I played Palladium for years and know it well. For a long time RIFTS was my favorite RPG after D&D.
Palladium's house system is very simple. You roll stats for your character and then pick a class, often called an OCC in Palladium parlance. Your class then determines your skills and what level of Hand to Hand combat training your character has. That is the crux of it.
Depending on the Palladium game you are playing, you may have additional character creation options such as choosing a race and gaining additional powers, stat modifiers, and so on. Some classes also give you powers. Your choice of skills can also modify your stats.
Once you have determined your basic hand to hand style and calculated your final stats based on various skill, racial, and class bonuses, you then determine your combat bonuses. You will have a certain number of attacks per round (essentially actions per round), and then bonuses to strike, dodge, parry, etc. Whenever you perform those actions in combat you roll d20 and apply the appropriate bonus. There are a number of different things you can do in combat, and your hand to hand style will determine how many attacks per round you get and some of your bonuses.
The Palladium system is kind of a mess though, so I ended up clarifying and house ruling it quite a bit to make it functional. For example, under the basic rules, lets say you have two attacks and your enemy has four attacks. Basically you roll initiative, and higher roll goes. You make an attack and the enemy parries or dodges, then they go and do the same to you and you get to choose your response, parry, dodge, etc. Combat is essentially a series of opposed rolls.
But right away you can see some wonkiness in the system. For example, according to RAW, unless your hand to hand style gives you auto-parry, or auto-dodge, it costs you your next action to parry or dodge. So for example, the enemy attacks you first and you dodge. That dodge just cost you your next action, meaning you don't get to attack back because you just dodged. The enemy then gets to attack you again. You dodge again. You are now out of actions and pretty much just stand there stupidly while they get two more attacks on you. Its awful and unplayable as written. Most people conveniently ignore this rule.
Melee combat works a little better because most hand to hand styles give you auto-parry meaning you can parry melee attacks as a free action without losing your next attack. But auto-dodge is very rare and combat styles, races, or class abilities that offer it are highly sought after. In the RIFTS RPG, auto-dodge is one of the class abilities that makes Juicers so nasty powerful.
Auto-fire and missile attacks are kind of screwed up too, and the skill system doesn't give you much in the way of customization. Your class determines your skills which work on a percentile basis. Most classes in Palladium are extremely front loaded. Essentially the only things you gain by levelling up is a minute skill % boost, a paltry number of hitpoints, and some additional hand to hand bonuses and perhaps an additional attack. Really the hand to hand combat stuff is critical, everything else is pretty much worthless.
I house ruled most of the Palladium combat system to make it actually work. For example, I house ruled that using an attack to dodge does not also mean you lose your next attack. I also gave bonus attacks to most classes since your attacks also function as your actions in combat.
For mecha combat, you start dealing with mega-damage which has its own issues. Also I recommend just treating mecha combat the same as character combat. Some Palladium games like Heroes Unlimited have these wonky rules for dogfighting which work off the crappy Palladium skill system. I recommend ignoring those completely.
If you are interested, I can post up my fixes to Palladium combat. I haven't played in years though. Once 3e and d20 came out I never looked back. And unfortunately, Siembieda hates d20 and refuses to convert it. That's sad because a well written d20 version of Palladium's games would sell a bajillion copies.
