June 21, 2026 • 23 mins
A comprehensive technical guide written by Jouni Smed and Harri Hakonen. This textbook defines the fundamental components of games, such as rules, goals, and conflict, while exploring the mathematical and computational structures necessary to build them. The authors utilize the Model-View-Controller architectural pattern to describe the anatomy of a computer game and outline the various professional disciplines and phases involved in modern game development. Extensive tables of contents reveal that the book covers specialized topics including procedural generation, pathfinding, and decision-making alongside networking challenges like latency compensation and anti-cheating measures. Ultimately, the source serves as a bridge between academic computer science and the practical requirements of the entertainment industry.
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
So picture this. You're playing a game and you round
a corner in some dark digital dungeon and boom and
enemy suddenly springs an ambush.
Speaker 2 (00:09):
Oh yeah, your heart just completely jumps into your throat.
Speaker 1 (00:11):
Right, And in that split second, you know, you're not
thinking about code or like pixels on a screen.
Speaker 2 (00:16):
Oh of course not.
Speaker 1 (00:17):
You're just thinking, wow, that felt so real. Because we
play these games expecting this organic spontaneity, right, We really
want that digital world to feel alive, we do.
Speaker 3 (00:27):
But the truth is that organic feeling is entirely fabricated,
like completely, when you actually step behind the curtain of
game development, all that spontaneity just vanishes. You're looking at
this landscape of cold, hard, purely deterministic code.
Speaker 1 (00:44):
Which is so wild to think about.
Speaker 3 (00:46):
It is because computers are well, they're rigid machines. You
literally cannot be spontaneous. Everything you feel in that dungeon
is just a meticulously crafted mathematical illusion.
Speaker 1 (00:56):
And today we are ripping open that code to see
exactly how developers pull off that trick. We are doing
a deep dive into this brilliant textbook. It's called Algorithms
and Networking for Computer Games by Juni Smed and Harriet Conan.
Speaker 2 (01:11):
It's a fascinating read, it really is.
Speaker 1 (01:13):
And our mission today is to figure out how programmers
manipulate math and psychology to trick your brain. We're going
to start from the foundational rules of play and go
all the way down to the invisible algorithms that basically
manufacture chaos.
Speaker 3 (01:28):
Yeah, and to understand the math, we first have to
agree on what we're actually trying to simulate, right, right,
Because when you strip away the high resolution graphics and
you know, the fancy haptic feedback controllers, Smed and Hakonan
argue that an interactive world requires one specific crucial ingredient
to separate it from just a static puzzle.
Speaker 2 (01:46):
And that ingredient unpredictability.
Speaker 1 (01:48):
Okay, let's unpack this because the book uses a really
specific word here, which is conflict. Yes, conflict, And when
I hear conflict, my mind immediately goes to like fighting
a digital dragon or racing against a rival car. But
the authors argue it's actually way broader than that, much brighter. Yeah,
because think about a Sunday crossword puzzle, right. It's challenging,
(02:10):
it has rules, it has a goal, but is it
a game.
Speaker 3 (02:13):
Well, by the strict definitions used in game architecture, a
standard crossword puzzle is not actually a game. Wait really yeah,
because it lacks non determinism. A crossword puzzle just sits there.
It doesn't fight back, you know, doesn't adapt.
Speaker 2 (02:27):
To your choices.
Speaker 1 (02:28):
Okay, I see.
Speaker 3 (02:29):
So conflict in this specific context means you are facing
an opposing force or some random process that actively obstructs you.
Speaker 1 (02:37):
Right, So if you add a ticking timer to that
crossword or I don't know, you're raising a friend to
finish it first.
Speaker 3 (02:42):
Suddenly have non determinism. Exactly, You've injected chaos, and now
you have game.
Speaker 1 (02:46):
Okay, So in a single player experience, developers have to
artificially inject that chaos. They have to simulate an opposing
force using AI, which the authors call synthetic players.
Speaker 2 (02:57):
Right, synthetic players.
Speaker 1 (02:58):
But here is the most counter intuitive part of this
whole illusion. For me, to make an AI opponent feel
like a real, living human, developers actually have to break it. Yes,
they have to make the AI significantly worse.
Speaker 3 (03:12):
Well, you have to consider what computers are actually capable of, right,
Like a machine can calculate your character's exact coordinates aim
with pixel perfect precision and just eliminate you the exact
millisecond you enter its line of sight.
Speaker 1 (03:24):
Right, It's basically the Terminator exactly.
Speaker 3 (03:27):
It possesses superhuman perfection, but playing against flawless perfection is
incredibly boring and frustrating. Completely, it feels robotic, and it
instantly shatters that illusion of playing against a living, breathing
entity in a shared space.
Speaker 1 (03:41):
So it's all about simulating human flaws. And there is
this amazing specific detail from the text about how developers
engineer this.
Speaker 2 (03:48):
Oh the reaction time.
Speaker 1 (03:49):
Yes, when you take a synthetic player by surprise, say
you flank an enemy in a shooter game, the programmers
hard code a deliberate zero point two to zero point
four second reaction time delay before the AI is even
allowed to shoot back.
Speaker 3 (04:03):
Yeah, and that specific window of time is absolutely no accident.
It simulates the cognitive processing time of a human being.
It basically mimics panic, panick.
Speaker 1 (04:13):
Right.
Speaker 3 (04:14):
Yeah, So when you surprise an enemy and they freeze
for like a third of a second before scrambling for cover,
your brain subconsciously registers the ODEA.
Speaker 1 (04:23):
Loop, the Obie loop.
Speaker 3 (04:24):
Yeah, observe orient decide act, you recognize that slight hesitation
as human cognition, and the illusion holds.
Speaker 1 (04:31):
Wow. But this introduces a massive headache for the game designers,
doesn't it.
Speaker 2 (04:36):
Oh a huge one.
Speaker 1 (04:37):
Because if you program these synthetic players to act somewhat unpredictably,
and then you give the actual human player the freedom
to do literally whatever they want, how on earth do
you guarantee the game still tells a cohesive story.
Speaker 3 (04:49):
Well, you've hit on what the authors called the narrative paradox.
It is the central tension in all interactive storytelling.
Speaker 1 (04:55):
A narrative paradox.
Speaker 2 (04:56):
Yeah.
Speaker 3 (04:57):
So, on one side of the scale you have plot coherence,
the there's in the designers. They want to deliver a
well paced, dramatic, emotionally resonant story.
Speaker 2 (05:05):
Like a movie exactly.
Speaker 3 (05:07):
But on the other side you have character believability and
player agency. You need the player and the AI to
have the actual freedom to ma choices.
Speaker 1 (05:17):
Because if I have total freedom, I might just decide
to wander off into the woods to pick digital mushrooms
and completely ignore the terrifying dragon that's supposed to be
attacking the castle.
Speaker 3 (05:27):
Right, and then the pacing is completely ruined. The story
just grinds.
Speaker 2 (05:30):
To a halt.
Speaker 1 (05:31):
So how do they fix that?
Speaker 3 (05:32):
So the industry generally tackles this tension from two different directions.
The first is a character centric approach. Okay, here, the
AI characters are highly autonomous. They act on their own program, desires,
and needs, and sometimes they even use a hybrid communication system.
Speaker 1 (05:49):
Wait, what does that mean.
Speaker 3 (05:50):
Well, they speak in character to the player, but simultaneously
they send out of character signals to the game's background
systems to try gently nudge the plot forward organically.
Speaker 1 (06:01):
Oh that's clever, it is.
Speaker 3 (06:02):
The story basically emerges from the bottom up.
Speaker 1 (06:04):
But the problem with the bottom up approach is that
it can quickly turn into the chaos of everyday life. Right,
real life isn't inherently structured like a three act cinematic blockbuster.
Speaker 2 (06:14):
No, it definitely isn't.
Speaker 1 (06:16):
So the alternative is the author centric approach, which relies
on something called an invisible drama manager.
Speaker 3 (06:22):
Yes, the drama manager, which I love.
Speaker 1 (06:24):
Think of it like a stage director secretly walking among
the actors, whispering in their ears, completely unseen by the audience.
Speaker 2 (06:32):
That's a perfect way to put it.
Speaker 3 (06:33):
The drama manager is constantly running math in the background,
monitoring metrics like player tension and pacing.
Speaker 1 (06:40):
So that's washing what I do constantly.
Speaker 3 (06:42):
If the algorithm's determined you've been wandering the woods picking
mushrooms for way too long and the tension is dropping,
the drama manager whispers to the AI enemies to spawn
an ambush just out of your line of sight.
Speaker 1 (06:54):
To get my heart rate back up exactly.
Speaker 3 (06:56):
Or conversely, if you are low on health and completely overwhelmed,
it tells the enemies to pull back a bit or
to miss their shots. It subtly manipulates the parameters of
the world to push you toward the intended emotional beats.
Speaker 1 (07:09):
But even with a brilliant invisible director, the developers still
have to physically build the paths the story can take.
Right they do, and the text maps out game stories
using these geometrical graphs. The most basic one is just
a linear story. Episode A always leads to episode B,
which leads to episode C. It's just a straight line.
Speaker 3 (07:28):
Yeah, and linear development is incredibly cost effective, but it
offers almost zero agency. You're essentially just walking through a movie, right.
The theoretical opposite of that is a fully branching structure
where every single choice you make leads to a completely different,
unique continuation of the game.
Speaker 1 (07:46):
Which sounds like the holy grail of gaming until you
actually do the math on the combinatorial explosion.
Speaker 2 (07:52):
Oh, the math is terrifying.
Speaker 1 (07:53):
It really is. Let's say you have a scene with
three dialogue choices, and each of those choices leads to
three entirely new scenarios. By the time you reach the
fourth major decision point in the game, you aren't programming
one game anymore. You're programming eighty one completely different games.
You'd have studio spending twelve years and half a billion
dollars just to make a five hour campaign.
Speaker 3 (08:15):
It's completely unsustainable. So developers rely on a highly calculated
compromise called parallel pass. Parallel pad right, the story branch
is out for a while, allowing you to make choices,
take different routes, and express your agency. This provides that
crucial illusion of free will ah illusion. But eventually all
(08:35):
those diverged branches are forced to converge back into major,
unavoidable story nodes.
Speaker 1 (08:40):
So I might use diplomacy to talk my way past
the guards, and you might just kick the door down
with explosives typical exactly, but thirty minutes later, we both
end up standing in the exact same throne room for
the exact same final boss fight.
Speaker 3 (08:53):
Yes, the game just acknowledges are different methods in the dialogue.
It keeps the studio from going bankrupt while letting us
feel like we are the actual authors of our own fate.
Speaker 1 (09:03):
So the illusion of free will is maintained by carefully
hidden constraints exactly, And that reliance on nondeterminism, you know,
on generating a feeling of unpredictable chaos within strict mathematical limits,
brings us to the very bedrock of how a computer operates.
And here's where it gets really interesting for me, oh
for sure, Because whether we are talking about parallel story branches,
(09:26):
or that zero point three second reaction delay for the AI,
or even simulating a dice roll, games need randomness to function.
Speaker 2 (09:34):
They desperately need it.
Speaker 1 (09:35):
But a computer processor is a purely deterministic machine. It
only executes the exact logic gits it is fed. It
cannot flip a coin. True randomness in a computer is
a total myth.
Speaker 3 (09:46):
It is developers literally have to fake it. Yeah, they
use algorithms to produce sequences of numbers that just behave unpredictably,
and these fall into two main categories, which are quasi
random and pseudorandom.
Speaker 1 (09:58):
Oh hey, let's break this down well.
Speaker 3 (09:59):
Quasi random numbers are sequences that actually have a hidden
structural rule, but they just appear random to a naive observer.
Speaker 1 (10:06):
Right, So, think of a sequence that alternates strictly between
even and odd numbers, but the numbers themselves jump wildly
across a massive range. Good example, if you just look
at a short sample of that, it feels totally chaotic,
but there's a rigid skeleton holding it together to ensure
an even spread of events over time.
Speaker 3 (10:23):
Yeah, and that even spread is really useful for certain
visual rendering tasks. But when we need numbers that pass
rigorous statistical tests for actual chaotic unpredictability, we need pseudorandom
number generators.
Speaker 1 (10:38):
Pseudorandom.
Speaker 3 (10:39):
Yes, and the foundational algorithm detailed by Smed and hecanin
is the linear congruential method or the LCM.
Speaker 1 (10:47):
The LCM now it sounds like high level calculus, but
it's really just a simple mathematical loop built on four parameters.
Speaker 2 (10:53):
Right. It is surprisingly simple.
Speaker 1 (10:54):
You have the modulus, which we'll call M. You have
the multiplier A, the increment C, and a starting value
which is known as the.
Speaker 3 (11:00):
Seed exactly, and the operation itself is just basic arithmetic.
So the algorithm takes your seed value and it multiplies
it by.
Speaker 2 (11:08):
A, and then it adds C.
Speaker 1 (11:09):
Okay, easy enough, right, But then it.
Speaker 3 (11:11):
Divides that total by the modulus M and whatever the
remainder of that division is. That remainder becomes your first
random number, the remainder, right, yeah, Then the algorithm takes
that brand new number, plugs it back into the start
of the formula is the new seed, and runs the
entire loop again.
Speaker 1 (11:27):
So picture a clock face. Let's say our modulus is twelve,
so we have a standard twelve hour clock. No matter
how wildly you multiply or add numbers together, when you
divide by twelve and take the remainder, the answer is
just spinning around the dial, right, that's right. It will
always land on a notch between one and twelve.
Speaker 3 (11:45):
It's a really elegant way to constrain infinite math into
a usable range. But because it's a closed mathematical loop
operating within that fixed clock face, the sequence of numbers
will eventually run out of unique combinations, it starts repeating
itself exactly.
Speaker 1 (12:01):
Oh wow.
Speaker 3 (12:02):
The length of this unique sequence before it finally loops
is called the period. So if your modulus is twelve,
the absolute maximum period you can achieve is twelve numbers.
Speaker 1 (12:12):
And a repeating loop is the death of unpredictability. Like
if I'm playing a digital card game and I realize
the deck is dealing me the exact same sequence of
hands every twelve rounds, the illusion completely shatters. It does
I can predict the future. The game is basically broken
at that point.
Speaker 3 (12:28):
So to prevent the player from ever seeing the loop,
developers use unimaginably massive numbers for the modulus. But you
can't just pick any large number.
Speaker 1 (12:38):
Why not?
Speaker 3 (12:39):
You want a very specific mathematical structure, ideally a prime number. Specifically,
developers often use Mrsenne primes.
Speaker 1 (12:47):
Okay, wait, so why a prime number? If I just
pick a huge round number like a billion, doesn't that
just give me a billion notches on my clock? Face?
Speaker 3 (12:54):
It does, but it introduces this problem of coprimality to primality. Yeah,
your modulus clod phase shares a common divisor with your multiplier,
the math will start skipping notches.
Speaker 1 (13:05):
Oh I think I see.
Speaker 3 (13:06):
Imagine a twelve hour clock and your multiplier forces you
to jump by threes. You hit three, six, nine, twelve,
and then you're right back where you started.
Speaker 1 (13:15):
You only generated four unique numbers, even though your clock
has twelve spaces.
Speaker 3 (13:19):
Exactly, by using a massive prime number for the modulus,
you guarantee it shares no divisors with your other parameters.
It forces the algorithm to step on every single unique
notch before it's ever allowed to loop.
Speaker 1 (13:32):
That is genuinely brilliant, and the text mentions a common
Mersen prime used is two to the thirty first power
minus one, which is over two point one billion massive.
So the clockface has two point one billion unique notches,
and because it's prime, we hit every single one. The
sequence still repeats eventually, but the period is so incomprehensibly
(13:56):
long that a human playing the game will literally never
live long enough to notice the pattern.
Speaker 3 (14:01):
True, but there is a huge vulnerability in this closed loop.
Speaker 1 (14:05):
Wait really, because I'm looking at this formula, MA and
C are hard coded by the developer. The only variable
that starts the whole chain reaction is the seed exactly.
So if I turn on my console, boot up the game,
and the default seed value is just the number one
every single time. Wouldn't the math just spit out the
exact same sequence of random events every time I play yes?
Speaker 3 (14:25):
The game would play out exactly the same way. The
ambush that terrified you in your first playthrough would happen
at the exact same millisecond in your second play through.
That ruins everything, right, So to fix this, developers have
to inject a tiny spark of real world physical chaos
to kickstart the math. They will program the game to
fetch its starting seed from highly variable, totally unpredictable sources
(14:49):
from outside the game's.
Speaker 1 (14:51):
Code, like grabbing the computer's internal clock time down to
the microscopic millisecond of the exact moment you press start
yes exactly, or pulling data from the tiny erratic temperature
fluctuations of the CPU, or even the microscopic tremor of
your hand on the computer mounts. They literally capture a
fraction of physical reality to see the digital illusion.
Speaker 2 (15:14):
That is amazing, it's really cool.
Speaker 3 (15:16):
But once you've seeded the algorithm and it's churning out
billions of numbers, you still have a massive problem. Another one, Yeah,
how do you actually know the illusion works, you have
to test it rigorously, right, and the text outlines several
empirical tests, like the poker test, where yougroup the generator's
output into hands of five and see if they match
the real world statistical probability of drawing a full house
or a flush. That makes sense, But the most revealing
(15:39):
diagnostic for the linear congruential method is called the spectral test.
Speaker 1 (15:44):
The spectral test, Okay, it sounds like ghost hunting.
Speaker 3 (15:46):
It does, but it's actually a highly visual geometric test.
So imagine taking the sequence of number your algorithm produces, yeah,
grouping them into pairs, and plotting those pairs as x
and y coordinates on a massive two.
Speaker 1 (16:00):
Okay, I'm picturing it.
Speaker 3 (16:01):
If your generator is producing true chaotic randomness, that graph
should look like pure uniform television static. There should be
absolutely no pattern.
Speaker 1 (16:11):
But the LCM isn't true chaos. It's built on fixed
multiplication and addition.
Speaker 3 (16:16):
Exactly because of that linear mathematical relationship. If you zoom
out and look at that TV static, you will realize
that dots aren't actually random at all. They align to
form a lattice of perfectly parallel lines. Wow, they are
mathematically tethered together. And if you group the numbers into
triplets and plot them in a three D space, those
lines become parallel planes.
Speaker 1 (16:35):
So the illusion has literal seams in it. The randomness
is basically stacked in layers.
Speaker 3 (16:40):
Yes, the spectral test measures the distance between those parallel planes.
If the planes are too far apart, it means there
are massive predictable gaps in your random spread, and you
don't want that. No, So a high quality algorithm uses
parameters carefully calibrated to push those planes as tightly together
as possible, basically blurring the lines until the human eye
(17:04):
and statistical analysis only sees pure static.
Speaker 1 (17:07):
Okay, So let's say our math past the spectral test.
The algorithm is incredibly robust, and it just generated a
massive pseudo random number, let's say one point eight billion. Okay,
but I'm playing a digital board game and my character
just needs to roll a standard six sided die. How
does the code shrink a massive one point eight billion
output down to a tiny interval of one to six
(17:30):
without destroying the delicate randomness we just engineered.
Speaker 3 (17:33):
Well, if you take the lazy route, you absolutely ruin
the die.
Speaker 2 (17:36):
Yeah.
Speaker 3 (17:36):
Most basic approach, which the text calls the Monte Carlo
method is to just divide your massive random number by six.
Speaker 1 (17:42):
And take the remainder like the clock face right.
Speaker 2 (17:44):
But this warps the distribution.
Speaker 1 (17:45):
Because the maximum limit of your huge random number generator
probably isn't perfectly divisible.
Speaker 2 (17:51):
By six exactly.
Speaker 1 (17:52):
Think of it like having a pizza with twenty slices
and you need to divide it evenly among six people.
Everyone gets three slices, but you have two slices left.
Speaker 2 (18:01):
Over, yep, the remainder.
Speaker 1 (18:03):
And if you just hand those remaining slices out to
whoever is closest, two people end up with more pizza.
In the code. That means the numbers one and two
end up with slightly more mathematical real estate than three, four, five,
or six.
Speaker 3 (18:16):
Which means the digital die becomes mathematically loaded. Over the
course of thousands of roles, the player will absolutely notice
that they are rolling ones in twos more often.
Speaker 1 (18:25):
And it feels completely unfair it does.
Speaker 3 (18:27):
So to solve this, developers use something called the Las
Vegas method.
Speaker 1 (18:31):
I love the Las Vegas method because it's so uncompromising.
It essentially guarantees a perfectly uniform distribution by simply throwing
the excess pizza slices directly into the trash.
Speaker 3 (18:43):
That's pretty much it in terms of the code. If
the algorithm generates a huge number that happens to fall
into that uneven remainder zone at the very top of
its range, the code literally intercepts it.
Speaker 1 (18:55):
It just catches it.
Speaker 3 (18:56):
Yeah, it discards the number silently and goes right back
to the start of the loop reroll.
Speaker 2 (19:01):
It repeats this.
Speaker 3 (19:02):
Invisible process in a fraction of a millisecond until it
generates a number that falls cleanly into the perfectly divisible range.
Speaker 1 (19:09):
And only then does it show the die roll to
the player.
Speaker 3 (19:12):
Yes, it sacrifices precious computing power and time purely to
guarantee absolute fairness.
Speaker 1 (19:18):
It's beautiful. But so many game mechanics have nothing to
do with rolling dice, right. They are about managing time
and flow, like when does the next wave of zombies attack?
Or when does a rainstorm start?
Speaker 2 (19:29):
Get pacing?
Speaker 1 (19:30):
Yeah, how do you pace the game so the player
doesn't get bored but also it doesn't get completely overwhelmed?
Speaker 3 (19:35):
Well, translating raw randomness into organic feeling events over time
requires discrete probability distribution, okay, and The most vital one
detailed by Smet and Hacona is the Poisson distribution.
Speaker 1 (19:46):
Right, and the book has this fantastic example of an
asteroid mining colony in a strategy game. The designers want
the spaceport to feel like a bustling, living economy, so
they determine that, on average, the colony should receive seven
cargo haulers every single rotation period.
Speaker 3 (20:03):
Now, if the code just spawns exactly seven haulers, evenly
spaced out every single rotation, well, if the spaceport just
feels like a sterile assembly.
Speaker 1 (20:11):
Line, it doesn't feel alive, not at all.
Speaker 3 (20:14):
But the developers don't just program seven haulers. They feed
that target average of seven into the poison distribution algorithm.
Speaker 1 (20:21):
And what does that do.
Speaker 3 (20:23):
What this math does is translate a flat average into
a dynamic curve of likelihoods for any number of events.
So on most rotations you might get six or eight hollars.
It feels pretty normal, right, but the math allows for outliers.
Suddenly you have a rotation where only two haulers show up,
and your economy slows down. That ek sets in, and
then without warning, the Poisson curve hits a rare probability
(20:44):
and fourteen haulers arrive at the exact same time.
Speaker 1 (20:47):
The sirens go off. Your spaceport thrown into total logistical chaos,
and you are just scrambling to manage the influx.
Speaker 3 (20:54):
Yes, the Poisson distribution guarantees that if you average it
out over a thousand rotations will equal exactly seven. But
minute to minute, it generates these organic lulls and terrifying
spikes of activity.
Speaker 1 (21:07):
It creates the actual pulse of the game. That feeling
of panic when those fourteen hollars arrive, that rush of adrenaline,
when you barely manage the crisis. You know you are
having a genuine emotional reaction to a probability curve.
Speaker 3 (21:20):
You are reacting to an engineered ilusion. And really, that
is the ultimate takeaway from Smed and Hakonan's work. The
magic of a digital world isn't magic at all.
Speaker 1 (21:29):
No, it's not the Next time you are playing a
game and you find yourself marveling at how a synthetic
player panicked and missed a shot, or how the narrative
seamlessly adapted to a chaotic decision you made, or how
a sudden rainstorm perfectly matched the dramatic tension of the scene.
Just remember the math churning beneath the surface.
Speaker 2 (21:46):
It's all math.
Speaker 1 (21:47):
It is the intricate, silent work of invisible drama managers
keeping the narrative paradox in check. It is the uncompromising
fairness of the Las Vegas method, silently discarding uneven numbers.
And it's the linear congrential method spinning a massive prime
numbered clock face, generating chaos from a single seed of
physical reality.
Speaker 3 (22:07):
It is entirely deterministic architecture masquerating flawlessly as wild living unpredictability,
which actually leaves us with a rather profound implication to
consider long after you take your headphones off.
Speaker 1 (22:19):
Ooh, laid on us.
Speaker 3 (22:20):
Well, think about it. If human developers working with just
basic processors can use deterministic loops, prime numbers, and hidden
distribution curves to create such a convincing, unbreakable illusion of
random chance, chaos, and free will inside a digital box, well,
how do we know our own universes supposedly random events
aren't doing the exact same thing? Oh wow, how do
we know the quantum physics of our reality like the
(22:42):
very fabric of chance in our universe isn't just a
cosmic linear congruential method running on an unfathomably large prime.
Speaker 1 (22:49):
Modulus that is heavy. So the next time you're walking
in the woods and a twig snap's unexpectedly, maybe ask
yourself what the seed value was. Thanks for joining us
on this deep dive. Keep questioning a code
So picture this. You're playing a game and you round
a corner in some dark digital dungeon and boom and
enemy suddenly springs an ambush.
Speaker 2 (00:09):
Oh yeah, your heart just completely jumps into your throat.
Speaker 1 (00:11):
Right, And in that split second, you know, you're not
thinking about code or like pixels on a screen.
Speaker 2 (00:16):
Oh of course not.
Speaker 1 (00:17):
You're just thinking, wow, that felt so real. Because we
play these games expecting this organic spontaneity, right, We really
want that digital world to feel alive, we do.
Speaker 3 (00:27):
But the truth is that organic feeling is entirely fabricated,
like completely, when you actually step behind the curtain of
game development, all that spontaneity just vanishes. You're looking at
this landscape of cold, hard, purely deterministic code.
Speaker 1 (00:44):
Which is so wild to think about.
Speaker 3 (00:46):
It is because computers are well, they're rigid machines. You
literally cannot be spontaneous. Everything you feel in that dungeon
is just a meticulously crafted mathematical illusion.
Speaker 1 (00:56):
And today we are ripping open that code to see
exactly how developers pull off that trick. We are doing
a deep dive into this brilliant textbook. It's called Algorithms
and Networking for Computer Games by Juni Smed and Harriet Conan.
Speaker 2 (01:11):
It's a fascinating read, it really is.
Speaker 1 (01:13):
And our mission today is to figure out how programmers
manipulate math and psychology to trick your brain. We're going
to start from the foundational rules of play and go
all the way down to the invisible algorithms that basically
manufacture chaos.
Speaker 3 (01:28):
Yeah, and to understand the math, we first have to
agree on what we're actually trying to simulate, right, right,
Because when you strip away the high resolution graphics and
you know, the fancy haptic feedback controllers, Smed and Hakonan
argue that an interactive world requires one specific crucial ingredient
to separate it from just a static puzzle.
Speaker 2 (01:46):
And that ingredient unpredictability.
Speaker 1 (01:48):
Okay, let's unpack this because the book uses a really
specific word here, which is conflict. Yes, conflict, And when
I hear conflict, my mind immediately goes to like fighting
a digital dragon or racing against a rival car. But
the authors argue it's actually way broader than that, much brighter. Yeah,
because think about a Sunday crossword puzzle, right. It's challenging,
(02:10):
it has rules, it has a goal, but is it
a game.
Speaker 3 (02:13):
Well, by the strict definitions used in game architecture, a
standard crossword puzzle is not actually a game. Wait really yeah,
because it lacks non determinism. A crossword puzzle just sits there.
It doesn't fight back, you know, doesn't adapt.
Speaker 2 (02:27):
To your choices.
Speaker 1 (02:28):
Okay, I see.
Speaker 3 (02:29):
So conflict in this specific context means you are facing
an opposing force or some random process that actively obstructs you.
Speaker 1 (02:37):
Right, So if you add a ticking timer to that
crossword or I don't know, you're raising a friend to
finish it first.
Speaker 3 (02:42):
Suddenly have non determinism. Exactly, You've injected chaos, and now
you have game.
Speaker 1 (02:46):
Okay, So in a single player experience, developers have to
artificially inject that chaos. They have to simulate an opposing
force using AI, which the authors call synthetic players.
Speaker 2 (02:57):
Right, synthetic players.
Speaker 1 (02:58):
But here is the most counter intuitive part of this
whole illusion. For me, to make an AI opponent feel
like a real, living human, developers actually have to break it. Yes,
they have to make the AI significantly worse.
Speaker 3 (03:12):
Well, you have to consider what computers are actually capable of, right,
Like a machine can calculate your character's exact coordinates aim
with pixel perfect precision and just eliminate you the exact
millisecond you enter its line of sight.
Speaker 1 (03:24):
Right, It's basically the Terminator exactly.
Speaker 3 (03:27):
It possesses superhuman perfection, but playing against flawless perfection is
incredibly boring and frustrating. Completely, it feels robotic, and it
instantly shatters that illusion of playing against a living, breathing
entity in a shared space.
Speaker 1 (03:41):
So it's all about simulating human flaws. And there is
this amazing specific detail from the text about how developers
engineer this.
Speaker 2 (03:48):
Oh the reaction time.
Speaker 1 (03:49):
Yes, when you take a synthetic player by surprise, say
you flank an enemy in a shooter game, the programmers
hard code a deliberate zero point two to zero point
four second reaction time delay before the AI is even
allowed to shoot back.
Speaker 3 (04:03):
Yeah, and that specific window of time is absolutely no accident.
It simulates the cognitive processing time of a human being.
It basically mimics panic, panick.
Speaker 1 (04:13):
Right.
Speaker 3 (04:14):
Yeah, So when you surprise an enemy and they freeze
for like a third of a second before scrambling for cover,
your brain subconsciously registers the ODEA.
Speaker 1 (04:23):
Loop, the Obie loop.
Speaker 3 (04:24):
Yeah, observe orient decide act, you recognize that slight hesitation
as human cognition, and the illusion holds.
Speaker 1 (04:31):
Wow. But this introduces a massive headache for the game designers,
doesn't it.
Speaker 2 (04:36):
Oh a huge one.
Speaker 1 (04:37):
Because if you program these synthetic players to act somewhat unpredictably,
and then you give the actual human player the freedom
to do literally whatever they want, how on earth do
you guarantee the game still tells a cohesive story.
Speaker 3 (04:49):
Well, you've hit on what the authors called the narrative paradox.
It is the central tension in all interactive storytelling.
Speaker 1 (04:55):
A narrative paradox.
Speaker 2 (04:56):
Yeah.
Speaker 3 (04:57):
So, on one side of the scale you have plot coherence,
the there's in the designers. They want to deliver a
well paced, dramatic, emotionally resonant story.
Speaker 2 (05:05):
Like a movie exactly.
Speaker 3 (05:07):
But on the other side you have character believability and
player agency. You need the player and the AI to
have the actual freedom to ma choices.
Speaker 1 (05:17):
Because if I have total freedom, I might just decide
to wander off into the woods to pick digital mushrooms
and completely ignore the terrifying dragon that's supposed to be
attacking the castle.
Speaker 3 (05:27):
Right, and then the pacing is completely ruined. The story
just grinds.
Speaker 2 (05:30):
To a halt.
Speaker 1 (05:31):
So how do they fix that?
Speaker 3 (05:32):
So the industry generally tackles this tension from two different directions.
The first is a character centric approach. Okay, here, the
AI characters are highly autonomous. They act on their own program, desires,
and needs, and sometimes they even use a hybrid communication system.
Speaker 1 (05:49):
Wait, what does that mean.
Speaker 3 (05:50):
Well, they speak in character to the player, but simultaneously
they send out of character signals to the game's background
systems to try gently nudge the plot forward organically.
Speaker 1 (06:01):
Oh that's clever, it is.
Speaker 3 (06:02):
The story basically emerges from the bottom up.
Speaker 1 (06:04):
But the problem with the bottom up approach is that
it can quickly turn into the chaos of everyday life. Right,
real life isn't inherently structured like a three act cinematic blockbuster.
Speaker 2 (06:14):
No, it definitely isn't.
Speaker 1 (06:16):
So the alternative is the author centric approach, which relies
on something called an invisible drama manager.
Speaker 3 (06:22):
Yes, the drama manager, which I love.
Speaker 1 (06:24):
Think of it like a stage director secretly walking among
the actors, whispering in their ears, completely unseen by the audience.
Speaker 2 (06:32):
That's a perfect way to put it.
Speaker 3 (06:33):
The drama manager is constantly running math in the background,
monitoring metrics like player tension and pacing.
Speaker 1 (06:40):
So that's washing what I do constantly.
Speaker 3 (06:42):
If the algorithm's determined you've been wandering the woods picking
mushrooms for way too long and the tension is dropping,
the drama manager whispers to the AI enemies to spawn
an ambush just out of your line of sight.
Speaker 1 (06:54):
To get my heart rate back up exactly.
Speaker 3 (06:56):
Or conversely, if you are low on health and completely overwhelmed,
it tells the enemies to pull back a bit or
to miss their shots. It subtly manipulates the parameters of
the world to push you toward the intended emotional beats.
Speaker 1 (07:09):
But even with a brilliant invisible director, the developers still
have to physically build the paths the story can take.
Right they do, and the text maps out game stories
using these geometrical graphs. The most basic one is just
a linear story. Episode A always leads to episode B,
which leads to episode C. It's just a straight line.
Speaker 3 (07:28):
Yeah, and linear development is incredibly cost effective, but it
offers almost zero agency. You're essentially just walking through a movie, right.
The theoretical opposite of that is a fully branching structure
where every single choice you make leads to a completely different,
unique continuation of the game.
Speaker 1 (07:46):
Which sounds like the holy grail of gaming until you
actually do the math on the combinatorial explosion.
Speaker 2 (07:52):
Oh, the math is terrifying.
Speaker 1 (07:53):
It really is. Let's say you have a scene with
three dialogue choices, and each of those choices leads to
three entirely new scenarios. By the time you reach the
fourth major decision point in the game, you aren't programming
one game anymore. You're programming eighty one completely different games.
You'd have studio spending twelve years and half a billion
dollars just to make a five hour campaign.
Speaker 3 (08:15):
It's completely unsustainable. So developers rely on a highly calculated
compromise called parallel pass. Parallel pad right, the story branch
is out for a while, allowing you to make choices,
take different routes, and express your agency. This provides that
crucial illusion of free will ah illusion. But eventually all
(08:35):
those diverged branches are forced to converge back into major,
unavoidable story nodes.
Speaker 1 (08:40):
So I might use diplomacy to talk my way past
the guards, and you might just kick the door down
with explosives typical exactly, but thirty minutes later, we both
end up standing in the exact same throne room for
the exact same final boss fight.
Speaker 3 (08:53):
Yes, the game just acknowledges are different methods in the dialogue.
It keeps the studio from going bankrupt while letting us
feel like we are the actual authors of our own fate.
Speaker 1 (09:03):
So the illusion of free will is maintained by carefully
hidden constraints exactly, And that reliance on nondeterminism, you know,
on generating a feeling of unpredictable chaos within strict mathematical limits,
brings us to the very bedrock of how a computer operates.
And here's where it gets really interesting for me, oh
for sure, Because whether we are talking about parallel story branches,
(09:26):
or that zero point three second reaction delay for the AI,
or even simulating a dice roll, games need randomness to function.
Speaker 2 (09:34):
They desperately need it.
Speaker 1 (09:35):
But a computer processor is a purely deterministic machine. It
only executes the exact logic gits it is fed. It
cannot flip a coin. True randomness in a computer is
a total myth.
Speaker 3 (09:46):
It is developers literally have to fake it. Yeah, they
use algorithms to produce sequences of numbers that just behave unpredictably,
and these fall into two main categories, which are quasi
random and pseudorandom.
Speaker 1 (09:58):
Oh hey, let's break this down well.
Speaker 3 (09:59):
Quasi random numbers are sequences that actually have a hidden
structural rule, but they just appear random to a naive observer.
Speaker 1 (10:06):
Right, So, think of a sequence that alternates strictly between
even and odd numbers, but the numbers themselves jump wildly
across a massive range. Good example, if you just look
at a short sample of that, it feels totally chaotic,
but there's a rigid skeleton holding it together to ensure
an even spread of events over time.
Speaker 3 (10:23):
Yeah, and that even spread is really useful for certain
visual rendering tasks. But when we need numbers that pass
rigorous statistical tests for actual chaotic unpredictability, we need pseudorandom
number generators.
Speaker 1 (10:38):
Pseudorandom.
Speaker 3 (10:39):
Yes, and the foundational algorithm detailed by Smed and hecanin
is the linear congruential method or the LCM.
Speaker 1 (10:47):
The LCM now it sounds like high level calculus, but
it's really just a simple mathematical loop built on four parameters.
Speaker 2 (10:53):
Right. It is surprisingly simple.
Speaker 1 (10:54):
You have the modulus, which we'll call M. You have
the multiplier A, the increment C, and a starting value
which is known as the.
Speaker 3 (11:00):
Seed exactly, and the operation itself is just basic arithmetic.
So the algorithm takes your seed value and it multiplies
it by.
Speaker 2 (11:08):
A, and then it adds C.
Speaker 1 (11:09):
Okay, easy enough, right, But then it.
Speaker 3 (11:11):
Divides that total by the modulus M and whatever the
remainder of that division is. That remainder becomes your first
random number, the remainder, right, yeah, Then the algorithm takes
that brand new number, plugs it back into the start
of the formula is the new seed, and runs the
entire loop again.
Speaker 1 (11:27):
So picture a clock face. Let's say our modulus is twelve,
so we have a standard twelve hour clock. No matter
how wildly you multiply or add numbers together, when you
divide by twelve and take the remainder, the answer is
just spinning around the dial, right, that's right. It will
always land on a notch between one and twelve.
Speaker 3 (11:45):
It's a really elegant way to constrain infinite math into
a usable range. But because it's a closed mathematical loop
operating within that fixed clock face, the sequence of numbers
will eventually run out of unique combinations, it starts repeating
itself exactly.
Speaker 1 (12:01):
Oh wow.
Speaker 3 (12:02):
The length of this unique sequence before it finally loops
is called the period. So if your modulus is twelve,
the absolute maximum period you can achieve is twelve numbers.
Speaker 1 (12:12):
And a repeating loop is the death of unpredictability. Like
if I'm playing a digital card game and I realize
the deck is dealing me the exact same sequence of
hands every twelve rounds, the illusion completely shatters. It does
I can predict the future. The game is basically broken
at that point.
Speaker 3 (12:28):
So to prevent the player from ever seeing the loop,
developers use unimaginably massive numbers for the modulus. But you
can't just pick any large number.
Speaker 1 (12:38):
Why not?
Speaker 3 (12:39):
You want a very specific mathematical structure, ideally a prime number. Specifically,
developers often use Mrsenne primes.
Speaker 1 (12:47):
Okay, wait, so why a prime number? If I just
pick a huge round number like a billion, doesn't that
just give me a billion notches on my clock? Face?
Speaker 3 (12:54):
It does, but it introduces this problem of coprimality to primality. Yeah,
your modulus clod phase shares a common divisor with your multiplier,
the math will start skipping notches.
Speaker 1 (13:05):
Oh I think I see.
Speaker 3 (13:06):
Imagine a twelve hour clock and your multiplier forces you
to jump by threes. You hit three, six, nine, twelve,
and then you're right back where you started.
Speaker 1 (13:15):
You only generated four unique numbers, even though your clock
has twelve spaces.
Speaker 3 (13:19):
Exactly, by using a massive prime number for the modulus,
you guarantee it shares no divisors with your other parameters.
It forces the algorithm to step on every single unique
notch before it's ever allowed to loop.
Speaker 1 (13:32):
That is genuinely brilliant, and the text mentions a common
Mersen prime used is two to the thirty first power
minus one, which is over two point one billion massive.
So the clockface has two point one billion unique notches,
and because it's prime, we hit every single one. The
sequence still repeats eventually, but the period is so incomprehensibly
(13:56):
long that a human playing the game will literally never
live long enough to notice the pattern.
Speaker 3 (14:01):
True, but there is a huge vulnerability in this closed loop.
Speaker 1 (14:05):
Wait really, because I'm looking at this formula, MA and
C are hard coded by the developer. The only variable
that starts the whole chain reaction is the seed exactly.
So if I turn on my console, boot up the game,
and the default seed value is just the number one
every single time. Wouldn't the math just spit out the
exact same sequence of random events every time I play yes?
Speaker 3 (14:25):
The game would play out exactly the same way. The
ambush that terrified you in your first playthrough would happen
at the exact same millisecond in your second play through.
That ruins everything, right, So to fix this, developers have
to inject a tiny spark of real world physical chaos
to kickstart the math. They will program the game to
fetch its starting seed from highly variable, totally unpredictable sources
(14:49):
from outside the game's.
Speaker 1 (14:51):
Code, like grabbing the computer's internal clock time down to
the microscopic millisecond of the exact moment you press start
yes exactly, or pulling data from the tiny erratic temperature
fluctuations of the CPU, or even the microscopic tremor of
your hand on the computer mounts. They literally capture a
fraction of physical reality to see the digital illusion.
Speaker 2 (15:14):
That is amazing, it's really cool.
Speaker 3 (15:16):
But once you've seeded the algorithm and it's churning out
billions of numbers, you still have a massive problem. Another one, Yeah,
how do you actually know the illusion works, you have
to test it rigorously, right, and the text outlines several
empirical tests, like the poker test, where yougroup the generator's
output into hands of five and see if they match
the real world statistical probability of drawing a full house
or a flush. That makes sense, But the most revealing
(15:39):
diagnostic for the linear congruential method is called the spectral test.
Speaker 1 (15:44):
The spectral test, Okay, it sounds like ghost hunting.
Speaker 3 (15:46):
It does, but it's actually a highly visual geometric test.
So imagine taking the sequence of number your algorithm produces, yeah,
grouping them into pairs, and plotting those pairs as x
and y coordinates on a massive two.
Speaker 1 (16:00):
Okay, I'm picturing it.
Speaker 3 (16:01):
If your generator is producing true chaotic randomness, that graph
should look like pure uniform television static. There should be
absolutely no pattern.
Speaker 1 (16:11):
But the LCM isn't true chaos. It's built on fixed
multiplication and addition.
Speaker 3 (16:16):
Exactly because of that linear mathematical relationship. If you zoom
out and look at that TV static, you will realize
that dots aren't actually random at all. They align to
form a lattice of perfectly parallel lines. Wow, they are
mathematically tethered together. And if you group the numbers into
triplets and plot them in a three D space, those
lines become parallel planes.
Speaker 1 (16:35):
So the illusion has literal seams in it. The randomness
is basically stacked in layers.
Speaker 3 (16:40):
Yes, the spectral test measures the distance between those parallel planes.
If the planes are too far apart, it means there
are massive predictable gaps in your random spread, and you
don't want that. No, So a high quality algorithm uses
parameters carefully calibrated to push those planes as tightly together
as possible, basically blurring the lines until the human eye
(17:04):
and statistical analysis only sees pure static.
Speaker 1 (17:07):
Okay, So let's say our math past the spectral test.
The algorithm is incredibly robust, and it just generated a
massive pseudo random number, let's say one point eight billion. Okay,
but I'm playing a digital board game and my character
just needs to roll a standard six sided die. How
does the code shrink a massive one point eight billion
output down to a tiny interval of one to six
(17:30):
without destroying the delicate randomness we just engineered.
Speaker 3 (17:33):
Well, if you take the lazy route, you absolutely ruin
the die.
Speaker 2 (17:36):
Yeah.
Speaker 3 (17:36):
Most basic approach, which the text calls the Monte Carlo
method is to just divide your massive random number by six.
Speaker 1 (17:42):
And take the remainder like the clock face right.
Speaker 2 (17:44):
But this warps the distribution.
Speaker 1 (17:45):
Because the maximum limit of your huge random number generator
probably isn't perfectly divisible.
Speaker 2 (17:51):
By six exactly.
Speaker 1 (17:52):
Think of it like having a pizza with twenty slices
and you need to divide it evenly among six people.
Everyone gets three slices, but you have two slices left.
Speaker 2 (18:01):
Over, yep, the remainder.
Speaker 1 (18:03):
And if you just hand those remaining slices out to
whoever is closest, two people end up with more pizza.
In the code. That means the numbers one and two
end up with slightly more mathematical real estate than three, four, five,
or six.
Speaker 3 (18:16):
Which means the digital die becomes mathematically loaded. Over the
course of thousands of roles, the player will absolutely notice
that they are rolling ones in twos more often.
Speaker 1 (18:25):
And it feels completely unfair it does.
Speaker 3 (18:27):
So to solve this, developers use something called the Las
Vegas method.
Speaker 1 (18:31):
I love the Las Vegas method because it's so uncompromising.
It essentially guarantees a perfectly uniform distribution by simply throwing
the excess pizza slices directly into the trash.
Speaker 3 (18:43):
That's pretty much it in terms of the code. If
the algorithm generates a huge number that happens to fall
into that uneven remainder zone at the very top of
its range, the code literally intercepts it.
Speaker 1 (18:55):
It just catches it.
Speaker 3 (18:56):
Yeah, it discards the number silently and goes right back
to the start of the loop reroll.
Speaker 2 (19:01):
It repeats this.
Speaker 3 (19:02):
Invisible process in a fraction of a millisecond until it
generates a number that falls cleanly into the perfectly divisible range.
Speaker 1 (19:09):
And only then does it show the die roll to
the player.
Speaker 3 (19:12):
Yes, it sacrifices precious computing power and time purely to
guarantee absolute fairness.
Speaker 1 (19:18):
It's beautiful. But so many game mechanics have nothing to
do with rolling dice, right. They are about managing time
and flow, like when does the next wave of zombies attack?
Or when does a rainstorm start?
Speaker 2 (19:29):
Get pacing?
Speaker 1 (19:30):
Yeah, how do you pace the game so the player
doesn't get bored but also it doesn't get completely overwhelmed?
Speaker 3 (19:35):
Well, translating raw randomness into organic feeling events over time
requires discrete probability distribution, okay, and The most vital one
detailed by Smet and Hacona is the Poisson distribution.
Speaker 1 (19:46):
Right, and the book has this fantastic example of an
asteroid mining colony in a strategy game. The designers want
the spaceport to feel like a bustling, living economy, so
they determine that, on average, the colony should receive seven
cargo haulers every single rotation period.
Speaker 3 (20:03):
Now, if the code just spawns exactly seven haulers, evenly
spaced out every single rotation, well, if the spaceport just
feels like a sterile assembly.
Speaker 1 (20:11):
Line, it doesn't feel alive, not at all.
Speaker 3 (20:14):
But the developers don't just program seven haulers. They feed
that target average of seven into the poison distribution algorithm.
Speaker 1 (20:21):
And what does that do.
Speaker 3 (20:23):
What this math does is translate a flat average into
a dynamic curve of likelihoods for any number of events.
So on most rotations you might get six or eight hollars.
It feels pretty normal, right, but the math allows for outliers.
Suddenly you have a rotation where only two haulers show up,
and your economy slows down. That ek sets in, and
then without warning, the Poisson curve hits a rare probability
(20:44):
and fourteen haulers arrive at the exact same time.
Speaker 1 (20:47):
The sirens go off. Your spaceport thrown into total logistical chaos,
and you are just scrambling to manage the influx.
Speaker 3 (20:54):
Yes, the Poisson distribution guarantees that if you average it
out over a thousand rotations will equal exactly seven. But
minute to minute, it generates these organic lulls and terrifying
spikes of activity.
Speaker 1 (21:07):
It creates the actual pulse of the game. That feeling
of panic when those fourteen hollars arrive, that rush of adrenaline,
when you barely manage the crisis. You know you are
having a genuine emotional reaction to a probability curve.
Speaker 3 (21:20):
You are reacting to an engineered ilusion. And really, that
is the ultimate takeaway from Smed and Hakonan's work. The
magic of a digital world isn't magic at all.
Speaker 1 (21:29):
No, it's not the Next time you are playing a
game and you find yourself marveling at how a synthetic
player panicked and missed a shot, or how the narrative
seamlessly adapted to a chaotic decision you made, or how
a sudden rainstorm perfectly matched the dramatic tension of the scene.
Just remember the math churning beneath the surface.
Speaker 2 (21:46):
It's all math.
Speaker 1 (21:47):
It is the intricate, silent work of invisible drama managers
keeping the narrative paradox in check. It is the uncompromising
fairness of the Las Vegas method, silently discarding uneven numbers.
And it's the linear congrential method spinning a massive prime
numbered clock face, generating chaos from a single seed of
physical reality.
Speaker 3 (22:07):
It is entirely deterministic architecture masquerating flawlessly as wild living unpredictability,
which actually leaves us with a rather profound implication to
consider long after you take your headphones off.
Speaker 1 (22:19):
Ooh, laid on us.
Speaker 3 (22:20):
Well, think about it. If human developers working with just
basic processors can use deterministic loops, prime numbers, and hidden
distribution curves to create such a convincing, unbreakable illusion of
random chance, chaos, and free will inside a digital box, well,
how do we know our own universes supposedly random events
aren't doing the exact same thing? Oh wow, how do
we know the quantum physics of our reality like the
(22:42):
very fabric of chance in our universe isn't just a
cosmic linear congruential method running on an unfathomably large prime.
Speaker 1 (22:49):
Modulus that is heavy. So the next time you're walking
in the woods and a twig snap's unexpectedly, maybe ask
yourself what the seed value was. Thanks for joining us
on this deep dive. Keep questioning a code
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