Mathematically Incorrect To Fold?
I have a mathematics background, so I know many of you will potentially (or almost certainly) have arguments.
I often read strategy articles, even some written by extremely successful players that advise to often call bets at the end of a hand based on the size of the pot. So, if in a fixed limit hold'em game, you face 1 big bet on the last street, you should call if your hand strength is moderate enough and there are at least x big bets in the pot already. There are many mathematical reasons why this is the correct play, and in fixed limit games they have been proven to be profitable in many situations.
However, I do think most players get into the mindset of always calling in these situations because mathematically it may make sense, or because a book tells
them too. I think this takes away from a player's ability to make some critical decisions based on other criteria that could or most likely be more valuable. Putting your opponent on a range of hands and making a read throughout the duration of a hand are the most valuable reading skills you can have in situations like this especially if you haven't played many hands against your opponent. Although I agree that there is much validity in most of these mathematical strategies, many players use these strategies in all situations, failing to instead use them in correct situations or when it is absolutely necessary.
Although calling bets on the end can be profitable in the long run in specific situations, and is an advisable approach to beggining or micro-limit players, it is often something that holds back a player's development. I think this is particularly true for players who want to learn other games (Stud, Omaha 8, Stud 8, Razz) after they have become a winning hold'em player where not losing bets on later streets is so crucial. It also hurts players who want to learn NL and PL variations as they could find it more difficult to get away from hands if they get trapped in this mindset of calling big bets on the end. Developing and strengthening your ability to read situations and play more correctly early on in your career is far more valuable than learning when to call one big bet on the end.
I often find players who in higher limit hold'em games play very predictable and although the strategies they employ are mathematically correct, they are failing to evolve into a stronger player and become easier to take advantage of. To be successful in higher limits, things like mixing up your play (disguising your hand strength) or making good decisions based on the information you have (from the hand or history against your opponent in similar situations) becomes much more important and often essential for you to become profitable. It is often more important than making mathematically correct plays. This is also surprisingly true for online players as there is software out there that gathers and organizes opponent data which makes mathematical and predictable players easier to manipulate. So, in conclusion learning to make the correct decision to fold on the end (either instinctively or through piecing together information you have gathered from the hand and your opponent) can become a much more valuable/profitable tool than learning when it becomes unprofitable to surrender a pot even when you face a bet small enough to justify a call based on the size of the pot.
A player with personality and excellent decision making processes is a far more challenging opponent than one who just makes mathematically correct decisions. So, although employing mathematical strategies is advisable, it should not be the only thing your game develops through and is certainly not the most important (unless you are a learning the fundamentals).