One of the things I love about Arkham is that if you think about role-playing your character, you very often stumble on some good tactics. In the case of Dexter Drake, I think he works a little bit more effectively if you remember that he's The Magician, not the Wizard. He doesn't have huge reserves of sanity and giant lore bonuses because he's not actually a dedicated spellcaster. He's a showman who happens, by way of his professions to have a lot of connections in the occult underground, and it's those contacts that make him valuable. Also: he's an artist. Like all artists, hecan do great things with enough cash, but he really benefits from having a patron. Okay, enough flavor talk. What does that mean in gameplay terms?
Well, here's how I approached Dexter the one or two times I've been dealt him. Magical Gift doesn't actually reward you for using spells, it rewards you for collecting them, so that's what I focus on. You start the game with Shrivelling, which is a good spell that Dexter can't use that effectively. With 3 Will and 5 Sanity, he just can't afford to use it that often. He doesn't cast it as reliably as the Professor would, or the Student if you build her for casting. He also starts with 3-choose-2 spells, but so few spells are worth using for Dexter that it's really not better than anyone else who starts with 2 randoms. As others have noted, he just doesn't start in a good place to accomplish much with magic. However, he does start in the Magick Shoppe, with $5. That means he can immediately buy another spell (choice of 3). So at the end of the first turn, he will have taken a wither, and then looked at a total of 6 other spell cards. (If you're *really lucky*, he'll also start with a Tome he can get another spell from.) In the basic game, that means he will have drawn 7 cards from a 40-card deck. As others have mentioned, combat spells in this game are not that great. Plus, you tend to find way mroe than you can sue anyway. So skip the combat spells. The utility spells in the deck come in 3 or 4 copies each. That means Heal and Voice of Ra each have about a 50% chance to show up, while Find Gate and Mists of Releh are better than even. Finding Wither is a near certainty. Now, sadly, most of these spells aren't that great. He can't afford to use Heal and doesn't really need to, he's mediocre at sealing gates, and with 5 Speed 4 Stealth 2 Focus, he can usually get where he wants to without using Mists. We still haven't actually done anything worthwhile.
The solution I found is that Drake works best as the assistant to a more powerful caster. He's so fast that on his second turn, he should be able to meet up with any other investigator in the city and give them his spells. Imagine setting up the Professor with Find Gate and Mists of Releh. Or the Psychologist with Heal and Shrivelling. Either way you have a powerhouse of a character. Unfortunately, you also have an even-more-useless Magician sitting around. What to do with him? Well, you have a few options. The first is to have another investigator give him money and send him right back to the shop. With his ability and his speed, he's better at spending money efficiently than most other characters. You also want to give him all of your Tomes. Not only can he choose what spell to learn from them, but he has enoug Speed that he has time read while still running around. If one of Harvey's 2 unique items is a spellbook, Dexter can actualy meet him in the admin building, read his book for him, and hand off the resulting spell on turn 1, freeing Harvey to amble into battle with his full 3 movement. Other cute tricks include giving all his possessions away, then taking out a bank loan and spending it on more magic. (I assume the bank doesn't repossess your spells when you default) I think people underestimate the value of trading equipment, and I think having a team "courier" is a viable role; I played a Photographer in a similar way recently. But in the long run, you do need all of your investigators to actually contribute something. I suggest giving Dexter 2 Wither spells and a sword, and making him a "troubleshooter." He can't handle the big monsters or the scary gates on his own. What he can do is use his 5 speed to run all over town, killing weak monsters as needed to to clear the path for the real heroes to get where they're going.
TL;DR: Dexter isn't great at personally completing major objectives, so he suffers in 2-investigator matches. But I think he can pull his weight with 4, as long as you have another spellcaster and ideally a wealthy character on the team.