SR3 has fairly specific grenade timing rules (SR3 p. 118). Grenades go off when any of criteria are met; they are checked in order:
- The next Combat Phase of the character
- The end of the next Initiative Pass
- The end of the Combat Turn
These are all very specific time references, but they require us to look at the Initiative section, starting on SR3 p. 100.
At the beginning of each Combat Turn, characters generate an Initiative Score. These scores are compared to determine order.
The count starts from highest Initiative Score and descends to zero; one full cycle is an Initiative Pass (SR3 p102, first column). When a character's Initiative Score is reached, it becomes that character's Combat Phase (SR3 p. 104).
Once every eligible character has taken a Combat Phase, all Initiative Scores are reduced and a new Initiative Pass starts at the top. Anybody reduced to an Initiative Score of zero or less does not get a Combat Phase during that Initiative Pass.
SR3 p. 103 reiterates the same timing paraphrased above, and adds the note that timed items always lose ties. If you need to split a tie within a given Combat Phase, the bomb always goes last.
So, example time!
Pass Score Character
1 32 Schneller-als-Sie does stuff, unrelated to Bombs-at-Midnight.
1 17 Bombs-at-Midnight throws Grenade A.
1 0 End of Pass 1 - Grenade A does not go off yet, none of the
criteria were met; Criteria 2 is the end of the NEXT Pass.
2 22 SAS does stuff to BAM; she reduces BAM's Initiative Score by 2.
2 7 BAM would have gone, if SAS hadn't done things...
2 5 BAM throws Grenade B.
2 5 Grenade A detonates; Criteria 1, but timed items lose ties.
Despite changes in BAM's Initiative Score, it's based on BAM's
Combat Phase, not Initiative Score 7.
2 0 End of Pass 2
3 12 SAS throws a Grenade C at BAM, because turnabout is fair play.
3 0 End of Pass 3
3 0 Grenade B detonates; Criteria 2, because BAM didn't get to go in
Pass 3. We'll say SAS looses 3 initiative from things.
4 2 When SAS would have gone, if BAM hadn't bombed her at midnight.
4 0 End of Pass 4
4 0 End of Combat Turn
4 0 Grenade C detonates, Criteria 3, because there are no more passes
and the turn is over.
I think the windows where somebody could pick up the grenade and throw it back are fairly obvious. Note that when the bomb goes off has nothing to do with what the ah... secondary thrower... does. It's based off when the initial thrower pops the spoon and lets fly.
I've left out any many of the details of the Initiative system as possible, like how values are generated and modified, because they're not relevant. It's worth noting that in SR3, an entire Combat Turn is very short in comparison to many other games - three seconds (SR3, p.100, middle of the second paragraph).
Also, there is equipment in Cannon Companion (p. 32, et. al.) that can make launched grenades explode on the same Combat Phase they are fired.