Continuous Challenge
A good game designer gives his players continuous challenges, each of which leads to another challenge, to keep them "hooked" on playing a game. This can be done by setting clear, short-term goals appropriate to the level of the player and the context within the game. Each challenge should satisfy some kind of learning objective. For example, answering a question, identifying a sample or completing a measurement or a portion of a map could be a challenge, part of a larger game.
Interesting Storyline
This isn't essential to every kind of game (for example, not for a scavenger hunt), especially when players are competing against each other. In that case, the excitement of the competition is likely to engage them. However, a good storyline can liven up a competition still further.
In various Internet forums and game-magazine columns about video and board games, a good plot or storyline is cited as essential to a good game. Oddly enough, a fantasy context makes players more motivated to succeed at a game. So instead of having students memorize types of ores, have them play as miners prospecting for minerals and needing to identify profitable sources. Rather than using games to escape from their studies, encourage students to use games to escape into their studies.
Flexibility
Make sure that there are many different ways to accomplish each goal. Simply plotting out a step-by-step progression through the goals can be stifling. As much as possible, let each player (or team) work out their own strategy to the endpoint while still keeping the game challenging and achieving the learning objectives.
Immediate, useful rewards.
Instead of just points towards victory, successful players (or the pieces or characters they're in charge of) can be rewarded with new capabilities, a new part of the board to explore or even a new task. These are surprisingly motivating, as the point of the game is not just to win it, but to keep playing.
Combining Fun and Realism
Many so-called games are actually simulations without goals and challenges. Excessive realistim can also be boring. But even good games often incorporate incorrect assumptions
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