Mathematically Incorrect To Fold?

Note: 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).

Great Post WBS, I agree that a lot of players put to much value in the math of poker. that is not to say that the may is not of value, just that some I feel over value it. The math I feel is more of a guideline than a hard and cold way to play;we are playing against people after all, not computers.

In limit games, it is usually not incorrect not to fold because of the pot size but because making a one bet mistake (calling with the worse hand) is worse than making a huge mistake (folding and losing the pot). This, in turn, makes the play a correct mathematical decision in the long run, but not all the time:

If I have middle pair and the pot is 15BB against a tough/savvy player on the end, I don't want to fold altough I'm probably beat because if the bet is 1BB, I'm getting 16:1 wich, if we figure even a small bluffing/worse hand chance, makes this a winner in the long run. But the thing is, how did I get there with middle pair ? Why didnt' I fold before the pot got so big ? Will villain bluff/ have a worse hand this 10% of the time ? Probably not. Pots don't get big by themselves unless you're playing in a very, very soft game (wich most online games nowadays aren't, even at low stakes).

So I don't think the problem (big leak) is calling a single bet on the end, it's calling several on previous streets with a moderate strength hand wich in turns build up the pot and makes us put in more money than we should. Because making a mistake on an earlier street and continuing with that mistake maginifies the hit our hourly takes, wich in turn makes our game less profitable/holds us back.

Also, I think NOT folding in big pots HU with fair hands makes you less exploitable than folding does, if we are talking LHE. C/C turn and river OOP with KK on Qs4s5s6s9x if the pot is moderatly big (7-8BB) can be better than b/f, especially against a thinking opponent due to WA/WB situation.

Thid doesn't mean that we shouldn't take on reads and info into consideration when making a play, on the contrary. Our pot odds and effective odds should be weighted against the most probable hand ranges of a certain villain. If it gets capped and I have JJ against a nit and an Ace flops, I'll probably let it go. But if I have AA against the same opponent and the flop comes 478 all spades, I will be tempted to think that I am very much in front since he won't cap 44,77,88, SC and the like and the only hand he can have me WB is AKs.

I don't think you are fully understanding WHY something is mathematically correct (or at least, you are not giving it a fair shake).

Poker isn't a "reads vs. math" game: having a read, putting a player on a hand, etc., IS doing the math, not something that is contrary to it.

Since poker is a game of incomplete information you can only assign certain probabilities to your opponents hand (their range according to your read). You then make your decision based on comparing the event probabilities (their hand : your hand) with the money probabilities (bet : pot). If you have a part of your equation wrong, then your decision will subsequently be wrong as well.

If you are 90% certain that you are beat in a hand (given your "read") and you are only getting 7:1 on your money to call, then you are making a mistake to call. Of course, quantifying the percentage of your read is one of the tough things to do in poker. But if you "know" your opponent will only raise preflop with AA, KK, QQ or AK, and you have JJ facing their raise, then doing the math here (18 ways to have a bigger pair, 16 ways to have AK) is essential to playing well in the hand.

Reads and math intrinsically go together, they are not contrary or opposed to one another.

Edit: excellent post Jeff. You can't make decisions in a one hand at at time bubble-- poker is a long term game.

Good post on an important issue.

Math is just one of the tools available to make correct decisions. As any tool, if used incorrectly, it will produce bad results.

I think it is important to realize that math is never wrong. It is the assumptions made that are wrong. Blind reliance on "rules" is not a good thing in poker. If you have a good reliable read in a situation, it should trump a general math rule.

On the other hand, there are many situations when math can be applied alsmost mechanically. This is especially true in tournaments where our read on opponents is limited and when stacks are so short that we often have to make decisions based on odds alone.

I think that not using enough math is a more prelevant problem than using it too much. Many people dislike math and don't learn even the basic applications to poker. They are doing a great disservice to themselves. Surely one can learn proper play by experience, but it takes more time and more lost money.

For example, I have seen many people call with flush or str8 draws on the flop against a single opponent with good-sized stacks. If they do this often enough, eventually they will realize that this is a bad play and stop doing it(especially if they use tracking software). It is much simpler, however, to learn pot odds and realize that such call is -EV since the odds are 2:1 against.

I think that poker math knowledge provides a solid foundation to build your game on. It saves a lot of time and money to learn "from experience". As long as a player realizes that math is just ONE tool available, proper application of math will help the game of a player.

That summarizes it all! Well said, AG.

I agree completely o MOTM, you can see the evidence in the first two comments. I hate the false dichotomy that the OP seems to insinuate, and that a lot of players would love to believe because they don't want to learn the math.

Now that is a bit of a misrepresentation of my statement, I went on to say:

that is not to say that the math(sic) is not of value, just that some I feel over value it.

The point was that most people UNDER value it, or at least a great many more do than overvalue it. In fact, it would be pretty hard to overvalue the math in poker, imo; use it incorrectly, maybe...
The general tone seemed to be that of underplaying the importance of math, and I couldn't disagree more.

Also true. To me it seems that people don't use the math and reads together which goes back what you and cheetah were saying earlier about it being a tool.