In Dark Heresy (and to an extent, WFRP 2.0), some combat has been as complicated as this:
PC wants to attack an Orc
PC has already suffered a critical hit from earlier (blood in his eyes), so he gets -10 to his attack roll
PC has higher ground than the Orc, so he gets +10 to his attack roll
PC is attacking defensively, incurring a -10 penalty to his attack roll
PC is standing in thigh deep snow, incurring another -10 penalty to his attack roll
The orc is being flanked by another PC, so the attacker gets a +10 bonus to his attack roll.
Half of those rules had to be checked out in the rulebook to make sure. Luckily, I made a quick reference table outlining these bonuses and penalties.
Even then, some quick math had to be done- at 11PM, already a bit drunk, this took a second or two to figure out. God forbid someone else mentioned another modifier we hadn't included yet.
If these new dice will make it as simple as adding a "danger die" to the attack dice pool for every complication or penalty mentioned above, it could potentially speed up gameplay quite a bit.