x -2)	+3.40

The EV of raising (+3.40) is lower than the EV of calling by 0.10 big bets. You should call when you are not that confident you have the best hand and hope a bad player calls also.

Large Pots on the River

When the pot is large, it does not take a high winning percentage for a bet or a raise to be correct. Say the pot contains 10 big bets and you have a 15% chance of winning and there are two other players in the hand. If you can successfully bluff 10% of the time with a raise, then a raise could increase your winning percentage up to 25%. We can compare the expected values of calling and raising to see which one is a better play.

Action	Computation	Result
EV of calling	(15% x 10) + (85% x -1)	+0.65
EV of raising if you can steal the pot 10% of the time	(25% x 10) + (75% x 2)	+1.00

Raising is worthwhile in a situation like this, but only if you have actually corrected estimated the percentages that all the players will fold. Your raise has to make both players fold which is obviously more difficult than getting one player to fold. For example, if both of your opponents will only fold 5% of the time when one of them has a better hand, then the chance of you winning has only gone up to 20% from 15%. Here is the expected value of raising against these opponents.

Action	Computation	Result
EV of raising if you can steal the pot 5% of the time (added to the 15% of the time when you have the best hand)	(20% x 10) + (80% x -2)	+0.40

If both of these opponents only fold 20% of the time, then a raise will be a losing play compared to calling. As usual, the equations show that knowing the players and how they play is crucial to the game. The equations by themselves do not provide an answer, it is the user input that is the key to the equations.

Why is it correct to call on the River with zero EV or slightly negative EV

If you play against the same opponents all the time, there is value to calling on the River even if the call has slightly negative EV. This is because your calls on the River will reduce the chances that other players will try to bluff you on the River and induce you to make the monumental mistake of folding a winner on the River. Since that is the biggest mistake you can make, there may be value in giving up a small amount of edge to prevent those mistakes from happening. Of course, this concept can be taken too far. You would not want to call when the pot odds is offering you 5:1 when you have only a 10% chance of winning.

Example

It is the River and your opponent has bet. You estimate you have a 25% chance of having the best hand. After your opponent's bet, there is 3 big bets in the pot. Calling would be a zero expectancy play (75% of the time you lose 1 big bet for a net of -0.75 big bets, 25% of the time you win 3 big bets for a net of +0.75 big bets, adding these two together gets an expectancy of 0 big bets). If you played this hand 1000 times, it wouldn't matter if you always called or always folded. However, if you fold on the River too often, your opponents may think you play weakly. They may be tempted to bluff or semi-bluff against you more often in the future in order to run you off the best hand. You do not want players to be taking potshots at you.

If you are seen as a player who folds when the going gets tough, other players will soon start to notice this and take advantage of you. You need to pick and choose to pay off on the river even with zero EV or slightly negative EV for future considerations. If the percentages seem close, even if it is slightly the worst of it, lean toward calling rather than folding. This should reduce other players taking advantage of you if they can assume you will fold to a raise or semi-bluff.

Last to act: Inducing a bet or call on the River with a check on the Turn

If you are last to act, there are times when you want to check on the Turn with a hand that you think is a favorite to be the best hand, but you are not sure. If you are ahead, you think your opponent may be sufficiently weak that he will not call a bet anyway. This means that when you do have a hand, it may be best to check on the Turn in last position, thus possibly inducing a bluff from a weaker hand on the River. If you are behind, you do not want to get check-raised. So if you check on the Turn and your opponent bets on the River, you will only lose one bet, which is the same amount you would lose if you had bet on the Turn. This type of play works best if a free card you are letting your opponent see on the River (it is a free card because you have chosen to check the Turn, which means if he is behind, he is seeing the River for free to get a shot at beating you), has a low chance of coming on the River to beat you.

Example

You have K♠9♠ on the button and you open-raise pre-Flop. Only the big blind calls your raise.

Your hand: K♠9♠
Flop: K♣8♠3♦

You bet and the big blind calls.

Turn: A♥

At this point you may want to check. It would be tough for your opponent to call another bet unless he had an A or a K. If he had a lower pair, the presence of the A on the Turn is going to be a very big scare card for him. Thus you are in a position where your bet may only be called by a better hand. Of course, your opponent may call with a worse K, but your kicker is fairly weak. Your opponent will now have a hard time calling with just a pair of 8's since there are two scary cards on the board. If the A did not show up, he may just hope you had AQ or something like that and keep calling you. When you check on the Turn, you hope he will make a bet on the River with a pair of 8's to try to get a hand like JJ or QQ to fold. But even if he checks to you on the River, he will be more likely to call a bet by you on the River with just a pair of 8's than he would have if you had bet on the Turn. If your opponent has a weak A, he will likely call on the Turn, at which point you may choose to check on the River and lose the same amount as if you had checked on the Turn and called his bet on the River. However, he could choose to check-raise which means you now have to pay an extra bet in order to see the River.

When a player raises on the River into two other players, it is rarely a bluff

When two or more players have already committed chips into the pot on the River, it is difficult to bluff. The probability that one of them will call a raise is high. By betting or calling, they have announced they have a hand that can win a showdown. So when a player does raise into two or more players, it is rarely a bluff and likely means a strong hand, oftentimes the nuts.

Here is an example. On the River there are three players left in the hand.
Board: A♥K♥5♣ [turn] 3♠ [river] J♥

The first player bets, the second player calls. If the third player raises, then it is unlikely that it is a bluff. With this board, it is probable that he has a flush or a straight. In order for a bluff to be successful, the raiser would have to induce both of the other players to fold after he raised. Since two players have already committed chips into the pot, and the pot is relatively large, it is highly likely that at least one of them will call and be the "sheriff".

Getting counterfeited

One of the worst feelings in Hold'em is to get a made hand counterfeited. This can happen when you already have a made hand using both of your hole cards, but the Turn or River allows for someone with just one card to have the same hand or better. Every time this happens to me, I weep a little inside.

Here are several ways to get counterfeited.

1. Two pairs getting counterfeited by a higher pair on the board.
   Your hand: 65
   Board: T-6-5 [turn] Q [river] Q
   
   You flopped two pair (6's and 5's). When the Q's show up on the Turn and the River, your five card poker hand is now Q-Q-6-6-T, the 5 in your hand no longer plays and is useless. This means that a player with a pocket pair 7's or higher, a T, a Q or a 6 with a 7 or greater, now has a better hand than your two pair.
2. Pocket pair getting counterfeited by two higher pair on the board.
   Your hand: 22
   Board: 5-4-4 [turn] 3 [river] 3
   
   On the Flop, you had two pair, 4's and 2's. By the River, you are playing the board. This means you have the worst possible hand because any player with any other card either has a better two pair, a straight or a higher kicker than a 5.
3. Flush using both of your hole cards counterfeited by four flush cards on the board.
   Your hand: 3♣2♣
   Board: A♣8♣7♣ [turn] 4♣
   
   You flopped a flush using both of your hole cards. But with the fourth club on the Turn, anyone would have a higher flush with just one club in their hand. It doesn't seem fair that they can use one card to make their hand when you can use two cards, but this is Hold'em, not Omaha.
4. Straight using both of your hole cards counterfeited by four cards to a straight on the board.
   Your hand: 76
   Board: T-9-8 [turn] J
   

You flopped a straight using both of your hole cards. But the Turn makes four to a straight on the board. This means any player with a 7 has the same hand you have, and any player with a Q would have a better hand.