Are the hit percentages predetermined?
I was playing a Terror mission last night where after my unit would enter an area, a Cyber Disc and two Drones would come around the corner of a building. All four of my other units were in a position to shoot. My sniper with DoubleTap showed an 85% chance to hit the Cyber Disc. So I fired missing once and hitting once. My heavy missed twice, and my two assault guys hit once and missed once. I wasn't able to kill the Cyber Disc. I then reloaded from a save point and tried again, and again, and again.
Every time I got the same scenario, sniper miss, then hit. Heavy miss, miss. Assault hit, assault miss. I tried different weapon modifiers, but after five attempts I decided either the game was cheating or I was just so unlikely that given an 85% chance to hit I missed 5 / 5.
It's not cheating as such; the game preserves it's random seed on re-load. Reloading a turn and repeating the same actions in order will produce the same results. This is because the game saves the seed it's using for the random number generator precisely to prevent this kind of constant reloading. Jake Solomon, the creative lead for XCOM was quoted in this article:
We use synchronous random in combat so the player can’t just reload when they miss a shot. Now, obviously there are ways around this, but this is a decent way of ensuring that the player’s choices do matter.
You can "game" this, if you like, by taking different actions and changing up your order. Assuming you are shooting at the cyber disc, try [something to miss], sniper, [something to miss], [heavy or assault to hit].
Bear in mind that the actually aim-scores will impact here. It's possible someone less skilled, or with an inaccurate weapon, would be unable to hit in actions 2 and 4. Likewise, your sniper could hit in actions 3 and 5, because he's got the most accurate weapon. And yes, if you do different things on these actions (aim at different targets), you may not get hits where you expect it. The sniper using action 2 might hit the Cyber Disk but miss the Muton in full cover you decide to aim at instead.
According to this article at PcGamesN, the X-com expansion will include an option to reset the random seed on loading!