Drop effects of the same type, stack together (meaning they add together, not multiply one another)
Medal of Fortune, makes it so when you defeat a monster, instead of 1 death giving 1 round of drop chance per category (Common, Uncommon, Rare, etc.), it will give 2 rounds of drop processing for each category.
So if there is a 10% chance for a Very Rare Tier drop, you will have 2 chances, to get a 10% Rare Tier drop.
Medal of Very Rare Gathering, increases the Very Rare Tier drop chance, by adding to it. If we use the above example, if the drop chance for a Very Rare Tier is normally 10%, it would add 10% to it, making it a 20% chance to receive a Very Rare Tier drop.
Medal of Prosperity, increases the base item drop chance for all tiers, after level considerations. This means, after level adjustments (As you out level a monster, their drop chances reduce), drop rates are increased by 50% (50% is not added), so again with the above example, if you have a Very Rare Teir chance of 10%, it would increase it by 50%. [0.10 * 1.5 = 0.15] Making your Very Rare Tier, a 15% chance. And to follow up on the Medal of Very Rare Gathering, it would then add its 10% on top of that, making it now a 25% chance.
Medal of Abundance, Increase Maximum Item Drop Quantity by +3. What this means, is if you have an item that drops in a quantity (basically anything that's stackable, so not gear), you have a chance on pickup, to have the quantity increase by an additional 3 items at maximum. So, if an item has a normal drop quantity of minimum 1, and maximum 2, the item increases the maximum to now be 5. This makes is so that you now have a minimum 1, and maximum 5, to get when the item is picked up. Some stackable items that are generally high in usefulness, are set to a 1 min / 1 max, so this item can greatly increase your rate of gathering those kinds of items.
Premium Service, +50% Extra Drop Rate. Much like the Medal of Fortune, where it gives an additional drop, consider this a +100% to an extra drop, and the Premium Service is a +50% increase. These effects are added both together, and for every 100%, it is a guaranteed additional drop roll for every monster you defeat. So if you weren't using the Medal of Fortune, and only have the Premium Service, per monster, you would have a 50% chance of an extra drop process occurring.
So, with everything above active, and if we continue the example of a base 10% Very Rare Tier drop chance, this is what you could expect with all of those active.
You will have 2 drop processes guaranteed, with an additional 3rd drop chance of 50%
For each successful drop process, you will have a 25% chance of a Very Rare Tier item to be selected and dropped.
If any of the items in the Very Rare Tier drop are stackable, you will have an increased quantity roll, to its maximum, by 3.
I hope this helps you understand how they each can help influence your ability to find items. I know it may sound a bit confusing, but be assured they all help you in their own way, each being a good help, when they are all combined the outcome can be very beneficial.
Edited by Banrukai, 29 July 2015 - 04:29 PM.