Probability 101

Something with a little meat on it today. I was going to revisit a bit talked about here with the two weapon/multi attack problem. The problem is there is a lot of points and areas that one could excel at over the other in some thinking on the problem. Too much for that today so I'll go over a bit of probability as a primer to that.

First bit about probability. Probability in the mathmatic terms refers to, the instances in which an event happens out of all possible events. The "all possible events" is commonly called the sample space, it's not so much all possible events as so much as the ones you can get to with your experiement. So from this figuring a simple one is rolling a 1 on a six sided die. There is only one instance of 1 out of a total sample space of 6, so the result for rolling a 1 is  1/6. It doesn't even have to be a singular number, it can be something more complex like rolling higher than a 4 on a six sided dice. The number of instances this happens is two, them being 5 and 6, causing the probability of rolling above a 4 to be 2/6 or 1/3 through reduction. Simple until you start looking into multi variable problems but I won't beat your head over those too much.

Another thing that I should prime on is the "average" number or mean which is the "center" of most bell curves(a term that isn't exactly needed for this right now). For all purposes at the moment this will mathematically work for us, it's determined by adding the highest and lowest number together and dividing by two producing the theoretical mean, it's useful for guessing where most of the dice will be rolling.  There is another form of averaging which is also called a mean it is taken through gathering data points, you take every item add them all together and then divide by how many items there were. This is how they get average life expectancy, age, and other thigns. It's not perfect but it's one of the useable estimations, there are others out there.

Such as mode. Mode is the instance in the sample space that is the most likely to occur.  Five people aged 20 , three 23 year olds, and one creepy 50 year old show up to an event. The mean of this is 24 and the theoretical mean is 35, the mean derived by the actual numbers is clearly better here but still not exactly close enough. The single 50 year old is generally known as an outlier in these, or an odd event that generally doesn't happen but is taken into account because it did. Because of this the mean has shifted far further than it should have. So by looking at the mode we'll see that there were five 20 year olds which is more than the three 23 year old and the one 50 year old. You now have what is your most likely event if that was what you were actually looking for. It's useful for what is called unequal distributions. Where the most likely instances of occurrence are not actually clustered. I'll make a poorly labeled graph to try and get the point across. The green curve if I could actually draw this right under some average measurements would appear to have a "peak" in the middle like the red curve when it plainly isn't true. Mode can shed some light on just how much it is skewed if you look at it with the average next to it.

The last bit of probability I want to talk about is the median. The median is not something I use that often but probably should. Effectively you take all data or sample space and sort it then find the exact middle based on number of items and say that's the middle. Half of everything you can see falls above this point, and half of everything falls bellow it. It's like the illegitimate offspring of the mean and mode but I prefer some actual number useage when it comes to my disecting of these problems.

Well hopefully this wasn't too horribly long, incomprehensible, or boring but in the future this may save me some trouble. It's funny as people find probability to be some mystic strange thing when compared to other math. While I just find it to be the only one I can come to understand. Might as well finish this with a question for you guys as it's becoming a trend. What things that seem hard to other people seem to naturally click with you?

Chihauhau the cat subsitute.

Humidity has been hovering above 90% for the past few days and the house I'm sitting has no AC beyond the master bedroom which I would rather avoid sitting in. Combine this with the couch I've been waking up covered in sweet with I was a little out of it yesterday so sorry for the lack of updates. Today won't make up for that as it's just some ranting as I'm still not comfortable or feeling well here.

I'm currently house sitting a pair of chihauhaus my mother has had for a few years now. I used to even be around when she first got them. She's generally a cat person but some siblings were found to be allergic to cats so we went to dogs. So no more cats were to be had.

We had a lab for a while which was fine. I'm not a fan of dogs, they are just too in your face all the time for me. Always needing to be near you or even in the same room as you. It's not my thing with a pet, I didn't mind the dog and was the primary walker and groomer for her but never really attached to it. After a long winded turn of events we were given a well bred chihuahua. She wasn't too bad at first being scared as could be but quickly learned to bark alot and nip at anyone trying to get into the house despite the general training against it. It never even really bit people as much as run up to a person and place her teeth on whatever is exposed, she learned she can't actually bite anyone but it was still annoying when people were scared and only encouraged it even when they did walk into the house.

Years later the lab had to be put to sleep and we found a less well bread Chihuahua to keep the first compnay. Very well adjusted though scared as can be. It took a while but as long as my mother was around she was fine and people could even pet the new dog or even pick it up. Later she started to bark follow the now dominant older Chihuahuas example so people arriving is a very noisy happening.

The both of them are a lot more forward when my mother is her, being protective to a degree. Otherwise they hide and don't do much when she isn't around, not including running to the door to bark at people. When she's around the both of them will mill about around her or sit on her lap, maybe even play with each other. Right now they're held up in her room which would be bad if they weren't liter box trained so she doesn't have to stay up all night to get them to go outside. They do that too but it's just a backup plan except for the past few days it seems.

They'd be a lot better if they weren't constantly cowering even when they come to meet me. In fact I have one who finally decided to come downstairs and sit on the couch with me but still acts like I'm going to beat it when I full well know it has no abuse in the past. Not even sure if it's better than the dog that is constantly leaning on my leg or always following me around the house.

Well that's that for the pointless rant. So the eternal question, dogs or cats?

Perpetual motion machine

Edit: Fair warning I thought I could explain this better. It's a bit rantish as is.

Busy day today hence why I'm a bit late. Currently trying to adjust my sleep schedule towards the earlier part of the working day as well as looking a bit. So this may be a bit short but it's been a subject I've been wanting to talk about for a bit.

In game design there is a bit coined as "Action Economy". What an action economy is depends on how your game works. For the most part it's what you are allowed to do on a turn and at what cost or risk compared to other options and the opposing side. The most basic idea is that "slower", more costly, or rarer options should do more than "faster",cheap, more common ones. Failing to do this shows a design flaw as you're paying more to do less unless you have very good reason to such as niche design but that's another topic.

The most basic way to think of action economy is with chess. Chess you move one piece a turn, that's it baring special moves that rarely do anything. This is balanced between the players, they get to test skill without anything hindering them beyond turn order.Now imagine if you could move two pieces under restriction, like two pawns or maybe a Queen twice if you sacrifice a pawn. What if white could move two pawns and black could move a queen twice if they sacrificed a pawn, is this an equivalent ability for both sides? From there it gets real messy as to what is fair and if you should even bother with your standard moves unless desperate? That's the most basic idea of action economy though I'll go a bit more into detail in other aspects of it.

Most RPGs allow one action a turn to keep things simple and delegate any sense of action economy to the individual options. I'll get to some of those options but the more obvious problem is in pen and paper games. On the tabletop there are always a few ideas that some things should give more actions a turn and this can lead to some very odd results.

To start I'll take an example and use D&D  3.5. In this edition of Dungeons and dragons you have the free actions, swift action, move actions, standard actions, and full actions that can happen on the same turn. Free actions is usually talking and allowing for monologing villains to say something before they go down or party members to do the same. Swift action is like a free action and happens "instantly"but only one may happen on your turn. Move action you only have one of and allows you to move. Standard action is your bread and butter for doing anything though you may also use it as a move action. Full actions use both your move and standard action up for their effect, the easiest example is the full round attack which I'll get into in a bit.

If all the allowable actions were roughly the same there wouldn't be much of a problem. Though some older ideas made it into the game and thoughts of the old classic "time stop" and "Delayed fire ball" show the principal of being allowed to do multiple things on your turn can lead to bad things. Time stop allows you to move around with impertinent for up to 5 rounds, the catch is you really can't do much, you can't attack anything directly even with spells. Delayed fireball lets you cast an improved fire ball and allow it to be delayed up to 5 rounds. The combination is obvious as you just cast all the fireballs on a single target then have them go off after time stop ends. Effectively getting 5 turns worth of actions to obtain a devastating effect when comparatively you took one. There may be some systems where many turns aren't as effective but here the more turns you get the better chance you have of standing on top of things.

This is generally called novaing. You use all available resources for an effect that hopefully wins the battle, in the case above unless that slot for timestop allowed for a devastating spell like no other that wouldn't have you using most of the delayed fireball spells you would seemingly be out of luck. So those instances I could understand it for boss ending super weapons that make DMs pull out their hair and usually games don't have this, they commit some other minor sins. D&D 3.5 has a concept of "full round attack" where fighters can perform up to 4 separate attacks, In a second I'll get into a failure in some aspects of their idea here but multiattacks needs an entire paragraph on it if not an entire post later going on about it.

In theory this sounds very good, often multi attack systems break games. Being allowed at minor disadvantage to attack multiple times easilymakes it combat wise seem like there is a second character on the groups side for the price of them not being as "powerful" as the first. Many video games use the idea too and give "light weapon" characters multiple small damage attacks usually half damage than their one attack higher damage counterparts, mathematically the half damage weapons are better on the base level. Assume this is 50% chance to hit for single attacker and two hits attacker. The single attacker simply has a 50% chance to hit the target and 50% chance to not hit the target. The two hit attacker has a 25% chance of hitting with both weapons, 50% chance of hitting one weapon, and 25% chance of missing all together. As if that wasn't enough the averages are better for the two weapons if you were looking for that, but that is for another time. This is a disparity in Action Economy as clearly two weapons are "better" for it's actions, other factors could be taken into account such as damage reduction, critical, on hit effects, or a variety of other things and frankly has been argued into the ground a lot with how often it comes up. Unluckily for you guy I rarely visit forums so I'll come back to it again.

D&D 3.5 had the idea in there as a way for the fighter to show his prowess in combat. The problem is that it fails quite easily. D&D 3.5 works on base attack bonus where you are given a bonus to the dice you roll, the full round attack works by decreasing this for every attack after the first. At the highest "core" level you have 20 BAB. So your first attack gains a +20 to the roll, the second a +15, third a +10, and fourth a +5. Seems reasonable until you assume that the defenses you are rolling against are increasing at roughly the same rate. So if the thing you're attacking can only get hit on a roll of  10 or better for a single attack your second attack will only hit it on a 15 or better. This leaves your third and Fourth only hitting on a natural 20 which is an auto hit. This is great however for things that aren't actually a 'challenge' to your level as you'll easily have a shot to land all four attacks on them, everything else you do have a good possibility for 2 attacks though. Now not only the fighter gets this, but it's the one who gets it the best. Others don't generally reach 4 attacks a turn or +20 base attack bonus.

I'm not quite wanting to bash D&D on this as it seems like a good thought. It just doesn't have quite the execution I'd need to be to not have extra nearly pointless rolling. Maybe it works better in practice than my experiences show but considering once you hit melee range and aren't moving away it's expected for this mechanic to kick in. With it being the standard for higher end fighters a little more thought could have been given to it though out of all the multi attack systems that are inbuilt in the system it isn't the worst I have seen.

Other systems use some hoops to jump through to gain additional attacks a turn that don't have much penalty beyond what you have to do to get it. WoD comes to mind but it's been so long I can't remember the ways to do it. Effectively you just become two sources of damage with no way around it. You're better than everyone who hasn't done this or has a gimmick that allows them to keep up leaving you at a game warping effect. One system I know of called Cthulhu Tech has muti attacks built in and it seems like it should work until you get higher in your attack stat, in which case the penalties are meaningless for the extra action penalties you get. Also it's dice pool system is so widely swingy towards low results or high that if you're getting high it doesn't matter.

Though the end result is sorta the same. The more moves you can take the better, standard actions are just for people who haven't found a way to slap more on which seems to be a problem to me. Some systems run with the idea but give options all around.The problem comes up to which is "superior" or just flat out useless. Seeing that is really hard like with the chess example which is better? I wouldn't have a guess at that. A bit more thinking in things that change the amount of actions you can take in a game seemingly don't get much thought in my opinion.

A little longer than I wanted, and possibly a bit schizophrenic in nature due to re editing a few times. I'll possibly get into this later time in hopefully not a format that is easier to chew.

Statistical analysis

An image I didn't make? Madness. QWOP will have more to do in a minute though.

There has been a long standing tradition in games to take a nature vs nurture approach in games. Nature being your innate abilities that are largely unchanging, though can grow in minor ways , and skills which are constantly being increased in decent numbers. There is a lot of weird things to this, so I'll begin with the parts I know decently well.

I know there were other games around when chain mail became Old Dungeons and Dragons but I just don't know how to find them, a lot were probably lost to the passing of time. But D&D had Stats. Back then stats didn't matter quite as much, in fact I think it had weird system of bonus EXP when you did things involving the bonus from your governing stat and magical things.

First things first, D&D is rooted in wargames so is a little weird at times. I know the modern statistics are Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. Don't know if any were added along the way and not in the mood for long research, which I may take up later for fun, on the original game. I do know stat "bonuses" were calculated completely differently making an 18 in them a godly thing. Supposedly wasn't too different throughout the years until 3.5 started making them mater a lot more and be prerequisite to a lot of feats which were needed, or spells cast, or even just hitting something.

The approach to this is a little weird. A lot of stats line up with one thing, sword hitting things intelligence hitting another, and in latter editions exceptions get made everywhere. 3.5, and possibly 3rd, in general had feats or little extras that you can get when you level up allow you to use Wisdom to fire bows and arrows. Strength has added to accuracy for melee attacks, except for light weapons which could use dexterity if you took the feat for it. Wisdom is some where between common sense, experience over time, and flat out natural instinct as every natural animal has high wisdom. The more "what is this stat actually representing?" of all of them is Charisma. It's always been described as a "force of personality" while having attractive races get bonuses to it and ugly races getting penalties, until 4th edition but another box of dead horses.

What does this all mean? Stats, attributes, and characteristics are somewhat silly. Though they serve a purpose. Table top gaming or even computer RPGs need some amount of abstraction to not be horribly cumbersome and not understandable by the people who use them. This is where QWOP comes in, it's a game that is realistic to a degree. You don't hold left or right to move the guy along, you actually go to the source of how he goes about moving muscular movement. Legitimately categorizing how a character should realistically go about things would be about as elegant as making QWOP man jump a hurdle, it can be done but I doubt most people will enjoy it. All games use some form of abstraction for this reason, reality isn't clean and fun. The most we can ask is that we can only eye roll a little at the designers choice and keep them constant. I'll probably revisit this under different systems, nWoD had I think 9 stats in total and comparing it to D&D could be fun.