Well, I have maged on f2p for quite a while, and let me tell you, there are many tricks that could make your training easier. Here are a few things I have gathered from my own experiences that may help you, share unknown information, and dispel myths about the magical arts pertaining to f2p players.

Contents:
Just click on the following sections to jump directly to that section.

Section I: Ways to Train

Section II: The Gear
Section III: The Training Spots
Section IV: Quests
Section V: A Few Quick Tips for Pures
Section VI: Final Notes and a few Random Facts and Tips

Section I: The main ways to train

Offensive Spells
Offensive Spells involve the spells whose purpose is to simply damage the enemy. These involve the basic strike, bolt, and blast spells, as well as Crumble Undead. Theses all give a base amount of exp, plus 2 xp for Magic and 1.33 xp for HP or Def per each point of damage done.* Usually, the most cost efficient spell to use is Fire Strike, which on average returns the most experience for the cost. However, this can be very slow. Stronger spells tend to cost more, but can deliver the experience much quicker. Also, note that if you choose the defensive attack style on your staff, you will get defense experience from any damage you deal. Pures especially need to watch for this.

NOTE: According to the new Jagex area guides, Ice Giants are weak to fire magic and ghosts are weak to magic in general. Use this information to help you get the most out of your training!

Crumble Undead
I feel it is important to point out that if you can afford to blow the runes on Crumble Undead (1 chaos, 2 airs, 3 earths), it makes a great training spell for level 39, especially considering it has a max hit of 15! Varrock sewers are perfect for using this spell (two areas where you can cast spells on Zombies, Skeletons, and Ghosts from across water). No free world staff auto casts this spell, so you can choose an Earth Staff or Air staff, depending on which would save you money, or which type of rune you have an excess of.


Curse Training
One of the fastest growing ways to train mage in f2p is through failed curses (Confuse at Level 3, Weaken at Level 11, and Curse at level 19). The basic premises involved wearing full armor (plate and kite, and of any metal), along with any weapon (b-axe or war hammer preferred, but NO daggers or 2h), and casting curse spells. DO NOT USE ANY STAVES OR AMMULETS THAT BOOST MAGIC! Because of the massive magic attack penalty, each curse should fail. Since curse provides exp regardless of success, and since success prevents further use of curse on the same enemy, this greatly speeds up the process. Some popular areas to do this are Lessers in Wizards Guild and Zombies in Varrock Sewer (near the area where the Key for Silverlight is found you can safely curse zombies from across the water). Other lesser known areas you can use include Hob Goblins from the Cow Pasture near the Crafting Guild (across the water) and the Zammorack Monk in the Staircase of Varrock Castle's ground floor (he seems to be unusually resistant to curses). If your range level is 40, wearing green draghide vambraces further helps to lower your magic attack and thus make sure curse fails. It is important to note that doing this will NOT make your HP rise, so train a second combat skill (strength, attack, and range if you are a pure, defense as well if you aren't a pure) for HP experience. Curse training is renown for its cost efficiency (more so than Fire Strikes even!), as well as the need for alot of clicking and slow speed.

Teleportation
Teleport spells provide some of the highest exp per cast of all spells. The best spell for this in f2p is Falador Teleport. All you need (besides runes) are an Air staff (true for any teleport in f2p) and water runes. However, Teleportation spells are pretty expensive (Laws cost about 300 ea, and thatfs in bulk!). Again, you do not gain any HP, so be sure to train a second combat skill (besides prayer) for HP. It is a pretty fast way to train though, and gets great reactions from people who think you're a nut for wasting laws like that.

Alchemy
The premise for alchemy is to use either Low Alchemy (21 mage) or High Alchemy (55 mage) to turn items into gp. The preferred spell is High Alchemy, which can actually return a profit on the spell, so this section will focus solely on High Alchemy. Alchemy ideally works best with fletching, especially for magic long bows. However, in f2p, if you do smith steel plates or such for smithing experience, using alchemy can get you more GP than selling them to players or stores, plus give you great magic exp. Both spells require nature runes and fire runes, but it is much more effective to use a fire staff then to buy individual fire runes. Also, you can note all of your items so you dont have to bank too often (though I recommend depositing your money once in a while to prevent losses due to death by random events). Again, not HP exp is gained, so train those other combat skills for it! It is fast exp (the highest exp per spell available in f2p), and if done right can create a profit. Still, there is very little that can be bought in f2p that turns a profit via alchemy (steel plates are actually a loss; the bars that go into it can be sold for 600 each, or 3000 per plate, versus the 1200 you get via alchemy). The only viable option is rune med helms, available for 10k ea, and few players sell those in bulk.



Section II: The Gear

NORMAL TRAINING/PKING:
F2p, as it is to be expected, is limited in the gear available for mages. The best magic attack bonus a f2per can get is +25. Here is the basic setup for any mage:
Blue Wizard Hat (+2 Magic)
Black (Dark Wizard) Robe or Blue Wizard Robe (+3 Magic)
Magic Amulet (+10 Magic)
Magic or Elemental Staff (+10 Magic)

A few things to note: the Blue wizard hat is better than the Black wizard hat, which provides only +1 magic. However, for robes, both blue and black are equal.

Extra stuff to wear:
Anti-Dragonfire Shield (if you have it) or Wooden Shield
Leather Vambraces
Leather Boots
Cape of Any Color
Leather Chaps (if you don't use prayer/are a pure)
or
Monk's Robe Bottom (if you use prayer)

Avoid Shade robes. They do not help magic, only prayer, and the bonus is less than the much more cheaper Monk's Robes.

Location of each Item:
Staves--Zaff's Staff Shop in Varrock, 1,500gp each.
Amulet of Magic--Player Made, purchase for 500 gp - 1k gp
Black Robe--Drop from Dark Wizards (Level 7 and 20). People leave them on the ground near the Dark Wizards circle south of Varrock.
Blue Wizard Robe--Drop from Blue Wizards in Wizard's tower.
Blue Wizard Hat--Drop from Blue Wizards, Imps, and sold in Betty's Magic Emporium in Port Sarim
Anti-Dragonfire Shield--Duke Horatio after starting Dragon Slayer, can get it earlier from other players
Wooden Sheild--
Tutorial Island, Falador Shield Shop, or spawn outside the Northern Varrock Wall.
Leather Vambraces--Player made, the shop in Al-Kharid usually has some in stock due to the crafters selling them.
Leather Boots--Spawns in Wizard's Tower and Al-Kharid, sold in Thesselia's Clothes Shop in Varrock, Player Made
Capes--Dropped by highway men, sold in Thesselia's Clothes Shop, sold in Champ's guild
Leather Chaps--Player made, Usually Available in Al-Kharid General Shop
Monk's Robe Bottom--Spawn on second floor of monastery, players there will usually get it for you.

CURSE TRAINING:
Curses require a different setup; the goal this time is to get the lowest magic bonus possible. To do this, wear the following:
Full armor of any metal (plate body, plate legs or skirt, full helmet, kitesheild)
Metal 1 hand weapon of any metal EXCEPT daggers (B-axe and war hammer seem to be good choices)
Fancy or Fighting Boots (give -3 to Magic)
D-hide vambraces if you can

Fancy or Fighting Boots are acquired from the Security Stronghold.

This will net you a nice negative mage bonus of about -68 to -78 (depending on whether or not you wear d-hide vambraces). Remember, do not wear a power or magic ammy, nor a staff if you want the lowest possible magic bonus!

Section III: The Training Spots
Having the right gear and spells is great, but so is the right training spot. This can depend on your style of training.  Your training will go much faster when you train on lower level monsters.  Sure you can safely mage many higher monsters from the safety of a esafe spotf, but trying to kill a level 100 monster and continually splashing spells is both slow training and a waist of runes.  Always train on something that has a combat level 2-3 levels below your magic level (not combat level).  You find that the overall xp per hour is far better.

Offensive Spells
Low levels:
Chickens (Champs guild, Chicken Coops near Falador, Draynor, and Lumbridge)
Goblins from behind the sheep pen near Lumbridge

Mid-Levels: Guards in Varrock behind fences
Barbarian Village (watch out for the ranging Barbarian)
Lesser Demon in Wizard tower (bring Tele-grab runes)
Hill giants from a safe spot
White knights in Falador
Edgeville Jail Guards--There is a small jail in which there are two guards inside, two outside. If you close the gate to the building, you can safely mage the guards inside. Then go in, close the gates, and kill the guards outside. Low levels can also technically use this, but two things stop me from recommending it: first, there is a skeleton near the wilderness that occasionally roams nearby and attacks unwary opponents; second, there are some players who will enjoy opening the gate to let the guard come out and attack you. Should be you caught inside when this happens, they can simply close the gate whenever you try to leave, indirectly killing you.
Black Knight in Port Sarim's jail (bring telegrabs for drops)
Hobgoblins near crafting guild (you can mage from across the water, bring telegrabs for drops)

High Levels:
Lesser in Wizard Tower (don't forget tele-grab runes)
Lesser in Karamja Volcano (numerous safe spots there)
Hill giants (Edgeville Dungeon)
Ice Giants in Blurite Dungeon (there are a few safe spots, and these are weaker to fire based spells!)
Black knights (I recommend a higher level since they are aggressive, so you might get attacked if one spawns behind you).
Ghosts, Zombies, and Skeletons in Stronghold of Security floor 4 (Ghosts are weakest of the three to mage)
Supposedly Ankous in the Stronghold of Security are good for mage as well (Crumble Undead?), and drop frequent laws. I hear there are some safe spots too.

Crumble Undead
By far the best (and subsequently most used) area to use this spell is in Varrock sewers, where in two places you can mage undead creatures safely from across the water. I haven't experimented too much, but another area might be the gated cemetery in the wildy, but the threat of pker's makes it too unreliable. Stick to the sewers, and world hop if you have a hard time finding a less crowded world. Also, the release of the Stronghold of Security has brought a whole dungeon level crawling with undead for you to Crumble! There are a few safe spots, but these monsters are at a MUCH higher level than their counterparts elsewhere, so I recommend it mainly for those with high levels. Do not by any means go to Karamja, there are no safe spots there, even though some of the rocks would make it seem as though there were.

NOTE: Supposedly, according to the new area guides by Jagex, Ghosts are weaker to magic attacks because "Magic works better on enemies with no body. Thus, if you are doing this purely for exp, you might wish to venture further into the Sewers to find ghosts, or alternatively got to the Stronghold of Security floor 4, and attack ghosts there, though they are stronger than ghosts found elsewhere. Be warned, however, that ghosts in f2p do no drop anything.

Curses
Zombies across the water in Varrock Sewers, Lesser in
Wizard Tower, Zammorak Monk in Varrock Castle. Any leveled player can safely use those. Aside from random events, you should not be attacked by anything.
Also, it is not confirmed, but supposedly cows from outside a fence are great curse targets, as their hide is supposed to resist magic. Again, I am not positive on this, and doubt its true.

Teleportation
Duh. Obviously whatever city you teleport in.

Alchemy
If you have a lot of items to alch, you might want to go to a central market area, like Varrock Center, with your items noted, or a busy area like Draynor Willows, so that you aren't bored to death while alching. Both areas are near a bank so you can periodically deposit your gold. Alternatively, you can stand near the Wilderness north of Varrock and watch the fights that go on, but be careful not to accidentally click into Wilderness. Even if its level 1, if you donft pay attention, you could die pretty quickly.

Section IV: Quests
There are two f2p quests that give magic bonuses: The Witch's Potion and Imp Catcher.

For the Witch's Potion, cook some rat meat, bear meat, or beef until you burn one. Head to port Sarim to Betty's Magic Emporium to buy a Newt Eye for about 3-5 gp. Then head to Rimmington, stopping by the farm patch on the eastern side to get one onion. Talk to the Witch in Rimmington, asking her to bring out your Dark Side. Go into the house with Brian the Arrow salesman, and kill the small rats. You should get a Rat's Tail. Now go back and talk to the Witch, giving her the ingredients. After she tells you to, drink from the cauldron for your Quest Point, and 325 magic exp*.

Now head north from here to the south entrance of Falador. Kill the imps in anyway you choose until you have a Red Bead, a Black Bead, a White Bead, and a Yellow Bead. Go to the third floor of the Wizard's Tower and talk to Mizgog to start the Imp Catcher quest. He will ask you to find his magic beads. If you already got them as I told you to, talk to him a second time. He will reward you with an Amulet of Accuracy (a good substitute for a Magic Ammy until you can afford one) and 875 magic exp*.

Both quests can be done at level 3 Combat with not requirements, and give a nice boost to your magic training at the beginning.

Section V: A Few Quick Tips for Pures
Just some basic information for making a magic pure. First, make sure that Defensive is not highlighted on your staff. This will net you defense exp and screw your pure. Also, resist the urge to bury bones. Its hard yes, but prayer adds to combat levels.
However, it is safe to train range, attack, and defense. Range can be trained to less than your mage, and attack and defense can each be trained to less than half your mage level, if I am not mistaken. I highly suggest training range. If you are worried about the extra HP messing your combat level too much, train your mage via curse, teleports, or alchemy, so that range is the only source of HP exp, although more HP will help for the lack of defense. Range also allows you to be a very versatile PKer, able to change attack styles if needed, plus you can wear draghides, which give great defensive bonuses without increasing defense (although your mage attack will suffer).

Section VI: Final Notes and a few Random Facts and Tips
Keep in mind this guide is meant for f2p, but the basic premise remains the same for most of the methods. Notably, they have better robes and staves, more offense spells, and use Camelot Teleport over Falador Teleport.

Now a few random, somewhat fun factoids and a myth or two busted, and a few other tips:
Silverlight provides a magic attack and defense bonus of +1.
All daggers provide magic attack and defense bonuses of +1.
Contrary to popular belief, blue and black robes have the same bonuses, Blue and Black skirts have no magic attack or defense bonuses, and shade robes do not help magic.
Power ammies give a smaller magic attack and defense bonus than a mage ammy, yet provide other defensive bonuses that you may choose to use.
Bind is the only binding spell available to f2p. Almost useless alone, in team battles, if can help bring opponents down fast, especially if you have a ranger or two.
The enchants are good exp per spell, but very inefficient. However, you can turn a decent profit if you craft your own ammies, enchant them, and then sell them. The best to do this with on f2p are Ruby (Strength) ammies and Diamond (Power) ammies.

Well, I hope this guide is somewhat helpful. I would like to thank tip.it for providing the exp data I used in the early part of the guide. Happy Maging!

*Info for exp found on http://www.tip.it/runescape in their Magic Guide. It is their work, not mine, and I take no credit in the discovery of those numbers. All other parts of this guide are written by Indizle, for use only on the G.U.I.L.D.S. Mage Guild Forums at this time.


UPDATES:

10/29/09—Updated for the Guilds website by Kamakiri88
9/15/06--Added Hobgoblin Training Spot, Cleaned up Training Spot section, added more info about Crumble undead, added info on ice giants and ghosts
7/5/06--Added New F2P boots to Curse Outfit, Moved Guide to new GUILDS Forums
4/28/06--Added Curse Training Outfit to Section II: The Gear
6/22/06--Added Crumble Undead Info (with training spot), added new training spot for mid leveled mages.

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Last modified: 12/01/06.