Poker is a great game. I can have a fun game of poker with a lot of different types of people. Last summer, I went on holiday with my family, and some of the best moments were spent us all sitting around in the evening drinking beer and playing poker. Some of us have played lots of online poker, some of us barely knew the rules, but regardless of experience or skill level, it's still fantastic fun trying to figure out how each person plays, what they bet when they have good or bad cards, who is getting bored, who has the more obvious tells, etc. The game not only encourages social interaction, but creates some brilliant gameplay mechanics by utilising psychology of the players.
The great thing about using psychology as part of your game, is that firstly it's inherently accessible. People understand people. You don't need to read a rulebook to understand what a bluff is, you don't need months of practice to learn you can scare people by playing aggressively. If it's the main mechanic in your game, anyone can play! It's the ultimate in accessible, intuitive depth.
The second great thing about psychology is that it scales tremendously well - it's relevant at low level play, and equally relevant at high level play. Even at the highest levels of poker, players are still struggling to work each other out underneath the hats and the sunglasses. As players get better at noticing 'tells', their opponents get better at hiding them. Typical new players mistakes can be emulated by experienced players, pretending they are a new player. You have a bluff, then a double bluff, then a triple bluff. You pretend you have a strong hand when you have a weak hand. Then when the opponent works this out, you pretend to be pretending to have a strong hand, when you really do have a strong hand. When your opponent says "I KNOW you're bluffing this time!" and you turn over a hand full of aces, it's brilliantly fun in a way much more rewarding than simply calculating some odds
The third great thing about psychology is that it's different every day. The way a player plays poker could be different when he's tired, when he's hungry, when he's drunk, when he's had a lot of coffee, when he's bored, when he's angry after a recent loss, etc. If all these things should be factored into your analysis of your opponent, and that analysis affects the choices you make in the game, this creates an incredibly deep game!
The fourth great thing about psychology is that it doesn't get old. Predicting your opponent is not a mechanic which becomes out of date, and so games which involve psychology have an inbuilt resistance to time. Do you want players to continue playing your game for years and years? Add psychology.
The fifth great thing about psychology is that it's funny. I remember playing an old game of Team Fortress, and I was fighting an enemy with my rocket launcher, and he was trying to dodge my rockets, and because my rockets were a bit slow, I had to try to predict where he was going to go before I fired. At this particular time, he had a few options: there was some cover he could hide behind (but an accurate rocket might hit behind the cover), there was some open ground he could move into (staying vunerable to future attacks), and there was a bonfire that he could jump onto (but he'd get burnt and lose some health). It turns out, I shot a rocket at seemingly the most unlikely place - the bonfire, and at the same time, he jumped onto the bonfire and died from both the rocket and the burn effects of the fire.
I remember this moment because I laughed out loud at how ridiculous it would seem to a bystander, why would I fire there when only the stupidest of players would go there, and why would he go there, deliberately burning himself? That's something you remember, something you talk about, something you put on youtube. It's lodged in my memory as another brilliant psychology interaction in games. Where you're not interacting with some dumb robot, it's a real person, making real decisions, trying to work out who YOU are and what YOU'RE likely to do. And if you win because you saw their humanity, and emphasised with it, it makes you feel connected in a way that most computer games don't achieve.