What kind of gaming experiences does hiding game play stats and formulas cultivate?

There are varying degrees of providing players with information on their characters abilities - including but not limited to showing players their character's stats and how they tie into formulas such as total damage, damage reduction, etc. When these numbers and formulas are provided outright it can lead to a lot of min maxing / work to create an optimal build which can detract from simply enjoying the game by worrying too much about the numbers behind the scenes.

From a game design perspective I am looking for insight on:

 - Personal experiences with designing stat systems where most if not all the information was hidden from the player. Include the types of decisions you made on what to hide and what to show to the player as well as the reasons behind those decisions and how they impacted the way players play the game.
 - Personal experiences where you actively chose to provide as much information to the player as possible because you were against hiding information. Explain the thought process that drove you to this decision and the impact it had on the way players play the game.
 - References to / resources on how different games have approached designing their stat systems that hide most of the information from the players and how the design has impacted the way players play the game