How about we play competitive Pokemon instead?
Its got all the reads, bluffs, random chance, meta-gaming, math and strategy, and none of the gambling.
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Don't get me wrong. Poker is a great game. But if we're talking about "reading" the opponent, relatively simple decisions that have deep mathematical backgrounds... a large variety of "simultaneous choice" video games (Pokemon, being a turnbased game with 60% to 100% accuracy on common attacks), leads to very rich gameplay, interaction and reads.
I personally see Poker as just one game in a large family of simultaneous-choice, random-chance, incomplete-information high-skill gaming.
Magic: The Gathering is another one. The cards your opponent plays necessarily reveals information (the colors of cards reveals what kind of strategies they are going for, and your opponent chooses to reveal that information only when necessary). I've won games by "holding onto lands" (worthless cards), bluffing that I had a response against my opponent's moves. Just delaying a turn or two (keeping them cautious) bought me the time to draw the cards I really needed to turn the game around.
And I've lost games by going all in (assuming my opponent was bluffing, so I did a high-risk move), and lo-and-behold, my opponent had the "combat trick" needed to break my attack.