Has the game of texas hold em poker been beaten?

Question

I am no mathematician, I guess this is obvious. I hope this question is appropriate.

So, I know that in poker the opponents psychology matter, but imagine that you are playing against a perfectly logical foe - is there an algorithm that can be followed in order to play the absolute optimal game against a mindless foe?

I know that in math, a beaten game means a game that has all the odds of all the different situations figured out, as I understand it

Answer 1

If you are playing against a single opponent ("heads-up"), then there is indeed an algorithm that will guarantee you non-negative expected winnings. This is simply because of the symmetry of the game $-$ you are playing by the same rules as your opponent. Of course, your opponent can follow the same strategy, which means that your expected winnings will be zero.

But:

1. Such a strategy will inevitably involve making random choices about whether to bluff, call etc. So it might not agree with your idea of what constitutes a strategy.
2. Computing such a perfect strategy is beyond current technology. There are programs that play excellent heads-up poker, but I don't think any of them claim to play the perfect game.
3. As soon as a third player joins the table, there can be no such guaranteed strategy, because the other two players may (consciously or unconsciously) collude against you; and then you will have almost no chance of coming out ahead.