Games are usually the enemy of studying, but some elements of games can be used to improve learning.
Spaced repetition is an amazing technique for learning without understanding. Understanding is certainly superior and in a league of its own, but it is hard to command or even predict; and sometimes you need to memorize for a while before you can understand. One may compare this to gathering ingredients before you can cook. Before you can read sentences, you must know the words, and so on.
Spaced repetition takes advantage of a particular memory effect: The best time to repeat something is just before you forget it. Repeating many times in a row adds little after the first couple repetitions. Repeating at fixed intervals helps, but the best effect comes with increased intervals. You may for instance double the intervals, which is more effective than fixed intervals. But the best effect is when one actively recalls a fact just as it is about to be forgotten: It should take a little effort to remember it, but one should be able to do it.
Since our brain is not under constant surveillance, the only person who can know this time is ourselves. Conventional Spaced Repetition Software (SRS) starts with a standard model of human memory, then adjusts intervals down if people keep forgetting, or up if they remember everything. Good SRS lets the user mark the difficulty with which they remember. But there is an even better solution, at least in some ways, and the Duolingo online language site has found it.
When you start a study unit in Duolingo, the “learning meter” is empty. As you learn, it fills up until it is full. But as time passes afterwards, the learning meter begins to slide down toward empty again. You can see this for each topic, and for each “workbook” in a topic. (This is a session that typically takes 10-15 minutes to go through.) You can then go back and test yourself.
If you go back and run the test while you remember everything, you will certainly get the learning meter back to full again, but the experience will be rather boring. Duolingo is a very game-like learning system, where you have to translate back and forth, listen to sentences in the target language, describe pictures or pick from multiple choices. You never know what the next question will be. But if you know everything by heart, it is not very exciting. It is like winning chess against a small child.
On the other hand, if you wait too long and have forgotten the words or phrases, you will be thrown out after three mistakes and have to start that workbook over until you get it right. That is not too much fun either, even though it only costs you a few minutes.
The result is that the users themselves find out how long to wait to get the most rewarding “game” experience. If it was too easy, you learn to wait longer. If it was too hard, you make sure to return earlier next time. There is no need for the software to know whether you learn fast or slowly. All it needs to do is reward you when you get the balance right, and it does so with an exciting learning experience and a feeling of winning against a worthy opponent: Your own forgetfulness. You pick your battles, so with a little experience you pick the best time yourself.
I am not sure how easy this is to translate into other forms of learning, but I think it may be easy with anything that requires memorization of facts. Geography and history come to mind. Make small, focused units and a table where one can see which ones begin to slip. Adjust the speed at which they slide depending on past performance. It can probably be done better than it is in DuoLingo, but the principle works amazingly well. Humans are very good at learning things when having fun.