I (newbie GM) will be running the 1st episode of HotDQ for a party of 6. While the intro states that the difficulty of the encounters can be adjusted for parties != 4, it offers no guidelines to do so (except for one encounter much later in the game, where they instruct the GM to add a berserker for each player above 4).
We're all very new to 5E (didn't read anything or test until it came out), so, while I do want to challenge the players (no pampering!), I don't want to make the encounters so challenging that they don't have the resources to handle them (i.e., I don't want them to blow their daily resources for fights that should be manageable without those).
I read a few answers that applied to 3.5 and PF, but those offered more general advice–was hoping for some insights with 5E.
Thank you :).
Best Answer
There are guidelines for increasing the difficulty of an encounter. Basically, you calculate the XP budget for 6 characters. So instead of 100 XP for an easy encounter at L1, the XP budget is 150.
However I would not do anything at all with the encounters at first. Wait until your PCs are consistently breezing through them. Most groups need some time to get their feet under them, and the HotDQ part 1 encounters are not cake walks for parties of 4 PCs. Let them roll the encounters in part 1 if they can. Note you may want to use milestone leveling instead of actual XP for at least this level since they may not earn enough XP to advance this way.
That said, if you're looking for the actual guidance on leveling up the encounter, you'll need to deconstruct them a bit before you start. Take the monsters and recalculate the award XP, then figure out what you want to add. Use the chart from page 57 of the BD&D DM book to note what the difficulty multiplier for specific monster groups is (for instance if you have 2 monsters, the difficulty of their XP is multiplied by 1.5).
So let's take our encounter of 6 kobolds. Kobolds are worth 25 XP each that means our base encounter level is 150, however, with 6 of them that gives an encounter difficulty XP of 300. That's a medium encounter for 4 PCs. So if we want to up this by adding more kobolds, we'd need to change our difficulty modifier (since 7 is the next level). If we know our encounter budget is now 450, then we can divide that by 2.5, which gives us an actual budget of 180 XP, dividing this by our Kobold's 25 XP, we get 7.2 which tells us we need to add just one extra kobold.
This does leave us in a bit of a lurch when it comes to advancement XP. Since we add 50% more characters, but only ~15% more XP. This will be corrected by most encounters not needing this kind of scaling (use groups of different monsters more often than not). But can also easily be corrected by introducing the optional level up rules that ignore XP (what I'd recommend).
One other thing I've played around a bit with and haven't had enough time (or diverse enough groups) to do a full play test on is the idea of playing with the average HP and damage of the monsters. Basically, I always use the average HP and damage numbers for my monsters. This provides a different kind of difficulty tweak than adding extra monsters. Basically you could adjust the HP and damage up a bit (take 2/3 of the die instead of half, or more) and automatically make the encounter more deadly. I've mostly played with this the other way, reducing difficulty without changing numbers for a 3 person party. It worked pretty well, but may prove much more deadly if you raise the damage too much and find yourself oneshotting PCs.