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GRA is using a fairly complex combat system. Most of it is 'under the hood', but you'll need to get familiarized with it before performing well. First of all, the damage system is localized between your head, arms, legs and body. Being badly hurt in the legs will slow you down, taking damage to the head will reduce your vision, accuracy and charisma, and so on. More to the point, weapons have different damage types (piercing, impact, fire, chemical..) and armors will protect you only against some of those.
Like explained earlier damages are localized. Each body part has a given amount of hit points (depending on endurance and strength). Some body parts are harder (head) to hit than others (body). If any of your body parts HP goes below zero, you are dead. Except if you are a zombie, but that's not the point here :). Wearing an armor piece over a specific body part may reduce incoming damage. There's 3 levels of damage per body part: Okay, Wounded and Critical. The worst it become for one body part and the worst are the effects on you.
Weapons have different damage types. For example most pistols and rifles are “piercing”. Shotguns are “impact”. Melee weapons are mostly “slashing” and “impact”. But there's also plenty of exotic weapons with fire, chemical, or explosive damages. Armors typically protect you against common damage types but some of them may be better than the usual all-around ones in specific battles.
GRA feature the ability to act two times per turn, eating your stamina. This feature is especially useful during combat. While running, your accuracy is reduced but you can either move 2 times, or shoot one time and move, or shoot 2 times. Managing this ability correctly can allow you to shoot someone and go behind a cover in the same turn. However this feature has also some limits. The most obvious one being your stamina pool (some items / drugs may help you with that). Also in “running mode”, special shots like aiming or bust shot will decrease your stamina even more. Play around and mix walking and running state to find your sweet spot.
GRA is currently handling smoke and next versions will handle lights. So, if you throw a smoke grenade at an enemy, his accuracy will be reduced, but more importantly he may become unable to find you for a few turns. As a result, smoke grenades are really useful tool to use in large battles. This aspect of the combat system will be improved upon.
In 0.6.7 it's not yet implemented. However, it means that if a NPC (or you) has an object between your line of fire and his, then the chance of being hit is reduced. If a NPC is right next to a cover he'll get the protection but not the hitchance penalty from the said cover. This system should force NPC and the player to stay behind cover while fighting enemies.
At the moment, some weapons are able to break walls. In future versions, they will be able to destroy furniture (like cover stuff) as well. You will have to take that factor into account before fighting against groups of enemies.
Buy some bandages and First Aid Kits before a fight. Going into cover before using any item is beneficial as using them will pass a turn. You may also come across some specific skill or stat boosting items that you may want to use before going into battle. For example, steroids can give a huge boost to melee characters. NPC will do the same, and will try to heal themselves when wounded, if they have the gear to do so.
GRA is a procedural game. And as a player, you'll start with basically nothing. So, in the early game, uou will often be confronted against impossible odds. The only good advice is to flee. The people you've encountered will still be there anyway. And more to the point you could follow one of them to kill him when he is isolated. This is a good method to follow if you want to break into the military base.
Also, don't fight all the hostiles, especially when you don't really know if you can succeed. The damage system being semi realistic, you don't need a lot of hits to be killed. Also, if you're hunted by cops, sleeping in a hospital may be a very bad idea even if it restores your health.