Path of Exile

I made a (wannabe) Monte Carlo Simulator for the Twilight Lootboxes. Results inside.

Happy New Year Exiles,

So now that I got 4 free lootboxes, it got me thinking: what are the actual odds in these?

I’d like to invite you to think what are the odds of “winning”, if you’re going for the full set, when opening these boxes before you keep on reading.

I'm not sure anyone did it yet, so (since I'm done for the league) I put a poor man's / wannabe Montecarlo Simulator to check it. It can also be repurposed down the line if you want. Just set up the chances and a macro (absolutely legal in this case) pressing arrow down and pasting values, and leave it running for 20 min or so, should get you about 2-5k runs depending on your PC – or crash your excel.

It's nothing too fancy, I just went making it up as I needed, so it might look a bit like a Frankenstein but it gets the job done.


TL;DR:

The results:

Average 316.49
St Dev 98.27
Median 299
Max 931
Min 129
Count 4030

A histogram showing the 4030 runs.

Link for the excel file.


Discussion:

I made a model simulating 1000 boxes, which I imagined to be way too much and ran it 4030 times (that's a lot of boxes). However, turns out that an unlucky pal would have spent 931 boxes to get there apparently – so maybe it wasn't that much in the end. It is also worth noting that it didn't overflow (not opening all items in <1000 boxes) in any of the runs, but there is always a chance.

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With an average and median of about ~310 boxes or 930 USD / 9300 Points, it is no surprise that you should get the individual items once they come out. That's how lootboxes work after all.

If you are a gambling addict, however, you might be eyeing those 129 boxes, or the low end of the distribution. It is, after all, CHEAPER than the advertised full price tag of all items bought individually (that would be 7970 points for all items, including the combined ones). In fact, 7970 points translate to about 265.67 boxes, and 1388 runs were at 265 or lower box-count.

In other words, there is a 34.4% chance that you would do better opening boxes than buying the all the individual items at full-price. If we take into account the armour packs discounts (120 + 120 + 240), that brings the total to 249.67 boxes, and we had 1069 runs below that threshold, or 26.5% chance to win. I'm not sure about you, but I certainly expected way less than that. (And no, I won't get in the discussion of all the "extra value" of having 10x the 320 points Sunrise Wings rotting in your inventory, they are worthless after the first).

Model:

As for the model, you may see for yourself, and I'm sure there are more elegant ways of setting it up, but this one took me roughly 30 min to get to the finish line (clear speed meta in full effect). In short, the model is simulating 1000 boxes, checking where the first of each item appears and then checks where the second item of the ones that do the "Combine-Thingy" appears. (I'm sorry that my notation doesn't let you mess around too much in the first sheet without breaking it, but that's how I roll). The minimum boxes needed for the full set are the maximum of all these values for Rare, Uncommon and Common rarities. That means you got at least 1 of each item, and 2 of the ones you combine (1 for you and one to combine). And yes, for the record, I know, #ExcelNotTrulyRandom.

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Closing thoughts:

At 26.5% chance to “win”, it is not exactly UNETHICAL odds, but the fact that we have a closed market and so are left with the possibility of having 10 of the same item rotting in the microtransactions tab is certainly disheartening. I obviously would like to see either something closer to 40% with a closed market or an open secondary market to trade between players – even at the current odds I think it would be fine.

Since the chance is not ACTUALLY abysmal (I expected 10% or less to “win” coming in), if I were REALLY bored, I'd solve what is the optimal number of boxes to buy before (i.e. now) and then wait for the shop release in order to complete the set with the individual items – this way minimizing the points spent (if you're going for the full set). Since, let's say, at 90% completion, the expected value of the additional box opened is likely not worth the 30 points (which my model ignores and keeps pushing for the 100%). But I'll leave that exercise for the reader (or do it in the next release) – since my model is not exactly the best starting point for that.

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Have fun simulating lootboxes! And pointing out my mistakes in the worksheet (I've found a minor one already while typing this) – if that’s your kink.

Source: reddit.com

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