19+ year gamedev here. The way we did this in the PS2 era was to treat every timer as a countdown. Our games also used variable tick rates, so the epsilon method would not have worked for us.

I never knew about this bug but just hearing the laser gun firing at the start I could clearly tell I had experienced it as I recall the sounds of the two different rates of fires.

I really hope Agonizing Rectal Pain never unsubscribes so you have to keep reading his name at the end of each video

THEY MADE THE TIMER A FLOATING POINT NUMBER?!

It seems to be a really bad decision to use a floating point value to store the game tic like that. An integer completely avoids this issue; even a 32-bit integer has enough range for over 6 years of playtime at 20 tics per second. About the only advantage a float might have is that time values are written by developers in terms of seconds rather than tics, making it easier to change the tic rate during development, but even then, converting those values to integer tics at the first opportunity in the code is probably a better solution.

the moral of the story: just because it has a decimal, doesn't mean you should make it a float

Weird how I remember playing this game years ago, and being vaguely aware of this happening, but just dismissing it in the back of my head as the weapons overheating or something, haha

Unlike the floating points, we were precise in finding the reason for the bug.

There's more to the bug than this - if it was just a matter of floating point error in the time tick, you would have one shot fire one tick late, and then all subsequent shots would be at the regular rate, but one tick late relative to the beginning of the game.

The other part of the bug is that the target times are not calculated correctly.  Instead of adding the time delay to the previous time target to get the next shot, it adds it to the time at which the weapon was actually fired, resulting in each subsequent target time being almost a full tick late relative to the last one (because the actual time of firing was late).  This is why the bug doesn't appear to "fix itself" after one shot being delayed by a single tick, but rather has a additional delay for every single shot.

I FREAKING KNEW IT.
When I was a wee scrub I loved the Laser Gun (still do tbh) and everytime it started to slow down I just convinced myself that IT GOT DIRTY BECAUSE OF THE SAND. Talk about being stupid, but back then even a 6 year old me noticed that the gun doesn't work like it's supposed to be working.

Surprised how interesting I found this one! Looks like finding the issue was more difficult than fixing it.

thats cool, I never thought that floating point numbers can affect the game THIS way

this explains why so many rooms of Serious Sam felt completely unfair. I tend to take my time and I would probably have ended up just reaching the 3rd stage or so around when this bug shows up. I definitely noticed the sound of the laser gun changing, but I had/have so little experience with Serious Sam that I never noticed the weapon was actually firing slower! It's crazy how nobody on their team noticed it before releasing!

This variable math is also why Minecraft gets super jittery and whatnot the further away you get from 0.x.0 (spawn)

I've always been a bit sus of floating point. Feels like should avoid it if you're not really using it to show floating point numbers to users.

It's a good reminder – never use floating point variables if you need precision or may workaround without them. They could just count milliseconds in Int64 and this bug would have never occured.

This is why its absolutely crucial that when you're doing floating point comparisons to pick an epsilon that makes sense with regards to the units of change you expect to happen between each check. The 0.04 epsilon makes sense because of the tick rate they chose, whereas 0.01 is kind of a nonsense epsilon. Its a very easy mistake to make with regards to floating point comparisons, however, and I've seen even very experienced programmers make it. That's why I try my best to avoid floating point altogether.

Not sure if I have ever "encountered" that bug playing The Second Encounter. I played so much multiplayer back in the mid 2000s that the lag would slow down the weapon speed at times. Now, that I am not sure if the bug has a part of.

Lesson: never use constant values in your code that are not exactly representable.

Here's a fun fact. Your video was mentioned on a polish YT channel arhneu. It's in their latest "System error" thing. They basically simplified your explanation as a setup for the 1991 Patriot missile failure that happened due to the same floating point inaccuracy accumulating over time.
Cheers from Poland!