# Probability

I once saw an interesting math challenge: Assume X and Y are randomly chosen numbers, with each being equally likely to be any number between 0 and 1.  Take Y/X and round to the closest integer.  What is the probability that this number will be even (or odd)?

It turns out this problem involves using the a ratio distribution.  I felt that Wikipedia’s page on this subject was very poor, at the very least certainly unintuitive, so I hoped to come up with a more intuitive explanation.

(Note: This post does assume familiarity with probability distributions, using them to get cumulative distributions, averages, etc.)

# Pepper

In early November of 2008, we had taken in a stray that had been roaming around our apartment complex.  She immediately made herself at home.  She was the first cat I have ever had. We named her Caramel.

Little did I know that only a few days later, at the end of the very same month, I would find another stray in our apartment parking lot.  It was already dark when I came home from work.  After I parked my car, a cat came out from under another car, meowing.  In the darkness, I thought I saw a collar.  I figured since we had good luck with our first cat, we could try to do a favor for this one.  I told FO about her.  FO went out to look at her.

# Game Music Announcement

I thought I’d made some game music available. Since other places have quite a bit available, I have no plans to make anything complete, but will focus on stuff that I had a harder time finding.

I’ll start with my favorite song from R-Type II (the underwater theme from stage 2), and the essentially complete Bionic Commando Elite Forces. Yes, a game I reviewed in a former life. By “essentially complete”, I mean I believe I neglected only two tracks on the GBS, and both were more like sound effects than songs.  As is, there are already a couple of remaining songs on the soundtrack that are quite short (such as the music for some boss fights, or overhead zones).

I’ve read that Miyamoto often doesn’t like putting some finishing touches on games: Things like a nice title or menu screen.  He prefers working on the actual game.  Likewise, my interest started flagging after I got these songs ripped and uploaded, so some perks (custom tags or descriptions) are missing.

# When does repetition become tedious?

Some things probably are objectively repetitive. A basketball player that practices by standing at the free throw line for hours, trying to sink shot after shot, is doing something that almost must be considered repetitive.

However, a basketball player that would do that would be hoping to GAIN something from the experience. In that case, obviously, to improve his free throw.

I think that’s the real distinction between something that is superficially repetitive, and something that is tedious. An experience is tedious if it has no challenge and nothing to teach, yet it drags on repetitiously.

So, once again, the standard of CHALLENGE is the important one. Whether or not something is tedious has little to do with whether you do one thing in a game, or two, or many. (Some misguided individuals may claim, for example, that Super Mario Bros. is repetitive, because “all you do is run and jump”)

When you play Punch-Out, while you have only a few moves to use, you are challenged to use those moves in different combinations, with different timings, with better reflexes, with different strategies. It is not tedious.

I have heard some people complain about R-Type, due to its checkpoint system, because having to replay part of the same level is “repetitive”. But the reason the game makes you do this is because it is trying to get you to learn the level. It is entirely analogous to practicing at any skill (like free throws) to improve. Once you have the skills needed to beat the level, you can beat it, and quickly, too. It is not tedious.

On the other hand, what is Wind Waker trying to teach by having you sail for minutes at a time, while nothing else happens? It is not a challenge. It isn’t anything. After you’ve done it a few times and have gotten whatever point there was to get from the experience, you have to do it again and again. It always takes too long. It is tedious.

You can do other things in Wind Waker, from sorting the mail, to fighting enemies, to carrying around pigs. But whenever you are sailing, sailing will be tedious.

In Final Fight 2, you can beat any enemy, or even any group of enemies, by jumping kicking back and forth. After you know this, there is no challenge in having to execute this simple strategy over and over. You do not need to use any variations in executing this strategy. You theoretically could use other moves, such as punches or throws, but no challenges are based around this. And even after you have the ability to beat the game, the game still takes forever. It is tedious.

# Checkpoints and Challenges in Videogames

Perhaps in a video game my desire is to progress forward through a linear sequence of challenges. In the 80’s, I might have died at the end of a level containing multiple challenges, requiring me to return to the beginning of the level and repeat all of the challenges up to the one on which I died. This is frustrating and monotonous. If I die enough times, I lose all my lives and must start the entire game over. This will drive away most users.

In the 90’s, I might have died at the end of the level, returning me to a mid-level checkpoint, requiring me to retry only the last couple of challenges in the sequence. I can die as many times as I want and simply return to the checkpoint in time. However, if I have to repeat this enough times, I still get frustrated with having to redo challenges I’ve proven I can pass, and many users will still be driven away.

In the 00’s, I might have died at the end of a level and been returned in space, not time, to a respawn point, allowing me to keep all of my progress and collected items and requiring me to retry only the challenge that killed me. Many fewer users will now be driven away. If the challenge itself is too difficult, users unable to surmount it will check out, but this is due to the difficulty of the challenge itself, not to the difficulty of retrying the challenge, as in prior revisions.

What is the point of making players play through a sequence of challenges?  And have you proven that you can pass certain challenges?

Goldeneye is an excellent example. Think of how many challenges you have to pass to beat Aztec. The opening, when enemies have you outnumbered and you barely have cover, and they attack with grenades. The long distance sniping. Jaws. The race against time at the end as unlimited enemies pour into the base.

And when you think of that stage, you realize his comment that “after you pass something, you’ve proven you can pass it” is wrong. The point isn’t to just be able to barely squeak past that opening, quick save. Just barely squeak past the sniping, quick save. Just barely squeak past Jaws, quick save.

The point is to be able to be SO GOOD and SO CONSISTENT at those challenges that you can pass them, and still be able to handle more. And once you are consistently good at those parts, it is less frustrating to have to do them again — because now you’re good at them! Even in a long, multi-challenge stage, you will get through the challenges you are good at quickly, and only get caught on the challenges you still have trouble with.

Otherwise, if you’re still having trouble there, then you have NOT proven you can really get past those parts.

This is really the only way to train players to be that good at challenges.

Vagrant Story is also a great example for a game that does not pull punches in challenging sequences. And in an RPG — a genre some people still claim cannot have challenging games!

Like the Snowfly Forest, where, maybe after wandering around in circles, lost for an hour, you might finally stumble upon the Dragon boss — only for him to hit you with his breath attack and kill you instantly (the wussy way to have done this would have to have the maze and the boss be two separate challenges, with a save point between them).

I had been recently replaying the game when I was reminded of a similar point. You have to get through a maze in a limited amount of time — and near the end you discover it’s not just a maze. You also have to beat a boss in the time limit! And you succeed, you beat it, you’re happy — but the timer’s still counting down! You still have farther to go! And even after you’re out of the maze, you’re not home free. You can’t save yet. If you die, you’ll still have to redo the maze, and the boss. But the save point is not a gimmie. There are flying enemies before the save, in a room with a sheer cliff face, so they might be able to take potshots at you while you have trouble retaliating.

But what people like that author miss is, that those challenges are difficult or stressful to get through is what makes them rewarding once you get through them. Take away the challenge, take away the satisfaction.

Why do they miss that? Maybe these people never beat games that were very good, so they don’t know what they’re missing.

# Archiving Old Posts

I have spent well over a decade on the internet, making what I would like to think of as considered posts, frequently on videogames. The only problem with this is that they are scattered over message board services, rather than archived on my own site. Consequently, I am now planning on archiving some older posts I may come across that are interesting and may be able to stand on their own.

# The Quartic Equation on the HP50g

(Note: This post is not actually finished yet.  I am posting it early so I can check it on my phone, and see if I can download all the programs from this page to my calculator)

I have a fondness for calculators, and particularly for the TI89 (/ Titanium) and HP50g (/ HP49g, HP49g+), which are capable of doing symbolic math such as algebra and even calculus.