Opponent modeling is purely advantageous, but not necessary
* Q: What’s a Nash Equilibrium or “game theory optimal” strategy? – Failed Math, Port Perry, Ontario A: An equilibrium strategy is one that wins the most money possible against a perfect opponent (this does not mean an opponent who can see your cards, but one who always knows your range whenever you take an action and makes the best choice against that range). In the game “rock, paper, scissors,” the equilibrium strategy is to randomly choose between the three options, choosing each one a third of the time in the long run. Finding equilibriums in poker is much more complicated, but the concept can be useful when you’re playing lots of hands against tough opponents. For example, if your opponent bets half the pot on the river after a particular series of actions, the pot is offering him 2-1 on his bluff. If he were a perfect player, the right thing to do would be to call his bet a third of the time, since if you called more he’d exploit you by never bluffing and if you called less he’d exploit you by always bluffing. In reality, of course, our opponents are never perfect, and so the idea of playing an equilibrium strategy at the table is usually pretty academic. *
You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up.
But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equilibrium that would be optimal in actual game against specific strategies.
Your opponent has 1352 different hand combinations. Assume he is playing the Nash equilibrium strategy. Make the perfect plays based on this. If he plays worse than the Nash equilibrium strategy, you beat him. If he plays perfectly, you tie.
Assuming your opponent plays perfectly works in chess. Chess programs are stronger than the best humans now.
You you can't do that assumption because you don't know what the strategy is. You can calculate Nash equilibrium only if you know the strategy your opponent is using. In full no limit hold em there is no single strategy winning strategy, so you don't know the strategy your opponents are using.
An optimal strategy’s goal is to loose the least against any arbitrary strategy. It is a strategy that is impossible to exploit in poker because poker has antes.
Poker players must seek maximal strategy. A maximal strategy’s goal is to win as much as possible against a specific strategy.
For example, you would raise more often when the antes are higher, regardless of the other player's strategy.
The optimal strategy beats everything but an equally good strategy, and ties against itself, but it doesnt necessarily maximise profits against other bad strategies.
If you are able to identify flaws in your opponents strategy then you can play non-game theory optimal to increase your profits against that perceived strategy. Doing so comes at the cost of you yourself no longer playing the best strategy though.
There exists strategies that gives higher yields vs certain unbalanced strategies than the game theory optimal strategy (or strategies - for all we know there are several optimal strategies in limit hold'em).
For instance - in limit poker if your opponent will never raise, call every street, but not call the river with anything less than a pair, regardless of what you do, then bluffing every river is a more winning strategy than the game theory optimal strategy. The game theory optimal strategy would include times when you do not bet the river, for balance, but knowledge of your opponent's flawed strategy would tell you that betting 100% of the time has a higher yield.
I'd like to add that how poker players generally define as their main goal, to maximize expected value: http://en.wikipedia.org/wiki/Expected_value
You can solve equilibrium for simplified poker games like just Heads Up with only shove or call an all-in options though.
It's theoretically possible to find Nash equilibrium over all possible strategies but that's not winning strategy. You just lose as little as possible. You lose against most/all strategies.
Take for example Kuhn poker (https://en.wikipedia.org/wiki/Kuhn_poker). It's very simple but first player has several optimal strategies.