[hannibal5]

I can see the possibility for confusion here.

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.

[iopq]

Yes, you can.

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.

[hannibal5]

>Assume he is playing the Nash equilibrium strategy.

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.

[jib]

No you don't need to know what the opponents strategy is. You calculate based on worst case (ie op playing perfect) and worst case is you break even. There is no way to maximize profit but you can play unexploitable, ie at a minimum not lose and possibly win assuming op doesn't play perfect.

[hannibal5]

In poker optimal strategy is not winning strategy.

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.

[ianstallings]

Yes I tend to agree here, that "optimal" strategy could be defined as making the least amount of mistakes. While a poker player also needs to minimize mistakes, sometimes to increase your expected value in future betting rounds or future hands one can make a mistake and get more value from it.

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

[iopq]

That's just not accurate. An optimal strategy beats everything but itself, against which it ties. Are you talking about rake? Because antes are included into the poker strategy.

For example, you would raise more often when the antes are higher, regardless of the other player's strategy.

[jib]

I think the point he is trying to make is that if your goal is to maximise your profits then it is not always optimal to play the nash equilibrium strategy. That is true.

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.

[ianstallings]

Yeah in heads up play using a Nash equilibrium to "balance your range" and play a more unbeatable strategy while also using it to calculate probable hands your opponent holds might be helpful, but it's far from a solution to the problem of devising a winning strategy that always works. I think that's why he calls it academic. Because it won't work in the real world.