A mindgame can be described as a strategy, action, move, or set of moves that can be used to trick, manipulate or psychologically pressure the opponent, making them "play your game". Mindgames are part of a player playstyle alongside their technical skills over one or more characters, and compose the metagame.
Forms of Mindgame
There are many ways to perform a mindgame, however in most cases they complement or depend on each other.
Predicting and Punishing
One of the most basic forms of mindgames, revolves around the idea of studying the opponent, learning his/her behavior and any traits of their playstyle, such as patterns, and proceed to punish them whenever they use these. In addition, the individual traits of the character used are also taken in consideration. Because of this, predicting is mostly effective when the player knowns how the opponent's character functions (amount of lag after attacks, range, weight, etc.).
The simplest form of predicting and punishing is after the opponent uses a attack with considerable lag, such as a Smash Attack. For this reason, Smash-Spammers can be easily punished as the player will soon realize how often they use the attack and knowns the exact amount of time they can act after the opponents throws a Smash Attack.
To successfully be able to read the opponent's movements, the player must put him/herself at risk in some occasions, as the opposing player may also trying to predict. With this in mind, the player will take in consideration all the options he have to punish the opponent. For example, when the opponent is grabbing a ledge trying to recover, the player will try to predict how the opponent will react, as he/she will have many options: rolling forward, jumping, using a ledge attack, jumping down, etc. Another example is when using Ganondorf's Flame Choke chain-grab, where the player will try to predict where the opponent will tech to in order to tech-chase. Among the Smash community, predicting an opponents move or behavior is often known as a 'read'.
Luring or baiting is a form of mindgame where the player tricks the opponent to put him/her into a vulnerable position. Similar to predicting and punishing, the player forces the opponent to react in a particular manner and punishing that. Because of that, luring an opponent is also related to predicting, learning to read and punish the other player's habits.
Tech chasing with Ganondorf's Flame Choke, as mentioned above, is a good example of baiting. After the opponent is caught a few times, he/she will become frustrated and either repeat the same tech, allowing themselves to be caught again, or try a different strategy in order to not be chain grabbed over and over.
Baiting can also be done by the player pretending to use a wrong move, manipulating the opponent into trying to punish, only to be overpowered. An example of that is pretending to throw a Pikmin with Olimar in midair, and instead do an Forward Aerial. Sonic can also perform this kind of strategy as his Down Special and Down Smash in Brawl look a bit similar. Samus can also do this by using a forward smash instead of a Missile since her forward smash looks similar to her animation when using Missile; this is effective at baiting out a reflector or shield to punish with a grab.
In Super Smash Bros. for Nintendo 3DS and Wii U, Rosalina & Luma are unique in terms of luring opponents, since Luma can still be controlled regardless of Rosalina's state, similar to desynching the Ice Climbers in Melee and Brawl. The player can still input commands for Luma even if Rosalina is stunned or under some other condition, such as sleeping or dazed. Rosalina can, for example, hold the shield long enough to break it, luring the opponent into attacking her while she is in a dazed state. Luma can then punish the opponent as the opponent comes to attack Rosalina.
A more agressive type of mindgame, where the player tries to force the opponent to react by limiting their options of counter-attack. Generally, faster characters benefit more in pressuring as their speed tends to make them more "unpredictable". However slower characters can also pressure as effective, as their attacks tends to pack more power, causing more "fear" to the opponent.
Dash dancing is a good example of pressuring, where the player uses the fast movements to incite panic to the opponent, threatening a possible approach. If the opponents acts recklessly trying to attack, the dash dance can easily retaliate with a dash attack or grab/pivot grab. The idea of pressuring the opponent in order to force him to shield and then proceed to use an attack that causes high damage to shields is another good strategy. The same applies into forcing the opponent to dodge and attack in the direction he is dodging to limit his movement.
Another way of pressuring is by attacking an opponent that is off-platform trying to recover. The player can proceed to attempt to do a Meteor Smash or a attack that causes vertical knockback, depending on the opponent's position. Characters with poor recovery generally are easy targets of this kind of pressure.
Spacing is the utilization of a character's range in comparison to the opponent's range to ensure their attacks make contact and that the opponent's do not. To space, you have to take into account the range of both your attacks and the opponent's.
Mindgames that revolves on spacing makes high use of prediction, baiting and pressuring. Combining all those traits make spacing very effective, as the player manipulates the opponent into the attack's range and pressures him/her by taking his/her safe-area on the platform.
The two key-factors to spacing are the character in question and stage being played. Both these factors complement each other, either in a good or bad way.
Each character has its own forms of spacing, depending on their ground and air speed and properties of attacks. Characters with disjointed hitboxes, such as the swordsmen Ike, Marth and Shulk, benefit from range alone as the hitboxes in their weapons makes the approach very safe (since if the opponent hit their swords it won't cause damage to the character). With that in mind, Ike's Forward Aerial is a very powerful tool for spacing due the range, speed and knockback. Other characters with fast aerial speed, such as Wario, Yoshi, can benefit from spacing relying mostly on that, as they can "dance" in the air thanks to the high air mobility.
In general, fast moves with good knockback are suited tools for spacing, such as tilts and even some faster Smash Attacks (such as Samus and Pit/Dark Pit's Forward Smash). Projectiles are considered the best form of spacing due their range. Other Special Attacks also fall in this category.
Lastly, sometimes the best way to perform a mindgame is by trying to attack from a new perspective, do something that generally isn't done, run away from the player habits. Since players tend to stick to their habits, even if unconsciously, countering this by doing something different is a good way to escape a situation.
Unpredictable players are the ones that can read a situation fast enough to do something the opponent isn't expecting and throw him off balance. A good example is using a move that is generally seen as dangerous due a specific drawback (range, lag, knockback, etc.) or because it was used "randomly" without a proper setup, but succeed into landing it because the opponent wasn't expecting it. It is a high risk, high reward strategy, but can sometime works when least expected.