*Games Psychics Play*
Preface: I think this game turned out to be gamist. I apologize if the setting (and anything else) is completely incomprehensible.

You need: -A special deck of 52 cards: 13 have a circle on them, 13 have a triangle, 13 and a 5-pointed star and 13 have 3 wavy lines on them (These are similar to the cards used to detect paranormal powers). If you absolutely must, you can use a deck of cards and use the suits instead.
-several tokens, coins or whatever

Actions:
When you want to do an action, the GM deals you 3 cards. You use your "real" psychic powers to guess each card, turning them over to see if you are right.
Successes:
0: You fail embarassingly!
1: You succeed barely at the last moment.
2: You succeed with style.
3: You succeed spectacularly! You are so cool! In fact, you become The God of The Game! While you are TGOTG, you are immortal and all your actions succeed spectacularly, but you do not gain Lucky Stars for the duration. This lasts until the GM decides you've had enough fun (can be 1 scene or several minutes depending on the tone of game you're playing). Several players can be TGOTG at the same time, but their actions must complement spectacularly.

Cheating: To get successes consistently, you probably need psychic powers in real life, in which case what are you doing playing RPGs;)?
The other way is to Cheat. There are 2 ways to cheat:
Peeking: Pay the GM 1 Lucky Star and you can peek at 1 card before making a "guess." You can do this as many times as you have Lucky Stars.
Begging: If you can get another player to give the GM 1 star, they can look at the 3 cards, and tell you how many of each suit there are.

Zero Stars: When your Lucky Stars pool reaches zero, after completing your successful action, *YOU DIE*. After 5? minutes the GM will let you return. When you return to play, you must come up with a rationale for your return, eg. if you were last seen in a car going off a cliff, you describe how you think you crawled to safety at the last second. It's obvious that you should create a spectacular death which leaves plenty of opportunies for cheating death and/or planting new adventure seeds (PC and GM).
When you return, you refill your Lucky Stars pool to 4. Gameplaywise, you can see that "dying" is not the hindrance it is made out to be in other RPGs, and is in fact a very viable game tactic.


CHARACTER CREATION: Choose 1 of these Origins:
-Sport: You won the genetic lottery by yourself. You overcame the odds and continue to strive to overachieve. Every time you fail, you gain a Star.
-New Boy/Girl: You were genetically engineered to have psychic abilities and were raised in the lap of luxary. Since you are beautiful/handsome, elegant and talented, you have high standards to live up to and therefore get 1 free Peek every 5 minutes.
-Homunculus: Some experiments don't turn out quite as expected, possibly because some experiments are performed by nutcases in their garages. You are a grumbling parasite upon the psychic community. Every 5 minutes, you can demand a Lucky Star from any player or the GM (but never the GM twice in a row) and also recieve an additional Star from the GM.
-Legacy: You come from a long line of werewolves/ shamans/ vampire hunters, etc. You are one of the true heroes of the world. Everytime you get reborn, you refill your pool to 7 Stars.
-Normal Folk: These groupies still make up over 99% of the world's population, serve to diversify the gene pool and provide moral support. Every 5 minutes, you can award 1 Lucky Star to 1 player (can be yourself).

Setting: "All the world's a casino!"
Contemporary with advanced genetic engineering. And psychic powers are real. Traditionally, powers happen randomly, manifesting as "sports" (cf. the genetic term). These days, genetic tampering has changed the odds.
Going public with your gifts ensures you a life of the spotlight and opportunity. Rich sponsors are known to aggressively pursue gifted individuals. You never know when a psychic detective will come in handy.
When there's no pressing matters at hand, it's time to cash in on your investments. Conflict must be made to satiate the public. There's a formality about the whole affair. Performing in front of an audience is a key. A quiet duel is not without its attractions, but there's just *something* about having thousands watching with their hearts in their throats.
The coin and fame are worthy prizes, but for the elite, the great ones, it's all about the game, the thrill, the eternal challenge.
... until next game, it's time to celebrate with a slow waltz into the night under a rain of floating dollar bills.
However, the traditional dreamspeakers, skinwalkers, etc. who have watched over their peoples from the shadows for millennia aren't thrilled by these glory-seeking pretenders.

Code of The Psychics: Think of the honour in old duels. Also consider the Code of modern-day magicians.
I'll explain the incorporation of "Cheating." Think about high-stakes card playing. All players are trying to look for an "edge" be it picking up a slight physical cue or something more outright. Since this world involves psychics who have ESP and whatnot, I don't think calling finding an edge anything else except "cheating" would be appropriate. It is also social commentary.

Tone: This setting might seem similar to my earlier EXO which feature duelling superpowered troubleseekers, but that game a fist-waving, gimmick-ridden, spastic freight-train world of noise and motion for people who can't shut up.
This setting is all about "the touch of class." It's about effortless brilliance and never losing your cool. The world can be lit by sweeping classical colours or the tacky neon of Las Vegas. But there's a knowing confidence and calmness to the preceedings.
The point of the game is to look and be cool. It's more important to "spectacularly" overcome impossible challenges in front of a crowd than nickel and diming your way along.

Author's notes: I thought the name "Games Psychics Play" evoked many cool images:). The game loosely references Hong Kong gambler movies, like the God of Gamblers and Conman films. I was also influenced by a review of the obscure 90s-era PC game Psychic Detective.
To do: -Advanced rules where suits mean something.

This sounds like fun.

One thing: the odds of success on three tries might not be as good as you think they are. Barring the use of stars, the odds (rounded) are:

0 successes: 42%
1 success: 42%
2 successes: 16%
3 successes: 2%

That seems a pretty high percentage for embarassing failure, and pretty low for succeeding with style. Consider allowing four tries:

0 successes: 32%
1 success: 42%
2 successes: 21%
3 successes: 5%
4 successes: 0.4%

- Walt

Walt: you'll earn stars like water, though.

Thanks a bunch for the stats, Walt. A 4 card hand might be more playable and aesthetically pleasing.

But, yeah, Victor has the right idea. GPP is supposed to be rather hard on the PCs to do stuff by themselves. Actually, they have a 58% chance of success out of 3 cards without spending Stars- that's not too bad actually.
The PCs are supposed to stall challenges, calmly talking themselves into and out of trouble until they have enough Stars to ensure God of The Game status, where they'll *totally* trounce whatever they're facing.
I was hoping that the core tense moments will be when the PCs have only a couple Stars- which shouldn't be *quite* enough to guarantee a GOTG success. They'll actually have to gamble on being able to guess the cards. Or they'll have to really try to stall the encounter to gain more Stars.
And there's a chance they might "die" after their success. I can imagine players telling each other, "Don't worry, just spend all your stars now. You'll die, but that's nothing to worry about!"

-Sport: You won the genetic lottery by yourself. You overcame the odds and continue to strive to overachieve. Every time you fail, you gain a Star.

-New Boy/Girl: You were genetically engineered to have psychic abilities and were raised in the lap of luxary. Since you are beautiful/handsome, elegant and talented, you have high standards to live up to and therefore get 1 free Peek every 5 minutes.

-Homunculus: Some experiments don't turn out quite as expected, possibly because some experiments are performed by nutcases in their garages. You are a grumbling parasite upon the psychic community. Every 5 minutes, you can demand a Lucky Star from any player or the GM (but never the GM twice in a row) and also recieve an additional Star from the GM.

Ring: Thanks for the extensive comments.

SPORT: You are correct that they seem like "If at first you don't succeed try, try again" types. But since the game is supposed to be about performing in front of audiences, sports won't be able to do things over as much as they'd like. A sport who continually embarasses himself when he's building up his stars in public is not going to please his sponsor.
Sports really want to try things over and over again, because they know in their hearts that they can succeed. Try this situation:
"I try to lift the Mr. Jackson's porsche out of the pool. You fail. I try to lift Mr. Jackson's porsche out of the pool. You fail. I try to- Mr. Jackson taps you on your shoulder, "What did you do to my car?!"

LEGACY: Yeah, I'm hoping these guys come off as noble, blaze of glory types (serious or parody). I expected that the 5? minute delay before you can come back will help control them. Legacy-types will probably really tick off the rest of the party by not being around when needed.

Updated origins:
legacy start with 7 stars/life (recall, every else gets 4)
sport 1 failure per min = +1 star
new boy/girl 1 free peek per 2 min
homunculus 1 from another pc + 1 from gm per 5 min
normal folk award 1 star to anyone per 5 min
Notes: Things are right now really slanted towards powergaming, which is what I wanted, I guess. Stopwatches are added to the list of required gaming materials.
Balance is such a tricky issue. I wish I could just FUDGE things by saying it's all up to the GM:)!

FWIW,

I was working at one point on a mechanic that is very similar, with an effect called synchronicity, which is a version of what you are doing.

In my version, you drew three cards from the synchronicity stack. You looked at all three cards, and chose one to represent your synchronicity. The GM or another player then did a blind shuffle, and you had to pick which one was "your card." Sort of a three-card monty gimmick. If you chose correctly on the first draw, you could do amazing things. If you got in the second pick, it was still good, but not spectacular. If it took all three tries, you succeeded, but with no real benefit. Of course, I used this as a meta-game concept, and not for normal resolution of conflict or action. There were other methods for that.

Anyway, maybe that would fit into your concept somehow as well.

Good luck,

Skippy

Skippy: Very interesting. Did you have a particular setting in mind? You might want to check out the Precog (Indie Games) thread for some very cool ideas.
The Blackjack Game Mechanism thread in RPG theory also seems to be another convergent idea.