Mithral armor has a redced arcane spell failure (ASF) chance. It can be pretty expensive for the first few levels, though.
Other than that, spells without a S component (somatic) are not affected by ASF. There are not that many of those spells but the still spell meta magic will make any spell lose its somatic component.
And last but not least there are a few arcane spellcaster classes that can cast in armor without any failure. Bards can cast in light armor (later also in medium and heavy with the arcane duelist archetype), as can summoners. The Magus is probably the closest thing to a "combat mage" you will find and can cast in light armor, medium armor (at level 7) and even heavy armor (at level 13).
The magus from UM is the most immediate solution,even thought he only has 6 spell levels.
Mithral armors and shields have the arcane spell failure chance reduced by 10%.
Multiclassing to Eldritch knight is another option,but for higher levels.
Other than that i can only think of house rules.
edit:as Blave ninjaed me said,he can pick metamagic feats.
He might be better off playing a magus. That's basically a wizard with less casting and more fighting, plus abilities to combine the two. The magus starts with casting in light armour and later progresses to medium and heavy.
Other than that, there's nothing to help with casting in armour.
There's a spell in the 1001 spells, pathfinder compatible that is called "Flex Armor". It's a 2nd level spell, doesn't have a somatic component and reduces your spell failure chance for 1 minute per level. It also increases max dex on your armor.
I'm not sure wether 3PP spells are a good advice.
I'm not sure wether 3PP spells are a good advice.
It's up to him and his GM. It's a good spell for the question of this thread, how to reduce arcane spell failure chance. I use it with my character, and the question wasn't what strictly pathfinder ways can I reduce asf%. Feel free to offer your "good advice".
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I'm currently a Fighter1/Wizard2, headed for Eldritch Knight.
At the moment, I wear a mithral chain shirt and just suck up the remaining 10% ASF chance. (So far, I've been lucky and have only fizzled a cantrip.)
For additional armor class (when I need/want it), I have a wand of shield.
At 5th level, I'll be taking the Arcane Armor Training feat, which will take my ASF down to 0%. (Though I might upgrade to a mithral breastplate by then, leaving me with 5% ASF.)
Feel free to click my name to check out my stats.
A Fighter/Wiz in a recent game picked up Still Spell versions of all his spells and wore Breastplate. He also carried about 5 wands.
Well another option I could think of is potentially going with Still Metamagic.
Armor interferes with the gestures that a spellcaster must make to cast an arcane spell that has a somatic component. Arcane spellcasters face the possibility of arcane spell failure if they're wearing armor. Bards can wear light armor and use shields without incurring any arcane spell failure chance for their bard spells.
Casting an Arcane Spell in Armor: A character who casts an arcane spell while wearing armor must usually make an arcane spell failure check. The number in the Arcane Spell Failure Chance column on Table: Armor and Shields is the percentage chance that the spell fails and is ruined. If the spell lacks a somatic component, however, it can be cast with no chance of arcane spell failure.
Shields: If a character is wearing armor and using a shield, add the two numbers together to get a single arcane spell failure chance.
Because with still Metamagic, you wouldn't be making any movement gestures, thus you would not be hindered by the armor in casting the spell. This, however, is only a partial solution since this would be increasing the spell level costs of quite a few spells.
Nvm... just realized Bwang beat me to it... -_-;
Metamagic feat Still Spell.
feats Arcane Armor Training and Arcane Armor Mastery.
Mithril Armor.
Ring of Force Shield.
Those are the only options I know of for a Wizard, though medium and Heavy armor certainly aren't the only way to improve your armor class. Of course if you're going to wear medium and heavy armor, you need to be proficient in it as well...
Good choice.
He should take a look at the archetypes. Some of them are cool, too.