Expert Concepts:
1. When to Fold
2. Big Mistakes
3. River Betting
4. Hold'em Edges
5. Adv. Game Selection
6. Expected Utility
7. Expected Utility 2
8. Poker Professionals
In other languages:
1. When to Fold
2. Big Mistakes
3. River Betting
4. Hold'em Edges
5. Adv. Game Selection
6. Expected Utility
7. Expected Utility 2
8. Poker Professionals
In other languages:
Big Mistakes vs. Small Mistakes
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In poker, a mistake is a play with a negative expected value. (For more information about expected value, check out our Expected Value article.)
Good gamblers understand that the only thing that matters is expected value. Luck means you win sometimes and lose sometimes. Over the long run, the luck will even out. The only thing that matters in the long run is the expected value of the bets you make.
So a small mistake is a decision with a small negative expected value. For example, you are playing $.50$1 nolimit and make a decision that has a $.05 EV. Five cents is not much money in a $.50$1 nolimit game, so this would be categorized as a small mistake.
So how do you know which mistakes are 'big' mistakes? Basically, you have to take into account three factors:
1. The quality of your hand against your opponent's actual hand.
2. The probability that your opponent would have that hand versus other hands under similar circumstances.
3. The size of the pot.
Let's analyze each of these factors in depth.
First, let's examine factor #1: your actual hand against your opponent's actual hand. If you knew exactly what you and your opponents held, you could figure out the probability of who would win using our Hand Simulator.
You  Opponent  Flop 
Your chance of winning in this situation is about 87%. Thus, if you bet $50 and your opponent called $50, you would expect to receive $87 on average. Basically, making that bet earns you a profit of about $37 in the long run.
Of course, you do not always know what cards your opponents have. Because of this, you must take into the account the fact that you are putting your opponents on a spectrum of hands. Here is an example of where you are uncertain of what your opponent holds. The reality of poker is that you will never know for sure what your opponent holds. Nevertheless, your reads of your opponent will enable you to make an educated guess of what your opponent's hole cards may be. Consider this example, where you have made certain reads on your opponent:
Your Hand  Board 
You have deduced that there are only two possible hands your opponent could have: A K or Q J. There is an equal chance that he holds each of these hands.
In this situation, the EV = 0.5 * (chance of winning against A K) + 0.5 * (chance of winning against Q J).
Your chance of winning against A K is about 13%, and your chance of winning against Q J is about 53%. Thus, in this example, your overall chance of winning is about 33%. As you can see, your overall chance of winning is highly dependent on the percentage chance you think your opponent has Q J versus A K.
Being able to reasonably estimate the chance than an opponent has a certain hand takes a lot of experience and skill. The important thing to remember is that when evaluating a mistake in retrospect, you need to factor in the chance that the opponent may have had a different hand. Poker is a game of limited information, which needs to be accounted for when evaluating the severity of a mistake.
The final component of analyzing the size of your mistake is the size of the pot. This is because the size of the pot affects the expected value of decisions you make at the table. For example, suppose your opponent bets $20, and you know through your infinite poker prowess that you have exactly a 25% chance to win. Should you call?
Well, it depends on the size of the pot. If the pot is $0, clearly not. That would be a mistake of roughly $10 ($40 * 25%  $20). However, let's say the pot is $100 before your opponent makes the bet. In this case, you would only be putting in $20 into a final pot of $140 ($100 plus the two bets of $20). Since you have a 25% chance to win, your expected value from the pot is $35. Since $35 is much more than $20, you should call. If you had folded, you would have made a $15 mistake.
The most obvious reallife example of how the size of the pot affects decisionmaking at the table is pot odds. Essentially, pot odds is a shortcut for evaluating factors #1 and #2. You assume that your hand probably is not good enough to win as is, and you assume that you will win the pot if you are able to hit your draw. Hence, the chance of hitting the draw is equal to the chance of winning. What the other players have does not matter since you are assuming they are able to beat you unless you improve your hand.
Thus, with pot odds, you simply calculate the expected value of staying in the pot. If the EV is higher than the amount of the bet, you go ahead and call.
There are many situations where people may make large mistakes and do not realize it. Consider this example:
Your Hand  Board 
You flopped top pair. There is $10 in the pot. A fairly tight player goes allin in front of you for $25. What do you do? Let's analyze this situation given the three factors mentioned previously.
Factors #1 and #2: Your opponent could have many different hands. He could have top pair with a better kicker (AK), a set (88), two pair (A8), or a draw (K Q). He could also have some other hands like a pocket pair (QQ) or top pair with lower kicker (A9), though these hands are much less likely.
Factor #3. The size of the pot. In this case, the size of the pot is small in comparison to the size of the bet. The pot is only $10, so your opponent's bet is 2.5 times the size of the pot. You need a fairly high chance of winning to justify the call.
Now, let's analyze the different hands your opponent could have, and the EV of calling if he actually had it.
Opponent's hand  Your chance of winning  Your EV  

Likely Hands  Top Pair, Good Kicker  13%  $17.20 
Set  2%  $23.80  
Two Pair  15%  $16.00  
Draw  62%  +$12.20  
Unlikely Hands  Middle Pocket Pair  87%  +$27.20 
Top Pair, Bad Kicker  82%  +$24.20 
As you can see, you should probably fold. You are at best a moderate advantage and very likely at a huge disadvantage. If the pot is so big that you are only putting in 10% of the pot, you should probably call. However, in this case, the bet is large in relation to the pot and you expect this player to probably have a good hand. Because of this, you should fold.
The above example illustrated a player making a huge mistake because he made a loose call. However, many poker players have the opposite problem: they make huge mistakes at the poker table and do not realize it because they think they are making "great laydowns." The decision to fold in a pot can be even more disastrous than the decision to call a bet.
For example, suppose you are playing a $5$10 fixedlimit hold'em game. There is $80 in the pot.
Your Hand  Board 
A player bets $10, two players call. You decide to fold.
Suppose it turns out that other the three players had the following hands:
Opponent #1  Opponent #2  Opponent #3 
It turns out that you had a 12.5% chance of winning this hand. In this situation, you would have put in $10 into a final pot of $120 on the turn. If you hit your straight on the river, you probably would have won an additional $10 to $20. Thus, in reality, you would only be putting in $10 to win about $135. If the 9 came out, you probably would not end up paying off on the river because the other players would start raising each other with four clubs on the board.
Thus, your mistake in this situation was worth $6.87. The EV of staying in the pot was about $16.87 and you would need to pay $10 to stay in that pot. In a $5$10 game, EV of $6.87 is a pretty big mistake, since that's about 0.7 big bets. Most people average a fluctuation of about one big bet per hour at each limit hold'em table they play, so this is a pretty big mistake.
Next Article: River Betting
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