How does a game system punish a player for having to roll dice? Provide an example. Thanks!
By using a dice resolution mechanic that doesn't reward skill or ability or training.
I'm only going to be talking about nWoD, since that's what the OP was asking about.
Your basic dice pool is based upon skill, ability score, and equipment (and other miscellaneous sources). This is then reduced by the difficulty of the task, to a minimum of 0 dice; any task that can be accomplished by elements of luck devolves to a Chance Die which has a 10% chance of success (or greater) and a 10% chance of monumental failure (Dramatic Failure, or sometimes called a Botch due to it's name in oWoD).
As long as your dice pool has 1 or more dice remaining, you roll the remaining dice. Each result of 8 or higher on the d10 is a success (roll 10's, and sometimes lower numbers, again for a chance at even more successes). Each result of 7 or less is a failure. According to the book (though a lot of Storytellers I've met don't always follow this) a single success is enough to get some positive result. Four or more successes is considered to be an "Exceptional Success" and comes with extra benefits for doing the task so very well.
Example 1: Jumping between rooftops to escape pursuit.
This is an Athletics check, generally modified by Strength. Nancy is a librarian that does a lot of running to keep in shape; she's only got a 1 Strength but she's got a 3 Athletics; she's also size 5 (typical human size). Our character is on a cluttered roof-top, providing only 5 feet of clear running room before she must jump, and it rained an hour ago so the roof is wet. So her starting dice pool is 1 (Strength) + 3 (Athletics) + 1 (great shoes), for a total of 5 dice. She's only got 5 feet of starting distance (-3 dice) and the wet roof is slick (-1) for a total dice pool of 1 (good thing she had her running shoes handy!).
Nancy takes her one die, decides she really needs to cross the gap between buildings, and spends a point of Willpower to get 3 more dice, now for a total of 4 dice. She rolls her dice, getting a fairly average roll of 1, 5, 10, & 6 for 1 success. Nancy did get a 10, so she gets to roll that die again (the "10 Again" rule) and gets herself another 6. Total, 1 success.
Using the jumping rules she clears 5 feet (her size) + 4 feet per success for a total horizontal clearance of 9 feet. Too bad for Nancy, the nearby building was 12 feet away, so she plunges to the pavement 48 feet below. Using the falling rules, she'll take 5 bashing damage as she hits the ground (unless she lands on broken glass or a fence or something that makes it lethal damage) where she's likely to lie in pain until her pursuers catch her and do whatever they were planning to do to her.
Note that a kind Storyteller could allow a Dexterity + Athletics roll to scrape at the side of the target building to reduce the falling damage; however, he doesn't have to.
Example 2: Stabbing a dirty cop that's trying to kill you.
Brock is a rough and tumble private investigator, with a lot of experience in close fights, so a Strength of 3 and a Weaponry of 3. He's investigating a corrupt city official when he is accosted by an uniformed officer working for the official. Brock decides that he needs to keep it close or the cop is going to shoot him dead, so Brock goes for his knife and tries to stab the cop.
Brock's good, and he's got a knife, so his die pool is 3 (Strength) + 3 (Weaponry skill) + 1 (knife) and it will do lethal damage. Unfortunately, WoD street cops are bad hombres, with a Defense of 3 and thin Kevlar vests (armor 1/2). Brock is taking a -4 to his attacks, reducing his seven dice to 3 dice.
Brock rolls the bones and gets a fairly average 3, 6, & 7, for 0 successes.
The crooked cop is not cool with this, so he backs up to the opening of the room and grabs up the shotgun he hid behind the door, using his whole action.
Brock knows he's in trouble now, but the Cop is between him and the only practical exit, so he tries to rush the cop and get the jump on him. He even spends a point of willpower, to roll 6 dice. He gets a 3, 8, 5, 6, 4, 7 for a total of 1 success. He lunges with desperation and cuts the cop lightly on the arm as the officer is bringing his street howitzer to bear.
The cop has dice pool of 3 ( Dexterity) + 3 (Firearms) + 4 (Shotgun) - 2 (Brock's Defense) - 2 (Brock's also wearing a thin Kevlar vest) = 6 dice. This cop is peeved, however, and decides to spend a point of Willpower to gain another 3 dice for a total of 9 dice of lethal damage. He rolls well and gets a 2, 9, 5, 8, 1, 10, 4, 6, 3 for three successes (and shotguns are 9 again). The cop re-rolls his 9 and 10 and gets a 2 and an 8 for a fourth success (apparently this officer has got a lucky shotgun). Poor Brock takes 4 lethal damage as load of buckshot stitches into his side and penetrates his formerly protective vest. Among other things, this shifts him to the -1 tier of wounds, so Brock takes a further -1 penalty to all actions until he can heal up.
Brock's in trouble, and now he's only got 2 dice of stabbing to work with. Brock might be better off trying to surrender, but the cop may decide that Brock "continued to resist and all attempts to calm the suspect failed. To protect myself I had to apply lethal force."
Note in both examples, the dice rolls were average, and the situations were typical of those one can expect in the festering World of Darkness. The only thing that was atypical was the level of skill and training of the characters involved; the PCs generally don't have 3 dots in the skills that are needed to save their bacon.
On the other hand, if both players had gone with a more descriptive and narrative account then there is a good chance that they'd have come through basically okay.
Nancy: "I've got my good running shoes on as a bust through the roof access door. Looking around I scamper to the ridgeline of the roof and sprint down in towards the edge. Using every bit of my momentum, running skill, and willpower I push off at the last second and sail into the night. I cross the twelve foot gap between apartment buildings and slam into the roof with a painful thump. Desperate to evade my pursuit, I scramble up the slick roof and head for the fire escape."
Brock: "As I realize that officer Chamber is working for the councilor, and that he's not planning to let me leave here alive, I pull my knife and place it right next to his groin. With a menacing growl I say 'Now, you and me, officer, are going to take a calm walk outside. You're going to stop at the coat room and go inside while I leave, or you're going to learn to sing soprano.' Then I give him just a slight cut in the leg, letting him know just how sharp my ghetto razor is."
I hope that clarifies what I meant.
