When you both play blindfolded, it becomes a meta game of knowing your opponent and how he plays, what patterns he uses, and then trying to change your own patterns to exploit what he thinks your moves are going to be and so on.
For character, I usually just let the game pick a random one for me. I found that after the initial fun of learning everyone's combos and special moves, the basic kicks and punches were all you needed. That was the real secret to MK: Precise use of high kick, sweep, uppercut, and block could pretty much beat anyone who made a mistake. If I wanted to show off (MK3), I'd pick Sindel and not allow one hit against me. I think I was the only person in town who used that character.
Another fun variant was to offer to only use one attack button (high punch, high kick, low punch, or low kick), and allowing your opponent to use all of them. Bonus fun: Let your opponent choose which button you are limited to!
Yes, this was the best kept strategy. Newcomers especially would focus heavily on learning the special moves, assuming the regular kicks/punches to be ineffective (or less effective). Big mistake.
That Liu Kang kick where he used both feet and sounded like a chicken was damn near impossible to defeat when your opponent was spamming it. Every now and then I could block and upper cut but mostly I would upper cut and start getting kicked again.
For character, I usually just let the game pick a random one for me. I found that after the initial fun of learning everyone's combos and special moves, the basic kicks and punches were all you needed. That was the real secret to MK: Precise use of high kick, sweep, uppercut, and block could pretty much beat anyone who made a mistake. If I wanted to show off (MK3), I'd pick Sindel and not allow one hit against me. I think I was the only person in town who used that character.
Another fun variant was to offer to only use one attack button (high punch, high kick, low punch, or low kick), and allowing your opponent to use all of them. Bonus fun: Let your opponent choose which button you are limited to!