I'm just getting into Pathfinder, as my first foray into RPGs. Of all the videos, tutorials and podcasts I've listened to, the GM tells the player to throw (for example, a perception check) and continues the story based upon that outcome. The GM makes no mention of the value of the throw he's expecting.
For example, there's something hidden in the room, the GM would expect a perception roll of 15 to uncover this, he doesn't communicate this expected value to the player, but he instead adapts his story to what the player did roll.
To me, as a new player, this makes the dice rolls feel redundant. I know they're obviously still effective, but as there's no communicated cause and effect to this, it feels as though the dice rolls aren't influencing the game.
Is is normal for the GM to say something like: "You hear something in the dark room, roll a 15 in Perception to find out what that is"?
I was trying to teach the game to my wife, and she brought this up. When I said (in our practice scenario), that the throw she made for 'climb' wasn't good enough and she unfortunately fell to the bottom of the pit, she immediately called foul play. I pleaded that I wasn't playing against her, nor with her, that I was not changing my expectations based upon what she rolled, but she remained unconvinced.
Best Answer
It depends on your style
When I first ran my first game, I kept all the rules transparent. Barring some things that could reverse-engineer the NPC's I didn't want them to be able to gauge, I let every last thing be entirely known to them.
"You need 3 successes (we were playing Shadowrun) at TN 6 to sink all the damage"
There is nothing wrong with giving information to your players. It's a great way to build trust. It encourages risk taking, and helps them make a character.
However, it does undermine your sense of control, and it can also cause a bit of flaw in the narrative. And that bit where I said it encourages risk taking can function in the opposite direction; if players are particularly risk averse they may choose to miss out on opportunities their character would take because they're worried about the numbers.
Really, giving numbers is like training wheels. It gives a sense of safety and helps people learn, but eventually it should come off.
Note that this is different than telling people the numbers they needed after events; this is done almost as frequently, though I tend to prefer not doing it except in rare cases (like an after-action report "You rolled a 1 on your Perception roll, so you thought the smugglers were in the warehouse when they were really on the street"). It can speed up play a little, and ease some of the concerns, but it doesn't really have the learning benefits that telling people numbers before play happens does.
As a GM, it is your prerogative to do stuff in secret, but it's also the only thing that has made people leave any of my games of their own accord.
Don't be a slave to the dice.
Now is as good a time as any to begin fudging results. You mentioned that your wife's character tried to climb out of a pit and failed. Was that expedient for your narrative or game? Feel free to say "We're skipping this because it's not interesting; you climb out of the pit." or even say "Well, this happened, but I don't like that, so you climb out fine." whenever it fits your purpose.
Just be sure to make results meaningful; if failure wouldn't be meaningful, then perhaps you should even skip the roll entirely. If it is meaningful, but it's not expedient to the plot, have something that matters to the plot happen on failure, like a piece of gear being damaged or the like (but don't be too brutal). Remember that this goes over better when you're doing it in the players' favor than when it hurts them.