The Ken Combo refers to a spike setup with Marth discovered and popularized by professional Marth player, Ken. According to Ken, the Ken Combo was initially developed in the original Super Smash Bros. using Captain Falcon's up aerial followed with a down aerial meteor smash.
The combo itself is as follows: a jump; a forward aerial; midair jump; and finally, a down aerial. However, some players refer to the entire chain of neutral aerials and forward aerials followed by the spike as a "Ken combo" due to its effectiveness in Melee competitive play. Despite having an arguably simple premise, the Ken Combo requires precise spacing to do it consistently, as the down aerial's spike can only be landed if the forward air is correctly spaced. Against fast-fallers, the tippered forward aerial must connect below the character, so that the opponent is sent upward and set to fall into the d-air after Marth jumps; if the tipper forward aerial is not landed, then Marth cannot land the down aerial spike after the jump. Conversely, against floaties, Marth must forward aerial the opponent from above so they are not sent out of his range.
The precise spacing needed to execute the combo is a result of the Sakurai angle in it - in Melee, attacks with the Sakurai angle initially send opponents at a 0 degree angle, but when knockback strength reaches a certain amount, the angle's size increases to 45 degrees. In addition to requiring Marth to properly know what angle the opponent will be sent, this also means that there is a window that Marth can perform the Ken Combo; outside of this window, the forward aerial either does too little knockback when the opponent is at too little damage, or too much knockback when the Sakurai angle starts forcing opponents to be sent upwards at a 45 degree angle.
Although difficult, it is possible to perform the Ken Combo without having to jump before using the down aerial, in what is known as the "jumpless Ken Combo."
Another variant of the Ken Combo, called the Reverse Ken Combo, can also be performed in Melee. It involves hitting with the forward aerial's rear hitbox that produces weak knockback while keeping the opponent in place, then following up with the down aerial.
In PAL regions, Marth's down aerial is a meteor smash instead of a spike, resulting in a slightly altered angle at which opponents are sent, as well as allowing the combo to be meteor canceled. A common workaround is to replace the down aerial with a reverse Dolphin Slash, in what is sometimes known as the European Ken Combo. A neutral aerial can also be used after the forward aerial, but opponents can potentially SDI out of the first hit.
In games after Melee
Brawl changed the Sakurai angle so that, instead of immediately sending opponents upward at a 45 degree angle, it gradually sends them at higher degrees until it does reach 45 degrees. As a result, by the time knockback is sufficient to trigger the necessary angle for a Ken Combo, there is too much knockback for the move to properly combo, meaning Marth cannot perform the Ken Combo in Brawl. This is continued in SSB4 and Ultimate.
In Brawl, several characters can perform their own versions of the Ken Combo, such as Wolf and R.O.B.. The introduction of hitstun cancelling, however, means that opponents can air dodge away from future hits or even hit back before the next attack can occur, drastically reducing their effectiveness compared to Marth's Ken Combo in Melee; many of these combos also only work at narrow ranges due to the reworked Sakurai angle, making them less reliable than a true Ken Combo. The changes to hitstun cancelling following Brawl mean that the Ken Combo theoretically can be performed in SSB4 and Ultimate, but it would still lack the same potency it had in Melee.