I did rand(1,165) 180 times in Excel. I then copied the values to a different part of the spreadsheet (so they don't keep recalculating) and sorted. Based on eyeballing, results are as follows:

90 came up six times

59 came up five times

52 came up four times

69 came up four times

81 came up four times

82 came up four times

143 came up four times

54 came up three times

106 came up three times

115 came up three times

141 came up three times

156 came up three times

Getting an "evenly distributed" result when generating random numbers is actually fairly unlikely. Getting some clusters is normal. My test was even more clustered than yours. Getting the same thing five or six times is fairly unusual but will happen occasionally. Getting the same thing three or four times is normal. The only solutions I can see (assuming you actually think it's a problem) are:

a: add more items

or b: make a "no duplicate drops" world option.

Sure, data is good, but as far as I can see the data shows that there's no problem with the random number generator. The problem is that people assume if you get a lot of an item that's not random, which is simply not the case.

I agree that the random number generator may be working fine given the fairly small pool of available items and the fact that much like the birthday example it is statistically much easier to get a duplicate of any item rather than duplicates of one pre-determined item (however, it may also be broken because on a moderate proportion of games I've had 3 or 4 of the same item after picking up less than 10 items, I don't know exactly what the available pool looks like but it needs to be fairly small for this to happen moderately frequently).

However what is more important is how the game feels. It feels like the random number generator is broken because I like plenty of others keep collecting multiple copies of the same item. This both feels wrong and is un-fun. The game would feel better and be more fun if this was fixed, either by significantly increasing the item pool (probably a time consuming solution), implementing a system which reduces the chance of giving already found items (much like the iTunes semi-random shuffle that others mentioned) or by fixing the random number generator (if indeed something is wrong with it).

I think something's wrong with your stats as you are mixing up common items (the gray ones) and uncommon items (the yellow ones) and also the rare ones (orange). The pool of common items is much smaller (about 74 or such) but should account for the majority of drops which can explain some repeats.

On the other hand, you get less uncommon items per game and they draw from a much larger pool of items (about 124 base and 165 for you with mods and DLC which sounds about right). I don't know how many uncommon drops you had what with the custom stuff but I see you found 6 uncommon items three times: Staff of the Furnace, Ignys Shortbow, Mirror Shield, Amulet of Flames, Amulet of Warding and Band Of Agility. This is pretty much a constant and it's weird.

Then there is the impossible stuff such as getting the same item three times in a row, even if its a common one. In my current game it was a Tear of Cyndrum.

Why not have an opt-in system where people who want to can have (I guess non-modded games only) a way where Stardock can look at the randomizer algorithm.

I have noticed some very odd behavior along the lines of the original poster too.  I notice I tend to get items that I'm guessing are around the same random number sample.  For example, in games where I find bows as loot, I tend to find a LOT of bows. 

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