We've all done it. Rolling a single die and have it come up a 1. That is so frustrating! It makes you want to say, "I wish I has not run/shot/etc at all."
A while back, I proposed a house rule to my mate Keith to have a fun way around this.
Enter the One Token. Holder of this token can re-roll a single die. It has to be a single die like a run roll, single to hit roll, single reserve roll. Roll that are ineligible are things like Leadership, to hit rolls that are rolled in multiples (examples to follow), or anything that has already been re-rolled. Once the roll has been made, you must accept the results even if they are another 1. That's tough luck. Once the re-roll has been made, the holder of the token passes it to his opponent.
Specifics on which kind of rolls are acceptable and which kind are not. The key is that it has to be a single roll. A SM Sargent with a Powerfist gets 3 attacks on the charge so none of those rolls are acceptable. But a Techmarine with a Servo-arm gets a single Powerfist attack. If that roll was a 1, it could be re-rolled with the token.
Single attacks that are rolled as a group are also off limits. A group of SM Scouts with Sniper Rifles get one shot each. As long as long as there are more than one of them, you can't use the token. The Sargent of the Scout Squad from the previous example, could use the Token as his attack is rolled separately (different BS and Character).
You can use whatever mechanism you want to determine who starts with the One Token. Whoever had it last at the end of the previous game (if you remember) could retain it. If you have never played with the person before, you could give it the person that loses the roll off for who goes first. Alternatively, each player could roll a single d6 and the first player to roll a 1 gets the token.
I have yet to play test this, but it seems like a good idea. It s restricted to the bottle neck rolls are really disappointing but don't change the game too much. Since the token changes hands, it evens out over time as both players have access to the same skill. Also, one could strategically not use it to deny giving it to his opponent.