It really isn't that hard in Texas Hold'em most of the time. You are usually only calculating for a few hands, and can memorize odds in advance (since while the combinations of cards is gigantic, the number of actual categories of combinations isn't that many)
That's wrong. Figuring out your true odds against multiple players who can hold an unevenly distributed range of hands requires a bayesian calculation that takes at minimum a few minutes for a human to perform, even using the best software tools for the purpose.
Strong players develop an intuition for this, making estimates on the spot, but they are frequently wrong and can't be very precise.
Just as the Naive Bayes algorithm is remarkably effective, a human approximation is often pretty good. Good enough that the strategy of the AI will be more important than its combinatorics.
