When an opposed roll is attempted it is a contest. There are many reasons a contest might occur and their significance in the game can be of little significance or great importance. In the case of standard contests a simple roll of one character’s skill versus the other works well (ties can work out as is best for the story or be resolved with another roll).
Chases can be resolved as simple rolls as well or can be played out with colorful detail added for drama and entertainment. Typically in a chase the character being pursued will attempt to ditch the pursuer by pulling a stunt to break contact allowing them a clean escape or an opportunity to hide. To start the fleeing character announces the type of stunt they want to pull and suggests a difficulty they are willing to risk (normally athletics or a vehicle operation skill is used for the roll). Then the fleeing character makes the roll, if successful the pursuer must also make the roll. If either fails they are temporarily out of the contest such as crashed, tripped, or stuck. If both succeed the chase continues, if both fail but survive they may renew the chase (Crashed their cars, but jump out and continue on foot).
No Win Situations
A character in a car being pursued by a helicopter in open terrain has very little chance of escape. In these situations the GM should use logic or encourage players to come up with a plan to change the odds. The car makes a mad dash towards a no fly zone and hopes the military will warn off the pursuers or a person on foot jumps off a bridge to escape pursuers in a car.
Game Masters should be cautious about prize contests in game, while they do exist and their are professionals involved in them some players may see them as a loophole to circumvent the character design system (note as a GM you should kill their character and make them start over with one less priority level than the rest of the group to discourage this behavior). A contest to win a ship or other reward can be fun, but a game where the master gambler uses his base 30 gambling skill to gain a revenue stream exceeding the rich character in the group obviously has a problem.
The game master should never let players know the result of a contest is fixed, it should be used very sparingly if at all but sometimes the adventure can’t continue unless a character picks up on a clue, spots the assassin slipping away in the crowd, or otherwise gains something necessary for the success of the mission. In these instances the game master should tell the player to roll the appropriate skill and then give them the information. I actually suggest never telling the players the target number of a roll, if they ask say thy don’t know or perhaps that it looks hard or looks easy if something they are preparing to do.
Sometimes players want to use a skill when it shouldn’t be used, trying to sneak past an alert guard in good lighting, or trying to convince a new car dealership to sell a car at half price. The Game master has two options depending on the severity, one is automatic failure, players may not like it but the homely male orc thug cannot seduce the heterosexual male elven guard no matter how many ranks he has in charm. The other option is to give modifiers, i suggest making the modifiers big, usually 5 or 10 depending on how ill conceived the plan is.