See here for the previous update if you missed / forgot it.

In this update, no new game content, but new graphics.

I wasn’t terribly happy about the graphical representation of the various nodes in the last update. Especially in the first two networks, if you didn’t read the descriptions of the nodes carefully, it was very easy to just click your way through them without really having a clue of what the network was actually doing. Needless to say, for a game that’s supposed to teach how the networks function, this is highly non-optimal.

Here’s the representation that I’m now experimenting with: the truth table of the nodes is represented graphically inside the node. The prior variable at the top doesn’t really have a truth table, it’s just true or false. The “is” variable at the bottom is true if its parent is true, and false if its parent is false.

You may remember that in the previous update, unobservable nodes were represented in grayscale. I ended up dropping that, because that would have been confusing in this representation: if the parent is unobservable, should the blobs representing its truth values in the child node be in grayscale as well? Both “yes” and “no” answers felt confusing.

Instead the observational state of a node is now represented by its border color. Black for unobservable, gray for observable, no border for observed. The metaphor is supposed to be something like, a border is a veil of ignorance blocking us from seeing the node directly, but if the veil is gray it’s weak enough to be broken, whereas a black veil is strong enough to resist a direct assault. Or something.

When you observe a node, not only does its border disappear, but the truth table entries that get reduced to a zero probability disappear, to be replaced by white boxes. I experimented with having the eliminated entries still show up in grayscale, so you could e.g. see that the “is” node used to contain the entry for (false -> false), but felt that this looked clearer.

The “or” node at the bottom is getting a little crowded, but hopefully not too crowded. Since we know that its value is “true”, the truth table entry showing (false, false -> false) shows up in all whites. It’s also already been observed, so it starts without a border.

After we observe that there’s no monster behind us, the “or” node loses its entries for (monster, !waiting -> looks) and (monster, waiting -> looks), leaving only (!monster, waiting -> looks): meaning that the boy must be waiting for us to answer.

This could still be made clearer: currently the network updates instantly. I’m thinking about adding a brief animation where the “monster” variable would first be revealed as false, which would then propagate an update to the values of “looks at you” (with e.g. the red tile in “monster” blinking at the same time as the now-invalid truth table entries, and when the tiles stopped blinking, those now-invalid entries would have disappeared), and that would in turn propagate the update to the “waiting” node, deleting the red color from it. But I haven’t yet implemented this.

The third network is where things get a little tricky. The “attacking” node is of type “majority vote” - i.e. it’s true if at least two of its parents are true, and false otherwise. That would make for a truth table with eight entries, each holding four blobs each, and we could already see the “or” node in the previous screen being crowded. I’m not quite sure of what to do here. At this moment I’m thinking of just leaving the node as is, and displaying more detailed information in the sidebar.

Here’s another possible problem. Just having the truth table entries works fine to make it obvious where the overall probability of the node comes from… for as long as the valid values of the entries are restricted to “possible” and “impossible”. Then you can see at a glance that, say, of the three possible entries, two would make this node true and one would make this false, so there’s a ⅔ chance of it being true.

But in this screen, that has ceased to be the case. The “attacking” node has a 75% chance of being true, meaning that, for instance, the “is / block” node’s “true -> true” entry also has a 75% chance of being the right one. This isn’t reflected in the truth table visualization. I thought of adding small probability bars under each truth table entry, or having the size of the truth table blobs reflect their probability, but then I’d have to make the nodes even bigger, and it feels like it would easily start looking cluttered again. But maybe it’d be the right choice anyway? Or maybe just put the more detailed information in the sidebar? I’m not sure of the best thing to do here.

If anyone has good suggestions, I would be grateful to get advice from people who have more of a visual designer gene than I do!

Some of you may remember me proposing a game idea that went by the name of The Fundamental Question. Some of you may also remember me talking a lot about developing an educational game about Bayesian Networks for my MSc thesis, but not actually showing you much in the way of results.

Insert the usual excuses here. But thanks to SSRIs and mytomatoes.com and all kinds of other stuff, I'm now finally on track towards actually accomplishing something. Here's a report on a very early prototype.

This game has basically two goals: to teach its players something about Bayesian networks and probabilistic reasoning, and to be fun. (And third, to let me graduate by giving me material for my Master's thesis.)

We start with the main character stating that she is nervous. Hitting any key, the player proceeds through a number of lines of internal monologue:

I am nervous.

I’m standing at the gates of the Academy, the school where my brother Opin was studying when he disappeared. When we asked the school to investigate, they were oddly reluctant, and told us to drop the issue.

The police were more helpful at first, until they got in contact with the school. Then they actually started threatening us, and told us that we would get thrown in prison if we didn’t forget about Opin.

That was three years ago. Ever since it happened, I’ve been studying hard to make sure that I could join the Academy once I was old enough, to find out what exactly happened to Opin. The answer lies somewhere inside the Academy gates, I’m sure of it.

Now I’m finally 16, and facing the Academy entrance exams. I have to do everything I can to pass them, and I have to keep my relation to Opin a secret, too. 

???: “Hey there.”

Eep! Someone is talking to me! Is he another applicant, or a staff member? Wait, let me think… I’m guessing that applicant would look a lot younger than staff members! So, to find that out… I should look at him!

[You are trying to figure out whether the voice you heard is a staff member or another applicant. While you can't directly observe his staff-nature, you believe that he'll look young if he's an applicant, and like an adult if he's a staff member. You can look at him, and therefore reveal his staff-nature, by right-clicking on the node representing his apperance.]

Here is our very first Bayesian Network! Well, it's not really much of a network: I'm starting with the simplest possible case in order to provide an easy start for the player. We have one node that cannot be observed ("Student", its hidden nature represented by showing it in greyscale), and an observable node ("Young-looking") whose truth value is equal to that of the Student node. All nodes are binary random variables, either true or false. 

According to our current model of the world, "Student" has a 50% chance of being true, so it's half-colored in white (representing the probability of it being true) and half-colored in black (representing the probability of it being false). "Young-looking" inherits its probability directly. The player can get a bit of information about the two nodes by left-clicking on them.

The game also offers alternate color schemes for colorblind people who may have difficulties distinguishing red and green.

Now we want to examine the person who spoke to us. Let's look at him, by right-clicking on the "Young-looking" node.

Not too many options here, because we're just getting started. Let's click on "Look at him", and find out that he is indeed young, and thus a student.

This was the simplest type of minigame offered within the game. You are given a set of hidden nodes whose values you're tasked with discovering by choosing which observable nodes to observe. Here the player had no way to fail, but later on, the minigames will involve a time limit and too many observable nodes to inspect within that time limit. It then becomes crucial to understand how probability flows within a Bayesian network, and which nodes will actually let you know the values of the hidden nodes.

The story continues!

Short for an adult, face has boyish look, teenagerish clothes... yeah, he looks young!

He's a student!

...I feel like I’m overthinking things now.

...he’s looking at me.

I’m guessing he’s either waiting for me to respond, or there’s something to see behind me, and he’s actually looking past me. If there isn’t anything behind me, then I know that he must be waiting for me to respond.

Maybe there's a monster behind me, and he's paralyzed with fear! I should check that possibility before it eats me!

[You want to find out whether the boy is waiting for your reply or staring at a monster behind you. You know that he's looking at you, and your model of the world suggests that he will only look in your direction if he's waiting for you to reply, or if there's a monster behind you. So if there's no monster behind you, you know that he's waiting for you to reply!]

Slightly more complicated network, but still, there's only one option here. Oops, apparently the "Looks at you" node says it's an observable variable that you can right-click to observe, despite the fact that it's already been observed. I need to fix that.

Anyway, right-clicking on "Attacking monster" brings up a "Look behind you" option, which we'll choose.

You see nothing there. Besides trees, that is.

Boy: “Um, are you okay?”

“Yeah, sorry. I just… you were looking in my direction, and I wasn’t sure of whether you were expecting me to reply, or whether there was a monster behind me.”

He blinks.

Boy: “You thought that there was a reasonable chance for a monster to be behind you?”

I’m embarrassed to admit it, but I’m not really sure of what the probability of a monster having snuck up behind me really should have been.

My studies have entirely focused on getting into this school, and Monsterology isn’t one of the subjects on the entrance exam!

I just went with a 50-50 chance since I didn’t know any better.

'Okay, look. Monsterology is my favorite subject. Monsters avoid the Academy, since it’s surrounded by a mystical protective field. There’s no chance of them getting even near! 0 percent chance.'

'Oh. Okay.'

[Your model of the world has been updated! The prior of the variable 'Monster Near The Academy' is now 0%.]

Then stuff happens and they go stand in line for the entrance exam or something. I haven't written this part. Anyway, then things get more exciting, for a wild monster appears!

Stuff happens

AAAAAAH! A MONSTER BEHIND ME!

Huh, the monster is carrying a sword.

Well, I may not have studied Monsterology, but I sure did study fencing!

[You draw your sword. Seeing this, the monster rushes at you.]

He looks like he's going to strike. But is it really a strike, or is it a feint?

If it's a strike, I want to block and counter-attack. But if it's a feint, that leaves him vulnerable to my attack.

I have to choose wisely. If I make the wrong choice, I may be dead.

What did my master say? If the opponent has at least two of dancing legs, an accelerating midbody, and ferocious eyes, then it's an attack!

Otherwise it's a feint! Quick, I need to read his body language before it's too late!

Now get to the second type of minigame! Here, you again need to discover the values of some number of hidden variables within a time limit, but here it is in order to find out the consequences of your decision. In this one, the consequence is simple - either you live or you die. I'll let the screenshot and tutorial text speak for themselves:

[Now for some actual decision-making! The node in the middle represents the monster's intention to attack (or to feint, if it's false). Again, you cannot directly observe his intention, but on the top row, there are things about his body language that signal his intention. If at least two of them are true, then he intends to attack.]

[Your possible actions are on the bottom row. If he intends to attack, then you want to block, and if he intends to feint, you want to attack. You need to inspect his body language and then choose an action based on his intentions. But hurry up! Your third decision must be an action, or he'll slice you in two!]

In reality, the top three variables are not really independent of each other. We want to make sure that the player can always win this battle despite only having three actions. That's two actions for inspecting variables, and one action for actually making a decision. So this battle is rigged: either the top three variables are all true, or they're all false.

...actually, now that I think of it, the order of the variables is wrong. Logically, the body language should be caused by the intention to attack, and not vice versa, so the arrows should point from the intention to body language. I'll need to change that. I got these mixed up because the prototypical exemplar of a decision minigame is one where you need to predict someone's reaction from their personality traits, and there the personality traits do cause the reaction. Anyway, I want to get this post written before I go to bed, so I won't change that now.

Right-clicking "Dancing legs", we now see two options besides "Never mind"!

We can find out the dancingness of the enemy's legs by thinking about our own legs - we are well-trained, so our legs are instinctively mirroring our opponent's actions to prevent them from getting an advantage over us - or by just instinctively feeling where they are, without the need to think about them! Feeling them would allow us to observe this node without spending an action.

Unfortunately, feeling them has "Fencing 2" as a prerequisite skill, and we don't have that. Neither could we have them, in this point of the game. The option is just there to let the player know that there are skills to be gained in this game, and make them look forward to the moment when they can actually gain that skill. As well as giving them an idea of how the skill can be used.

Anyway, we take a moment to think of our legs, and even though our opponent gets closer to us in that time, we realize that our legs our dancing! So his legs must be dancing as well!

With our insider knowledge, we now know that he's attacking, and we could pick "Block" right away. But let's play this through. The network has automatically recalculated the probabilities to reflect our increased knowledge, and is now predicting a 75% chance for our enemy to be attacking, and for "Blocking" to thus be the right decision to make.

Next we decide to find out what his eyes say, by matching our gaze with his. Again, there would be a special option that cost us no time - this time around, one enabled by Empathy 1 - but we again don't have that option.

Except that his gaze is so ferocious that we are forced to look away! While we are momentarily distracted, he closes the distance, ready to make his move. But now we know what to do... block!

Success!

Now the only thing that remains to do is to ask our new-found friend for an explanation.

"You told me there was a 0% chance of a monster near the academy!"

Boy: “Ehh… yeah. I guess I misremembered. I only read like half of our course book anyway, it was really boring.”

“Didn’t you say that Monsterology was your favorite subject?”

Boy: “Hey, that only means that all the other subjects were even more boring!”

“. . .”

I guess I shouldn’t put too much faith on what he says.

[Your model of the world has been updated! The prior of the variable 'Monster Near The Academy' is now 50%.]

[Your model of the world has been updated! You have a new conditional probability variable: 'True Given That The Boy Says It's True', 25%]

And that's all for now. Now that the basic building blocks are in place, future progress ought to be much faster.

Notes:

As you might have noticed, my "graphics" suck. A few of my friends have promised to draw art, but besides that, the whole generic Java look could go. This is where I was originally planning to put in the sentence "and if you're a Java graphics whiz and want to help fix that, the current source code is conveniently available at GitHub", but then getting things to his point took longer than I expected and I didn't have the time to actually figure out how the whole Eclipse-GitHub integration works. I'll get to that soon. Github link here!

I also want to make the nodes more informative - right now they only show their marginal probability. Ideally, clicking on them would expand them to a representation where you could visually see what components their probability composed of. I've got some scribbled sketches of what this should look like for various node types, but none of that is implemented yet.

I expect some of you to also note that the actual Bayes theorem hasn't shown up yet, at least in no form resembling the classic mammography problem. (It is used implicitly in the network belief updates, though.) That's intentional - there will be a third minigame involving that form of the theorem, but somehow it felt more natural to start this way, to give the player a rough feeling of how probability flows through Bayesian networks. Admittedly I'm not sure of how well that's happening so far, but hopefully more minigames should help the player figure it out better.

What's next? Once the main character (who needs a name) manages to get into the Academy, there will be a lot of social scheming, and many mysteries to solve in order for her to find out just what did happen to her brother... also, I don't mind people suggesting things, such as what could happen next, and what kinds of network configurations the character might face in different minigames.

(Also, everything that you've seen might get thrown out and rewritten if I decide it's no good. Let me know what you think of the stuff so far!)