I wanted to pull off Aseem's comment on there possibly being more than one way to play "correctly". That thread is too large to have a conversation on a sub-topic so here it goes...

First, semantics. I think there are many situations where there is more than one "profitable" move to make. Correctness as I use it is about maximizing profit over a statistically significant number of occurrences of the exact same situation. The correct play is the one with the highest EV. So the question then becomes, for a given situation, is there a "standard play" that has the highest EV of all available plays?

The answer IMHO depends on how sophisticated your opponents are. In my low-stakes play, I've run into 3 types of players:

1) Those who are (barely) capable of playing their cards. You know them. They check/call or bet/raise any piece of the flop right to the showdown regardless of acti0n, number of opponents or texture of the board.

2) Those who are capable of playing the situation. They take into account the board, possible draws, prior action.

3) Those who are capable of playing the opponents. They notice limp standards, raise standards, cold calls and steal attempts. They have a better sense of ranges of hands they could be up against, and what the action is likely to be on future streets.

Now against type 1 and type 2 players, I think there is only 1 correct play at any moment in time. Why do I htink this? Because type 1 will their cards the same each and every time, and type 2 will respond to a particular betting line by you the same way each and every time. A certain betting line has a very predictable and stable EV in this kind of environment. Given the same situation enough times over and over you could simply measure the EV of each line, compare them and conclude that one line is "correct" and all others, even though possibly profitable, are "incorrect".

Against type 3 players, things change. Table image impacts the future decisions of your opponents. Each play has an immediate EV relating to the profit or loss resulting on the current hand, but it also has an impact on the EV of all future hands. I think this is where you can get more creative and take different approaches to the same hand. I dont even know for sure if there multiple correct ways to play, but there is certainly a hard to quantify component of EV that one could use to defend alternate approaches.

After all that I dont know if I agree or disagree with Aseem. I think I more or less disagree with him, although there is a chance he is right under specific conditions.

All this is not to say that it is obvious what the correct play is or ought to be in any particular situation. Arguments about what is or isn't the correct line to take are completely valid. Unless you have a mountain of pokertracker data to back you up, some of the small differences in EV are not readily apparent.

From a game-theoretic perspective, it's certainly possible for there to be more than one correct way to play.

This might sound strange at first, as you could argue that, for any given hand and set of opponents there is one and only one play that maximizes expected value. This is true for an isolated hands, but when you consider a player's actions over many hands, there could be two or more correct sequences.

How is this possible. Since poker is a strategic game of incomplete information, how you play depends on how your opponents play. If you are playing against novices, they might not react to or even take note of your style of play. Against such players, there is only one way to play since you can't change their play by altering yours.

But more sophisticated players pay attention to your actions and adjust their play to yours. This creates a complicated feedback system where changing your behavior changes your opponents behavior and may cause you to further change your own behavior. Such a system could easily have multiple equilibria. Think of each equilibrium as a style of play, and you see that two different styles of play can be correct.

How do you end up with one style of play versus another? You could start in one stable equilibrium and some random event could shift all the players in a game to a new equilibrium. Or your equilibrium could be determined by your endowment of different poker skills. Players who are good at reading people may end up more naturally in a different equilibrium than players who are good at calculating odds.

Rog:

Interesting post. I believe that in 90%+ of SSHE games, for the vast majority of your villains, your first two scenarios hold true and there is one best way to play it.

I really think things only get interesting with mixing up styles at the higher limit games.

I also believe that, to determine the single most +EV play in any SSHE scenario, you would have to well versed on the interrelation of the following concepts:

1) Pot Size
2) Position
3) Hand strength
4) Villain's playing style (and hand range)
5) Pot Equity
6) Fold Equity
7) Pot Odds

I think that only with a solid understanding of how these seven main ideas interrelate can determine one most +EV play for any situation. I may be missing something, but I think you get the general idea.

By no means do I believe that every decision will always be incredibly clear cut and obvious (and I can admit I make plenty o' mistakes myself), but I believe that, with a mastery of theories by Ed Miller and David Skalansky, it becomes much easier to determine the most appropriate play.