This article deals with in-game competitions, contests, and games between D&D characters.
If two D&D characters challenge each other to a non-combat competition of some sort, how should it be resolved? A few places in the Player's Handbook suggest single opposed skill checks: a bardic song-and-dance contest is an opposed Perform skill check (p. 58), and a horserace should be an opposed Ride check (p. 60). Under ability checks, it recommends that an arm-wrestling contest simply be awarded to the character with the higher Strength rating, without any dice-check (p. 62).
I would suggest a series of checks for any of these situations, until one of the participants gains a lead of 3 points over the other(s). Each check (skill or ability) garners +1 victory point for the winner; or +2 points if the win was by a margin of 10 or more points; or 0 (zero) if the result was a tie. Some competitions will have a set number of "phases" until an end-point, at which time either a tie is declared or a sudden-death check may be made (for example, an archery or horseracing contest); others may continue normally until a winner is determined with 3 points (for example, wrestling, with the points garnered for each "pin" under the rules on p. 137). This method allows for an increase in drama as one participant steps closer to victory over time, while still having the contest usually go to the character with the higher skill or ability score.
Skill: Knowledge (Gaming)
With this suggested skill, you have learned the rules to one or more classical strategy boardgames, and are educated in the tactics and play of those games. Like all knowledge skills, it is Intelligence-based, trained-only (the luxury of learning boardgame rules is usually reserved for the nobility or academics), and a class skill for characters who are Bards, Wizards, Adepts, Aristocrats, some Experts, and all Dragons (being a cross-class skill for all other classes). Like the Perform skill, each rank of Knowledge (Gaming) gives you familiarity with one of the following games and its close variants: checkers, chess, backgammon (senet), go, mancala, wari, mah jong, dogs and jackals, and the "royal game of Ur".
This skill only covers boardgames with a significant strategy element, and does not cover games of raw chance or common gambling entertainments, such as dice, knucklebones, or most card games. (General gambling should be covered under "Knowledge (Streetwise)" from the Sword & Fist book, p. 10.)
Specific Competition Rules: Chess
Using the above rules for competitions in general, and the special skill in particular, we can simulate games of chess (in a variety of flavors) between characters in D&D. Characters must have at least one skill point in Knowledge (Gaming) and have selected "chess" as one of the games they have learned. There is a limit to the length of this competition measured in "phases" of 10 minutes apiece, at which point a stalemate is declared: this limit is (sum of player skill bonuses) + 1d6. In each phase, an opposed Gaming skill check is made, with victory points awarded as above, until one or the other achieves a lead of 3 points or a stalemate occurs.
As an additional element, you may include a choice of strategy for each character within each "phase". Each player involved picks a strategy, and places a single d6 on the table with their choice face-up, and covered with their hand; simultaneously, the selections are revealed and the chart below consulted for the modifier applied to the White player's next opposed skill check (who plays White and who plays Black can be selected in any manner at the start of the competition).
I'm indebted to Tim Grice for his article in Dragon #70 (Feb. 1983), p. 60, "The game within a game", for inspiring this approach.
Strategy #1 = general attack; #2 = build up own position; #3 = destroy foe's position; #4 = set a trap; #5 = trade down; #6 = attack foe's king. Result shown is the modifier applied to the White player's next opposed skill check.