I'm thinking of and RPG, FPS or a turn based game (does not really matter), where the player does not know his character(s) exact stats. Of course they exist as random variables of normal distribution inside the game engine. So no visible HP bar, Level, ATK or DEF. You can only determine it's status by it's signs of life (good mood, fatigued, dying, dead, etc...). With regard to casting spells, when your mana is running low, your chance of failing to cast a spell increases (so there is no "zero" point when you need to find the next gas station for refill). To measure your skill you can battle with monsters which has always have fixed (but yet unknown) stats.
The stats would improve as you use them, but each character would have a random talent set so some skills can be improved easier than others.
So my question for the game devs and gamers, is making the true self of your character a mystery a good idea?
From the answers it seems it depends on heavily the genre of the game.
For RPGs, I thought finding out what's good for your character is fun. From the responses, it seems it's not so fun because the players usually have an established play style and will try force it from their character for all costs.
The actual game idea I dreamed about is manager like game somewhat similar to the Pokemon game series. The main character has several champions and wanders around the virtual world and battles with others in an arena in a HOMM like fashion. And those champions would have the hidden stats. I didn't mentioned this in the original question because I don't wanted to bias the answers around this particular game concept.
For the feedback to the player (in both cases): There would be ratings similar to the elo ratings that a chess player has. One for the melee hitting, melee blocking, ranged hitting, ranged blocking abilities, and one for the magic abilities. Hitting the opponent with a sword will increase the melee hitting rating, if the enemy blocks the hit melee hitting decreases. If the opponent hit us with a sword, our melee blocking rating decrease, for successful block it increases, same for the ranged attacks. For the magic skill it's a bit tricky. High magic ability means: easier to cast spells successfully, harder to be affected by cursing spells, and easier to be affected by enchanting spells.
The standard abilities like hit points, toughness, strength, magic power, are estimated from the performance of the champion. These determine the actual damage dealt on successful hit. There would be "standard champions" that has a fixed and known stats, and the other champions' stats can be measured against them to bootstrap the system.
So if the player tries out all aspects of his champions he can find out the skillset his champions have, if the player don't like the skillset he can trade his champions to get the ones with skillset he likes.
So to get straight to point: Would it be fun if I center my game around the concept of getting to know your characters/champions, instead of serving all stats readily to the player?
It would be similar to the football players. The coach will need to see how their players perform in various positions to assign them to position that's the best for them. So he will need to try each one as a goalkeeper, defender or forward. After several matches it will be clear which position is good for them.