Why do we roll for initiative they way we do? It's needlessly slow and dull, even requiring table gimmicks to keep track. But here's a few facts:
If a player rolls a d20 and the GM rolls a d20, then the player has a 50% chance of beating the GM and gaining initiative.
After Initiative order is set, who goes first is no longer important after the first round since everyone is taking turns.
How do you speed it up? First, use team initiative. The players will have more flexibility that way and beyond the first round, it's just alternating turns.
The GM is the only one who rolls an Initiative die (d6). If he roll 3 or lower, the enemy goes first. If he rolls 4 or higher, the players go first. Want to spice it up? If the GM rolls a 1, then not only are the monsters aware of the heroes, they've set up an ambush. Their are more monstrous reinforcements waiting to spring on the heroes. If the GM rolls a 6 then the heroes have taken the enemy completely by surprise. Hey, sometimes you don't have to be stealthy to scare the hell out of someone rounding a corner.