Sometimes you just want to play Magic by yourself. Or at least I do.
I starting playing solo Magic before I played Magic Online, but I still play today. Sometimes I just don't feel like playing online, or sitting behind a computer. Also there is just something special about shuffling cards, tapping your lands, and windmill slamming down a Terra Stomper. Solo play is also especially good for playtesting a specific matchup. It's just you and two decks - play 100 games if you want to.
Don't I know what's in my opponent's hand?
This is really the only thing in your way from making this work, and I believe it is a very solvable problem. First, you have to separate what you know and what each "player" knows. You know player one has a Mana Leak in his hand but player two doesn't know this. All he knows is player one has two mana up and is playing blue, plus whatever other information he's gathered from that game/match. This is a very important distinction. Once you can separate in your mind what each player knows then you can make decisions for that player based on that information. So player two's Leatherback Baloth gets countered and he makes a mental note - "watch out for Mana Leak".
You might think that keeping up with what each player knows is a bit much, but it really isn't too bad. You just have to "track state" for two players instead of one and it probably makes you a better player. Also it's really not as bad as it seems because of the way Magic plays.
Duress? Yes, odds are you'll snag a good spell. Even if your opponent had nothing but creatures and lands it was still the right play. So, when you're playing single-player you cast the Duress even though you know your opponent has no viable targets because it's the right play. My point here is focus on making the right plays and don't get bogged down in what each player knows.
Now sometimes it's just too close and too important. Player one has two mana up with a Doom Blade and Mana Leak in hand. Player two attacks with a Leatherback Baloth. Do you Doom Blade the attacker now or save mana for a Mana Leak to try to catch his four drop? You start to decide what the right play is and you remember player two has a Vines of Vastwood in hand. So, when you cast the blade he's gonna kick the vines to void your removal and smash you for eight. Then you won't have the mana for a mana leak and he'll resolve a Skinshifter. You realize the game pretty much comes down to whether you cast Doom Blade right now. What's the right play? It's not obvious and it's really important. What to do? Roll a dice! Odds for Doom Blade even for Mana Leak. Keep your dice handy for important decisions that you don't want to make. I even use this when it's not a 50/50 split. So I ask would player one know to make this unusual and very smart play? Maybe - it depends whether he noticed X, Y, and Z. Ok then if I roll a five or a six then he makes the play.
How do you sit on both sides of the table?
Don't! Check it out.
You just play side by side. No need to move to the other side of the table or read upside down cards. Sometimes it gets a little crowded on one playmat. You can spread out if you want or just stack cards.
What about goldfishing?
Why would I ever do this?
It's fun. I really enjoy playing this way; It's like Magic Solitaire. Maybe I'm just weird, but what I enjoy most about Magic is trying to understand the complexities of the game. Build two decks with whatever cards you have and play them against each other ten times and you will learn a lot. Each matchup has a story to tell. If you pay attention to who won each game and more importantly why, then as you play more games your understanding of the decks, the matchup, the cards in the decks, and Magic in general increases.
Try it out!