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Emotions and Randomness - Loot Drops
by Chris Grey on 04/03/13 06:25:00 pm   Expert Blogs   Featured Blogs

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.


Even though randomness can be used to greatly influence a player's experience with a game, I haven't seen many people put much thought into crafting it. We've all got war stories about a rare drop that took us hours to get, if not tens of hours. Gamefaqs is loaded with forum threads talking about the despair of the random drop. Even worse are the threads made by people who got the drop in one go, bragging and taunting the rest of the community, as if luck with the random number generator were something they actively controlled. For better or worse, randomness currently colors the play experience tremendously; why not talk about crafting it more actively from our side so that these experiences are less accidental?

Today, I'd like to focus on drops. I'm being a bit loose with the word because I'd like the ability to talk about both items dropped by defeated monsters and the monster taming process in Ni No Kuni, where enemies randomly become recruitable after you beat them up. I'm going to avoid giving hard numbers wherever possible; my aim here is to give a few heuristics about how randomness feels to the player.

First, let's look at the way it's done now. Typically, designers look at the in-game economic value of an item and decide how scarce it should be. More powerful items either appear later in the game or drop with a much lower constant percentage chance. The idea here is that players should feel some kind of sense of accomplishment when they obtain the item, or at least see how lucky they've been. Either way, it'll bring the players to value the item, hopefully in accord with the designer. If players manage to get the drop in the average number of tries, if the designer has valued the item correctly, the player will typically have a similar valuation of and appropriate attachment to the item.

With a constant drop rate, here's the graph that captures the farming experience. You might be expecting a bell curve here, but I want to illustrate something else born from this data. To do so, we're going to change the vertical axis to reflect the following: assuming your players kill enemies until they get one of the items, here's how long the player population will be farming.


 Population of Players Still Farming for Their First Drop Over Time

Pay attention to the shape; the key point to notice here is that the graph never actually hits zero. That means some of your players are never going to successfully acquire the item, and they will have a terrible time trying to farm it because they will spend tremendous amounts of time doing a task the designer had only pictured them doing for a fifth of that time. Even the good feeling at getting the drop if they eventually manage to get it is generally overshadowed at this level. What's worse, the time farming the item will skew a player's value of it; most players will resent having to grind a massive amount of time if others did not have to, and they will focus their resentment on the item in question. Naturally, this resentment will also spill over to the game, and they will undoubtedly vent about how unfair the game is to anyone that will listen. These players will be overfarmed by the nature of the task, and this also ruins the otherwise carefully crafted difficulty curve. Their frustration can lead to quitting the game, and if this player was dedicated enough to stick it out that long, you probably alienated an incredibly passionate player. All this angst for a random drop that probably didn't matter much in the bigger picture of the game.

...and the Queen save the poor souls who feel compelled to get the collect all random drops achievement. That synergy can quickly lead to tens of hours of despair and compulsion, if there are many items or especially rare items.

The problem with using averages to balance in this case is myriad. In the graph, notice that about sixty percent of players will receive the drop before the average number of attempts, and half of the population gets the item significantly before the average. This means most players won't be seeing the event as many times as the designer probably designed for, and in reality, as any one player usually only goes through this process to get any one drop once, this will become the general consensus on how long the experience takes. Potentially a happy mistake, but it does diminish the feeling of effort the designer probably wanted the most players to feel. Of the rest, it can be expected that about twenty-five percent of players will take more than one and a half times the average to get the drop, and more than ten percent will take more than twice as long as average. If these players look to the rest of the player population, they will see their experience taking more than two to three times as long as the lucky half, respectively.

A designer with fixed resources would be drawn to craft the average experience when, in all honestly, it's the fifty percent who finished significantly early and the twenty-five percent on the tail that need the attention more. Additionally, the latter will be the ones to really begin to see the activity for the warts it has. If the designer neglects the tail experience and has several different drops required or encouraged in game, the designer will eventually fail all of their players; the more drops the player needs, the more likely that the player will be in that tail at some point in the game. By focusing on the mathematical average experience, the designer is effectively neglecting seventy-five percent of their players on any single drop.


Other Kinds of Randomness - Escalating Drops


I want to present two simple alternatives. The first is an escalating drop rate. Each time a player fails to get the drop at the end of the event, the probability it drops next time increases. This probability caps at a guaranteed drop, and once the item drops, the probability resets to some level. It can reset at zero if you only ever want one in the game; it can reset at the initial probability if you want to make the experience to get another item take the same amount of time, more or less, as the first time; it can reset at a high probability if you want the item to be valuable now but easy to come by later.

Here is the new chart for this experience.

 Population of Players Still Farming for Their First Drop Over Time With Escalating Drops


Notice how the line now hits zero on the right of the graph. It eliminates the abysmal experience we spoke of above. There will be unlucky players, but there's a cap on the amount of time they'll have to spend with their misfortune. There will still be war stories, but if designed well, the worst-case player experience can be designed for more easily, as it will more closely match the average. This can lead to those war stories that can enhance the player experience, as they feel like they struggled, but not much harder than the designer expected, which is nice way to give a bit of fiero. The angst of trying to get the item will always be fulfilled.

Additionally, if you set the initial drop rate low and let the growth rate accelerate, you'll have fewer lucky people as well. This could help if you want to make the player master a challenging fight through repeated attempts to potentially get a powerful item. It’s worth noting that the player who gets the item on the first try will have their difficulty curve distorted, even though this case tends to be more subtle than the player who takes many tries. Empowerment is not a bad thing, but it can lead the lucky player to think the game is much easier than it is because of a fortuitous break. In general, the escalating drop approach will make the experience a little more uniform for any given player, and usually, it will be relatively invisible to them.

There's a temptation here to wonder what would happen if you had to kill several of the same kind of monster before the item could even become available. If the player understands what's happening, and they know that they will be fighting several times before they could even get a drop, that fighting suddenly becomes work. Gambling in this form works because the payoff is potentially always right around the corner. It cannot be understated how powerful this force is to motivate. Asking someone to do something fifty times makes it a chore, and times ten through forty will not be savored because after the initial novelty of doing it, you know it will not net reward any time soon. If a task could be rewarded randomly after any one attempt, more attention to detail and care will go into it from the player. The player will appreciate the experience more if they feel like what they are doing could pay off at any moment, not just some long time in the future.


Other Kinds of Randomness - Diminishing Returns


This is the invert of above. The idea is that the player has a limited number of chances to get an item in game before it goes away completely. Typically, the initial probability of the drop will start high, and either decrease with each failure, or the event will disappear after a set number of attempts. Either way makes the drop impossible to get after a certain number of chances.

This randomness is tricky to deal with as you are, in no uncertain terms, guaranteeing that a percentage of your player base will never get the item. It can be more humane than the traditional way as you are giving no option to exchange time (farm) for in-game value. If the item has significant value to the player, and the player knows the stakes, there will generally be a significant amount of urgency put on the outcomes, and a skilled designer could use this as a way to make a large emotional mark.

There is an unspoken rule with these kinds of drops. They can be gamed by reloading. As with permadeath mechanics, players can still get some tension from the outcome while using the load function to try as many times as they want to obtain the drop. If the ability to reload is removed, as it was in Demon's Souls, then you may want to consider making the game short, but replayable, or having several different drops, only one achievable in the game. This can force players to actually have to adjust their playstyle based on what they got. Be careful with this kind of randomness, as it can easily inspire rage. You are very close to a core expectation of most players: "I am master of this game world, and given effort, I should not be deprived of anything I want."


 Some General Heuristics


Since most people aren't taught well to think about probability, I wanted to give a few guidelines to work with.

When in doubt, make a simulation. When you use any type of probability distribution besides the constant percentage drop, you do not need to do a full mathematical workout of all cases. I highly recommend writing a program (or bribing your friend the coder to do so) to simulate the effects and generate graphs of how the system behaves when tested a huge number of times. That information, while not guaranteed to be exactly right, will be good enough, and the calculations required to get an exact answer are not worth the time required to compute them in most cases.

Generally speaking, the more random drops the player is compelled to farm, the closer their total experience will be to the average experience overall, and the more likely they are to face the worst case short term scenario sometime in their experience. Look at it this way: if everyone rolls fifty dice, it's likely that the roll totals won't differ much, and everyone will have probably rolled at least a couple of ones. The trap here is subtle: you cannot assume that poor luck will only affect some players in this case; it is almost guaranteed to strike everyone. Design accordingly.

The reverse of this is true, too. A small number of random drops in your game will mean that the player experience will be very uneven and different from person to person.

People tend to be terrible at estimating probabilities in their head, and dry spells leave bigger scars than lucky breaks feel good. The lower the probability, the worse the estimation ability. This can manifest especially with rare drops; people tend to start becoming frustrated long before the average if they know the drop is rare going into the session. Additionally, people will typically experience negative emotion for a significant portion of a farming session they consider to be long, while players who get lucky tend to move on quickly after experiencing the short-lived joy over a drop.

People conflate luck and skill quite often. It might be interesting to investigate mechanics that would reinforce this: increased drops for skilled play would allow those who have already mastered what the game is teaching to move on to something more interesting to them, while giving the less skilled players a way to both potentially improve and still get whatever item is at stake. This is something I've rarely seen, but I think would have huge potential.

Randomness is lovely, and if players buy into what is at stake, gambling can be used to craft incredible emotional experiences. It's a shame that something so close to our hearts is so ill-understood because a little extra crafting of the probabilities behind the game mechanics could yield incredibly diverse experiences, both from game session to game session for any one player and between players. There is an amazing amount of potential, and I was only able to scratch the surface with a huge amount of text so all I can recommend for those who are willing to is: experiment.

As I didn't get to show examples this time, I'm splitting them off into another entry. When it is done, I'll link to it here.

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Matthew Downey
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Logistic curves/Sigmoid functions are beast.

Darren Tomlyn
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I really need to stop visiting this site until I've finished what I'm working on :-/

What this post needs, is the 'bigger picture' to provide the needed additional context for the use and existence of randomness in many activities, (not just (but including) games), in general, let alone just loot drops for games themselves, (which can then be understood in relation).

Which, of course, we don't have.

The main understanding that matters, is the relationship between games and competitions - about the process of competing by doing something 'for ourselves', or competing to be told whether you've won or lost, (i.e. got the loot drop you want/need - e.g. by a random draw).

Unfortunately, games and competitions are completely incompatible, (though the recognition for any particular activity can be subjective), and it doesn't help that an entire industry exists to try and convince people that games and competitions are still the same thing - (they used to be, but the word game changed quite a while ago, and is why we use the word competition (as an activity) instead, but this isn't fully recognised).

There is a good reason why the words work and gambling were mentioned while discussing the nature of such behaviour usually found n competitions:

Work is doing something that is productive - in this case the reward for the behaviour (the loot drop) is the main/only reason the behaviour itself exists and is taken part in. Doing something that is non-productive is called play, (and we do it because it's enjoyable, instead).

Gambling is when someone has something (usually money) invested in a particular outcome that is not directly under their control and/or influence. It should be no surprise that gambling mainly involves competitions (from the perspective of the gambler).

(Unfortunately, competitions tend to make more (reliable) money than games, which is why many 'games' companies are leaning in that direction, (and Zynga decided to jump in with both feet instead - though at least they're being honest about it), at the expense of games themselves.

Of course, when creators and designers don't recognise and understand when and how they are making and designing competitions instead of games, because they don't understand the difference, people suffer.

The lack of understanding of the relationship and differences of games, competitions and gambling IS causing tangible harm and suffering for some people. And those who want to make games should be part of the SOLUTION to helping people with that, instead of becoming part of the PROBLEM.

Chris Grey
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Thanks for stopping by; you've raised some interesting points. I understand your desire to see randomness justified in gameplay, but that would have easily tripled the size of the blog, only scratched the surface, and taken it well off course of the aim. To understand the whole is not to understand its part, and I wanted, here, to show a small piece of the puzzle that designers are not taught to craft.

It's a good question, though. Why have randomness? My first answer, honestly, is that life is fundamentally uncertain. Uncertainness that we don't understand looks like randomness. Therefore, randomness is a compact way of injecting one small feeling of life into an activity. It is a simplification, of course, but that which is completely deterministic, knowable, static, and known is typically quickly boring to people.

I don't agree with you that loot drops are necessarily viewed by the player as a win/loss scenario emotionally in my experience, nor do I see games and competitions are completely incompatible under the definitions I work by. I can assure you that some of the work I've done in my life for corporations hasn't been productive in outcome, and that play is not always enjoyable (the moment-to-moment experience of many play experiences can be the building of tension or stress). Very little in this life is totally controllable so almost everything significant we do can be viewed as a risk-taking or gambling.

I don't generally like to talk at this level of abstraction as it's quite difficult to agree on much., much less agree on a clear course of action.

I do appreciate your dedication to seeing people not suffer; my aim was to shine a bit of light on a common gameplay mechanic and show how the designer can craft the mechanic more soundly so that there isn't as much unintentional suffering. I hope the idea was heard.

Darren Tomlyn
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I understand perfectly what your post is for. Based on everything I've seen in how games are currently applied and designed, however, I'm just saying it's nowhere near enough - but that's a much bigger problem than can be dealt with in just one single blog post, which I appreciate - I just didn't know if it was something you recognised and understood.

So my post was just there to give you a small glimpse of the 'big picture' - which we are currently lacking, and is the root cause of many/most of the problems we have.

I know I wasn't anywhere near precise enough in the language I used in the previous post - but for a good reason - which is where some of your disagreements might/probably come from.

The reason for that being that what I'm working on is the foundations of what is required to understand how to use (the English) language to describe itself, consistently and accurately (as best as possible), based on how it actually functions and exists, (rather than just how we perceive it.) This will/should then eventually affect how we describe and perceive game, art, puzzle, competition, work and play in relation to each other, which is where most of the problems we have with how games are currently designed and created, comes from. The language we currently need to use to describe such things properly in such a manner, doesn't technically exist - but should, and would, if our understanding and perception of language was fully consistent in the first place, which is why I didn't use the very best (most descriptive) language I could in my post above.

The confusion between games and competitions, (assuming that such an activity we call a competition is even consistently recognised to exist), is what is causing a lot of the symptoms and problems to do with randomness in games and how its applied.

Since I'm currently working on more fundamental matters at the minute, it can sometimes take my brain a while to catch up with more specific symptoms and matters that are still grounded and based upon such problems - that may have been part of why my previous post was as it is.

If you do not understand how and why games and competitions are incompatible - an activity can only ever be one or the other - then that's simply because the current understanding of both is problematic - again due to how they are currently described and perceived in a manner that is not fully consistent with how the language is used and it's basic rules.

I could point you towards my current blog to explain why, but I'm loathe to do that since it's still not entirely consistent in itself, based on what I'm currently working on - though the specifics of this particular matter is not affected. If you're still interested, you can have a look, (click my name, and go to the contents page (linked from all the others) and read through form the beginning), but what I'm working on is a re-write that's far better and more consistent (with the 'bigger picture') - but also much harder to write :(


So, back to randomness - I didn't say this before, and I don't know if it is even necessary, but it might be, based on your reply above.

What we're dealing with here, is the relationship between:

1) Things a player (person taking part in such an activity) DOES, 'for themselves' - not the best description, but, again, if you really want that now, read my blog.

2) Things that happen TO a/the player.

Games are defined as and by the former - competitions, the latter. Games do not require the latter at all!

Randomness can be involved in both, but what you're talking about is the randomness involved in the latter, 2.

So, the reason why we have problems with what you're talking about, is when any randomness involved in 2, becomes more important, and even the reason for the existence of, 1. Because the nature of competitions are all about making what happens to the player the reason for the existence of any other behaviour, (which can involve a variety of things) - competing to be told whether you have won or lost, through a random draw or a judges opinion etc. - competitions are naturally incompatible with games, which is about a process of competing as and by the behaviour of 1, instead.

The line between the two can be completely subjective, which is where I think you are having problems, yourself, but any behaviour can only be one or the other, never both - it's either something we do, or something that happens to us, and what we're dealing with here, is purely the latter.


As far as the relationship between work and play is concerned, and how best to describe them, you appear to be letting the/my description of WHY we play affect what play is.

Work is productive behaviour.
Play is non-productive behaviour.

ALL human behaviour is either one or the other. Unfortunately, people perceive both based on how they are (subjectively) applied, rather than for the very basic behaviour (and states of such behaviour) they truly represent.

The standard method atm. of describing why we play, (since it's non-productive we need such a thing), is using the word enjoyable like I did. If you don't feel it is suitable, then maybe 'because we like the behaviour' would be better in your opinion?

Either way, the above descriptions are what truly matter, and, again, because of the problems we have in how we perceive play as and by being enjoyable first, at this time, people have trouble understanding how and why games can and do involve work, even if it happens to still be enjoyable, depending on how they are applied and perceived.

Again, making the product of any behaviour more important than, and the reason for, the existence of such behaviour, itself, is to turn something into work.

So, if we do something for what it is, (because we like it), then it's play - if we do it for what it produces, such as a reward etc., (i.e. a loot drop), then it is work.

The fact that it might be enjoyable, in itself, or a game, puzzle or competition, has nothing to do with it being work or play.

(Note: 'fun' is a completely different "kettle-of-fish".)

One of the other problem with work and play, is that people confuse using work and play to describe the act of using something, or the act of taking part in an activity - (e.g. working with clay, playing a musical instrument or a game) - for them being productive or non-productive, but the two are different, UNRELATED, meanings/definitions of such words, representing different pieces of information.


I hope this helps somewhat, but I'm afraid to get the full picture, you'll have to wait like everybody else, until I finish my re-write.

Jason Carter
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unless you work putting on a play

Darren Tomlyn
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I was deliberately limiting my use of work and play within the context of games. The use of play to describe a specific activity, is not really part of what work and play represent that confuses people, (unlike, say, competition(s)).

Jason Carter
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Hah, sorry jokes don't come across well over the internet. I meant play as in a theatrical play, it was a play on words. -_-

I enjoyed reading your responses, not that I completely agree with you.

I think I can both enjoy something and do it for the goal at the end. I enjoy creating things, I enjoy learning, in fact everything we do in life results in some sort of learning.

That, then, makes any sort of play, turn into something that could be taken as work. It is then subjective based on the intention of the person. If I build a house to get paid, it's work. If I build a house solely because I like the process of building, then it's play. But the end of a process is part of the process. So what if I enjoy the end product as well as the process?

I believe the two can be mixed. It also depends on what you consider productive. I could sit and watch TV all day. Is that productive? It could be. What am I learning while watching TV? Nearly everything we do is progress. So I do think your argument is a bit flawed.

I don't think the two can be split like that. It's all subjective to the individual.

Edit: Sorry that's a sort of jumbled response to a few of the things you were talking about. Just a few random points I thought of.

Brian Kehrer
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Progressive percentages made a big splash when Blizzard was talking about it in Lich King Expansion, and Sid Meier on Civ 5.

Terrible link here. Sid Meier discussed it in his GDC Keynote a few years ago.

Chris Grey
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WoW is going to be one of the concrete examples I'm writing about in the second post, and the game is better for the progressive percentage system implemented. Nice find.

Bart Stewart
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The idea of escalating percentages has an analog in the "priority aging" function in queuing applications. As a task sits in the queue waiting for execution, its priority is gradually increased. (Note that this works only for queues that implement priority, though; it won't help a simple FIFO queue.) Considering how long the priority aging trick has been around, there might be technical literature floating around with some useful analogical ideas for implementing percentage escalation in loot drops.

Another possibility for tailoring randomness to better satisfy gamers is the practice of peeking into a character's current inventory and past behaviors to see what they might need/want most. Armed with those numbers, you can condition random outputs to be more or less favorable to particular outcomes.

For example, if you've used a bow a lot, but you're about out of arrows and the game knows a big fight is about to happen, maybe the odds for arrows appearing in loot are increased. Alternately, you might occasionally lower the odds of finding arrows for a while to encourage the player to try other weapons or tactics.

This technique is more complex than a simple escalating/diminishing percentage. But there might be cases where the increased power to tailor results to specific players makes it cost-effective.

Jonathan Jou
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My favorite notion is always to make randomness the apparent phenomenon, but not the true inner workings: let there be a chance that someone might get lucky, but don't make luck the actual factor involved.

For instance, if a player happens to land a critical hit on a monster which has bitten and latched onto him, it becomes easier to dislodge the monster's tooth, based on where the player strikes and how much strength and dexterity the player possesses.

It's almost too easy to turn "randomness" into a sufficiently large set of unknowns that unpredictability occurs without chance ever coming into play. While some people will conclude that the only way to accomplish a goal will be repeated trials, others might be encouraged to carefully observe each attempt to find out what works and what doesn't.

This can only be made more enjoyable by working in "tells," such that the astute player can and is rewarded for adjusting strategy and keeping a close eye on the situation. Maybe the monster lets out a howl of agony when biting with an already loosened tooth, you can hear the sound of teeth rattling or dislodging as the fight proceeds, and inspection of the fallen monster would reveal that the teeth are too hard to remove without destroying, or perhaps some additional expertise with bone.

For me, it's always exciting when something that seems to be inexplicable and unpredictable to be completely consistent and well understood with effort; it reminds me of many real world experiences, and encourages me to pay more attention, not less.

I'm of the opinion that technology today makes this very possible, and hopeful that there will be more games which explore this notion going forward!

Steven Christian
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I used to always look for things like these and theorise different options.
Unfortunately, most games are boring and simplified and have prettymuch killed this instinct in me by now..

-Jaded Gamer

Chris Grey
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I do really like this approach. If designers were bold enough to experiment to really meld weighted probabilities with subtle tells, it could have incredible consequences. I do still encourage to not make everything look random but be deterministic, though. For an example of how that can go awry, look at Ultima 3. Because of processor limitations, they had the novel idea to entirely determine a successful attack by using which frame of the idle animation the monster was in at the time of attack. The animations were two frames in total, if I recall correctly, so attacking on frame 1 was a miss, frame 2 was a hit.

What happened was to most players, it was random. To the players who figured it out, the game became a cakewalk, as it wasn't balanced for some players hitting half the time while the others hit every time. It also spoils much of the tension of the combat. So by all means, if we can combine subtle tells to reward perception, but keep some uncertainty, we can make some amazingly rewarding experiences that won't get stale as quickly.

As a player, predicting the outcome little of the time is frustrating, predicting the outcome most of the time feels like mastery, and predicting the outcome all of the time is boring.

Jonathan Jou
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I'm glad you feel the same way I do! It's probably worth pointing out that the only difference between random and "unknown determinism" is how much information is available. The truly random situation is one where the input to the deterministic function is unknowable until the moment of evaluation, whereas, a seemingly random situation would be one where the input would be simply unknown.

For instance, something like the time of day, or the age of the monster might be readily apparent, but the hunger, nourishment, or mood of the monster might be difficult to ascertain. You don't know if your opponent had a liver problem or an old knee injury until you get off that "lucky" hit, and so on and so forth.

So it's not impossible to add unpredictability to the outcome without making the situation in any way actually random so much as it is unknown.

I do agree that a game can get too easy if it's too predictable, of course. There's some valuable balance between pointless frustration and pointless success, and I'd favor a nonlinear difficulty and reward curve over adding true randomness to the situation.


That's what we call "good game design." When the player does the right thing without even realizing it. I'm sure there's irony in there somewhere. Maybe I'm jaded too.

Zack Wood
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I always thought that in Diablo (in one player off-line mode) the game shouldn't bother dropping items that are only usable by other classes than what my character is. I understand for online play when you could share, trade, or sell, but in 1P it should recognize your character's class and only drop rare items you can actually use.

John Flush
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What about selling it all to gold up and then waste it another random drop location from the gamble store in town?

Maybe it doesn't bother dropping junk at all and just gives you coin. then I can decide to gamble whenever and not take as many trips to town to get rid of the loot. Torchlight 'fixed' this by letting me send my pet to sell my garbage, but again I can only think of how amazing it would be to just not get the garbage. Of course then the game has to be smart enough to know what I think 'garbage' is... I agree though, single player, garbage is always something I can't use by my class.

Zack Wood
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Yea, if my character is a Sorceress, Barbarian-only loot may as well be a stack of gold. In terms of non-class-specific stuff, it would be nice it the odds were just a little weighted in favor of magic boosting things (less chance of getting a melee weapon requiring tons of strength to use, for example).

John Flush
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My big beef with loot dropping is something should have dropped that would help me continue the game, but doesn't always. As such I end up doing boss runs all day until I finally get a loot drop that lets me continue onward. In single player I would eventually just Hex edit the game to keep moving forward. Blizzard knew this and saw it as something that 'ruined' the game and experience and forced me online where that wasn't an option. That is when I quit playing. Some people like to play really slow slot machines, I'm not one of them.

Kep Amun
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You mention making a tool to simulate drop rates and I've recently been introduced to a tool that actually lets you do that for any game to a certain extent. The tool is Machinations from Joris Dormans co-author of Game Mechanics, Advance Game Design. It's like a virtual circuit board, but for prototyping the flow of resources in games, and it's free. They have example diagrams for Monopoly, Risk, and Starcraft, but also games I didn't think would apply to such a simulation like Pacman and Tetris. Sure a program made to simulate just your game would be more accurate, but Machinations is great for a quick test of an idea and it's kinda fun to play around with the components.

I am not affiliated with the Machinations, Dormans, the book, or the site, I just had to use the tool for some assignments from my game dev class. If someone knows of another potentially better tool out there, I would be interested.

Try it out here: (free)

Ramin Shokrizade
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I always get excited when I see other people using quantitative methods to predict and improve consumer experiences. Kudos!

Andreas Ahlborn
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Very interesting article, it confirms a lot of suspicions I had how in most games that involve randomly rewarding players prizes or loots, the numbercrunchers try to blindly imitate raw probability from Gambling instead coming up with creative solutions that allows for weigthted probability.
It goes basically into the intuitive (but false) direction of giving randomness a sort of memory a knowledge about the players past encounters with randomness.
Its also a way of shortening the distance hard randomness rewuires the average to walk to get a "fair" chance to get lucky.

But I fear the monetarization-aspect of most games doesn`t favor this approach.

The recent year I played a multiplayergame (the specifics don`t matter) where you could earn virtual money ingame and spent it on prizeboxes. These prizeboxes contained 4 different types of items: common, uncommon, rare and ultrarare. They came of course in different flavors: the more expensive the box the higher the chance you could get an ultrarare item.

You could of course purchase these prizeboxes also with real money.

If you would visit the forum of this game on any given day: 50% of the conversations there would debate the unfairness/frustration that the drop of ultrarare items caused. People would post screenshots of extremly lucky drops (boxes that had 2 ultrares in them) or players would rant their dry streaks (one guy claimed to have opened 200 boxes without any ultrarare drop).
The community tried to reverse-engineer the drop-algorithm and with some thousand data records gathered arrived roughly at this conclusion: the average ingame time you had to spend to get all the ultrarare items was around 600 hours. The minimum time for the extrem lucky guys was around 300 hours. There were of course players which claimed to have sunk more then 300 Dollars into prizeboxes, played 2000+ hours (this data was publicly accessible so you check it out in their profile) and only half of the ultrare items dropped for them.

conclusion: while they were alienating a lot of your players with their business model. the game stayed healthy for 12 months and the developer managed to finance all the DLC it dropped during that year for free, basically financing the whole game only with the prizeboxes purchased with real money.
It was a classical freemium-game (depending on farming the few whales) disguised as a AAA-Multiplayer.

Jorge Ramos
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I have run into this problem in EVERY SINGLE pokemon game... especially in terms of getting the magic combination of a desired encounter/critter, combined with the nature/stats I am looking for, or even just getting to a level requisite enough to advance in the game.

Someone should translate this to Japanese (properly), and send copies to everyone at Game Freak and force them to read it until they realize just how much pain they have caused with their game mechanics with every progressive generation.