Re: Mental thingummy Math might work, although now it's sort of math + strange luck thingy; 4 is not really special to me, except from tvtropes I learned it's associated with "death" in Japan and it's a nice square number; and the only reason I check one clock 4 times in a row instead of 8 times for the other is because the 4-times-clock requires less buttons to check. I used to check it by going through the buttons until I didn't feel like I just started checking it (so basically consequently checking an alarm clock for 4 or 5 minutes straight). I sort of understand the probabilities like:
P(alarm not working with 1 check) = 0.50 for example, so assuming checks are independent (which they probably aren't) and the probability is .5 (kind of a over estimate of effects from lousy clock + human perception), then if I checked 1 clock only once, 1 out of every 2 days I would expect it not to work. P(alarm not working with 2 checks) = 0.50^2 = 0.25 ...If I checked 1 clock twice, 1 of out of 4 days I would expect it not to work. P(2 alarms not working with with 24 and 12 checks respectively) = 0.50^24 * 0.50^12 = 1.455 * 10 * -11 = 1.455/100,000,000,000 in about 273,972,602 years both clocks will fail once. So pretty much 0 right? The 12 and 24 checks are more by habit then by math now so hmmm...maybe I should lower the number of checks, but anyhow I am interested in your take on it.
OK, expected utility time!
"Utility" is a measure of how good/bad an outcome is. In this case, that includes whether or not you wake up at the right time, but also any other effects of checking and setting alarms - the time and effort spent checking (which you now can't use to do something else instead), annoying your sister, etc. The utility of each of these outcomes is how much you value them relative to each other (or, in the case of bad outcomes, how much you value avoiding them).
The "expected" part means how likely the outcomes are to happen. You're already doing that for the "wake up at the correct time" outcome. And it's not so relevant for the other outcomes, since checking the alarm will always take about the same amount of time, and... I'm actually not sure how frequently the checking annoys your sister, but maybe you do want to get an idea of the probability of that happening for each time you check, if that's something you value/disvalue significantly.
So to get expected utility, you multiply the probability of the outcome happening ("expected" part) by how much you value the outcome ("utility" part - this is negative if the outcome is bad). The probability weights the value of the outcome, so that the things that are most likely to happen get more attention, but unlikely things still matter.
When making a decision, you add up the expected utilities of all of the parts of the outcome that you care about, for each of the things you could decide to do. And then you do the thing that has the highest expected utility.
The expected utility for the side effects of checking your alarm (annoyance, time spent, etc.) are the same for each additional checking, because their likelihood is not affected by how many previous times you've checked. But the expected utility for waking up diminishes with each additional check, because the probability that the alarm is not already correct (and therefore the probability that the additional check will matter) goes down the more times you check. So at some point, the expected utility of the time spent etc. to check the alarm again will cancel out the expected utility of the slightly smaller chance of not waking up on time. At that point, the additional check is no longer worth it.
If you can get some data on checking alarms multiple times, it might be useful to calculate how many times you'll miss your alarm on average in a year, or in 10 years, with the alarm setups you're considering. I find that restating a number in several different ways is useful for figuring out how much to care about it. Useful for probabilities, and avoiding circular preferences in general.
So I managed to interpret my own graph wrong... the fact that the lines cross isn't what matters. What matters is that there's a point where "good stuff line" - "bad stuff line" (the total) starts sloping down instead of up - that is, the best number of times to check the alarm is at the peak of the blue line.
My first graph isn't such a good illustration of that - it would probably mean you graphed on a scale that went up to checking the alarm at a few hundred times.
So here's another graph that zooms in on the things you'd actually consider. Probably this goes up to something like 20 or 40 alarm checkings.
Ok. So I never did utility in my various maths classes, but I'll try to break your post down into variables and probability, which I do understand. I want that peak position of the blue curve +/- 2 for human random error.
P(x=X) = probability of outcome occurring when variable x equals X E(P(x=X)) = the expected probability of outcome occurring when variable x equals X
More specifically (for example): P(x=X) = probability of "waking up at the correct time" where x is a variable and X is the number of checks I do; I want this thing so it should be positive: E(P(x=X)) = + P(x=X)
Let's use Margo's data, because I share much of my genetic makeup and environment with her. (Since my ongoing battles with the alarm clock, I can't remember a time when it failed to wake me up.) According to Margo, she checks twice and only sleeps in once every 2 years (let's assume; obviously proper research should be more meticulously measured). I have two alarm clocks, so let's assume we can just divide the data: P(x=2) = expected probability of waking up on time with 2 checks = (all days except 1 every 2 years) / 2 = all days except 1 every 4 years = (4 * 365 - 1) / (4 * 365) = 1459 / 1460 And E(P(x=2)) = + 1459 / 1460
Given Margo's statement on her own checks, we can assume that checking the alarm more than twice will annoy her. Generally speaking, I want to stay on good terms with my sister and not have her check me into a mental recovery ward nor kill me. Y'know. The probability of her actually doing either is probably relatively low (she hasn't done too much yet), so let us assume: P(x> 2) = The probability of Margo getting seriously annoyed with me when the number of checks (x) exceeds 2 is 1%. She might tell you other wise. P(x> 2) = 100% And E(P(x > 2)) = - 1/100
Another outcome is the clocks breaking down from being over used. Naturally this affects my amount of funds, my faith in such devices, and the ability of "waking up at the correct time". I do not want this to happen. This can also happen temporarily if the power gets knocked out, but that is not something I can generally control. (Unless I buy a generator, or battery-powered alarm; unfortunately, I dislike spending money on un-fun un-essential things more than I dislike not waking up on time) This is a bit harder to guess, because over the last 1.333 year since picking up this habit, I switched to a different clock from the original one. But let use assume: P(x >= 24) = The probability of a single clock giving out because of being checked for more than 24 times (at least) is at least 1/(1.333 * days in year) = 1/486.667; so the probability of 2 clocks: P(x >= 24) = 2 * 1/486.667 And E(P(x >= 24)) = - 1/243.333
The only thing that confuses me in all this (or that it worries me not to understand though I think I got the gist of the stuff you're doing, even if I could not do it myself...) is what does it mean to "check" the alarms? It means that you wake up, turn on the light and look at clocks? Because that is what assumed, but I do not understand how that make the clocks give out, so I'm guessing that I'm not understanding something.
I don't hear my alarms. Lately it's been really bad. Sometimes, I hear it, put it on snooze a few times and them go on sleeping or if I try to wake up earlier than usual I simply do not hear it at all. To be fair, I do wake up when I need to. It seems that alarms only work when my inner clock agrees with it. Also yay, I have a tentative schedule for the first semester! If everything goes right, I get free Fridays and finish early on Thursdays so I get mega-long weekends. Also, aikido twice a week. I was worried I wouldn't be able to fit it in. I'm happy also about the fact that one of the subjects is with the teacher I wanted, because they had been inconsistent about who was gong to give it in the timetables they'd given us before. I just hope they don't make really bad changes when we actually do start classes... there's always stuff that is wrong with the timetables they give before classes start.
To check means (to me at least) to press a sequence of buttons to display that the alarm is on and set at a specific time. Because I'm pressing them more than normal, I have a feeling that they will wear out faster. XI I usually do it all at once while counting the number of times to 24 or 12 and standing in front of the clock.
I usually put the alarms on different radio stations at volume levels I can hear. That way, I hear the first one first (the morning news), get sucked into the story, and the second one starts up (a pop music station) blocking the first. So I usually listen to 1 or 2 songs + news while forcing myself to get up, and walk over to turn the second radio off. The secret to not snoozing too long is putting the clock more than a few paces away from you, I think.
I remember one term I had free Fridays, but spent most of them working in group projects. :I
Oooh, so you have that kind of clock! I get it now.
Yeah, my brother does that where you put the clock away from you. It doesn't work for me because I don't need to actually put the thing off to go on sleeping, I can perfectly do it with the clock screaming madly at me ;P . Or put it down and go right back to bed. But I like to keep it close, preferably under my pillow so I HEAR the thing at least. I don't oversleep often, anyway. If I know I have to get up, I do. The alarm does help, but I seem to lack the will to do it. I have a very hard time getting up earlier than 10.30 if I don't have school or any other kind of previous compromise. If I do, it's not much of a problem...
So much math. All statistics and sort of boring as math goes. Well, boring because it's not applicable to anything I'm doing at this exact time.
I do not use an alarm clock and could freely sleep in until like noon if I wanted to basically every day. It is kind of great, though I do about what Soff says and it'll usually be from around 10:30 to 11:30 when I get up. I should probably go to bed earlier but I kinda like the quiet time at night.
I think Margo (Mango) would be pleased at that, because she studied psychology and thus knows more about OCD and what not; she also has to occasionally put with me. I actually check one clock 12 times (3x4) and the other one 24 times (3x8). It's pretty weird. But before, I used to just stand there and check it until I couldn't remember starting checking it, which is probably more bizarre.
Unless Night Mare feels like tackling my very un-scientific math stuff, why not talk about...[looks around for something to talk about] d3?
Soff: I might also get Thursdays and Fridays off this quarter. Depending on how I switch my classes around - there's one that I really, really want to drop because it moves so slowly that it feels like waste of time, but I need to find something better to replace it with.
Clemon, I'm going to make a new thread for our math because we seem to be the only ones interested.
I'm vaguely interested, just got a lot of other things in my head to fuss over right now. I find stuff like geometry, trigonometry and some vector math more interesting in any case. Working with probabilities may be more useful if I start spending more time working on some functions and algorithms for a simple RPG combat system I've been sort of halfway creating for no real purpose. Other than being irritated by the systems used in other games that'd be a lot better if the underlying maths for these systems weren't flawed. (I'm looking at you Torchlight 2 )
Then there's a randomized story generation idea I could pursue, but that'd require me to be super knowledgeable about the mechanics of good story telling as well as a variety of maths.
You ever get annoyed about knowing exactly enough to get a vague sense of how something complex could be done, but not knowing enough to understand the details or have any ability to actually do it?
It's mostly just basic numbers at this point. 5 stats, a rough idea or what they'd each all do, and some specifics about what math is done when one guy hits another guy with a weapon to determine how much damage is done. It needs much work and I only have most of it sorted for melee attacks. Also it's a turn based system idea sorta like for an old Final Fantasy game from way back. Except I have no game to put it in, so eh. I guess I also have some partially formed thoughts on equipment and inventory, but my ideas there are potentially complex and could be irritating to many people in an actual game on account of having so statistics to consider to determine a best choice.
In the case of Torchlight 2, that game has armor that acts as a flat reduction to damage taken, but scales damage values up very quickly late in the game until armor effectively becomes worthless. There is a separate armor value for each element as well, so you can't really just focus on one armor type. The only protective measure really worthwhile in that game are the very rare items that reduce damage by a percentage.
And that sounds like an awesome academic paper that your friend wrote. I think a good player for playing D&D in person is very different than what you aim for in a video game though, so that's something to consider.
Yes, definitely. In-person is... more social and more flexible? I misunderstood and thought you meant tabletop game rather than video game when you said you were designing an RPG system |'D So that paper wouldn't really be relevant to what you're doing.
That sounds cool, though. Sounds like... making a system that's less prone to balance problems?
I dunno? Maybe it'd be more prone to balance problems. I'd have to test things. I was just making up a sort of different system because I could and it amuses me. Haven't you ever looked up all the damage formulas on an old Final Fantasy game before? Just to see what made it all tick so to speak?
Apparently first-person shooter games can improve teamwork, multitasking (?), problem solving keeping track of things you can't see, and keeping track of more things at once. And can make male players (and female players to a lesser extent) more likely to retaliate more aggressively.