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Author Topic: Random Stuff Part IV  (Read 29288 times)

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Kuildeous

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Re: Random Stuff Part IV
« Reply #500 on: August 06, 2019, 04:30:32 pm »
0

Your question comes off like "Is there a reason why my neighbor's bratty kid gets tiny little wheels on the rear wheel of his bike so that he can never fall off, doesn't he know Lance Armstrong would NEVER use those?!!?"
The extra hardcore way to write division is with multiplicative inverse. ab-1 instead of a/b.

Hell yeah!
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silverspawn

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Re: Random Stuff Part IV
« Reply #501 on: August 06, 2019, 04:33:57 pm »
0

I remember being kind of upset that people were using / for because I considered a fraction 2/5 to be, in some fundamental sense, a different thing than dividing 2 by 5, even if both lead to the same result. Like, the first is a kind of number, the second is two numbers and an operation between them.

... but nowadays I tell all of my private students to use slash instead if they write or :.
« Last Edit: August 06, 2019, 04:40:21 pm by silverspawn »
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sudgy

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Re: Random Stuff Part IV
« Reply #502 on: August 06, 2019, 09:26:50 pm »
+1

Is there a legitimate reason for elementary school to teach division using the obelus symbol () rather than the fractional notation? Or even the forward slash (/) if you must type expressions on a single line?

I see some of those math puzzles on Facebook, and it bugs me because there's an obelus, and nobody who maths for a living uses the obelus. 

And many of those Facebook arguments could be quelled with a properly notated fraction, but then that doesn't generate traffic.
Children like pictures.  An obelus is a picture of a fraction, you imagine the top dot being replaced with a numerator number, and the bottom dot being replaced with a denominator number.  The "/" is a metaphor for that as well, of course, but it's not quite as clear, it has that twist of perspective to it. It's particularly tricky to imagine the left number is somehow above the right number when you're roughly 8.
It is very useful for expressing the idea that division can be treated both like a function/operand where the operator and the divisor mutate the the first term to become a different, lesser tem, but it can also be treated like a representation, where the numerator and denominator are peacefully existing on the appropriate sides of the dividing bar, each playing their role in representing some value, and both values are part of how that value is represented.  And use of the obelus emphasizes that these are both actually the same thing.  This smooths to transition to algebra.

I don't think I realized that is like a fraction until high school.  I always had treated it as an entirely separate symbol, like +, -, or .
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Kuildeous

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Re: Random Stuff Part IV
« Reply #503 on: August 07, 2019, 09:04:17 am »
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It's interesting because the obelus combines the horizontal bar of the fraction with the colon of the ratio.

I have no idea if that's how the obelus became to be or not. It'd be kind of cool if it did. Actually, since Wikipedia says that the obelus can also be a dagger, the mishmash of bars and dots may be coincidental.

Still doesn't change the fact that it's taught early on and then abandoned, so maybe we shouldn't teach it anymore.
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LostPhoenix

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Re: Random Stuff Part IV
« Reply #504 on: September 17, 2019, 08:55:05 pm »
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Is there a legitimate reason for elementary school to teach division using the obelus symbol () rather than the fractional notation? Or even the forward slash (/) if you must type expressions on a single line?

I see some of those math puzzles on Facebook, and it bugs me because there's an obelus, and nobody who maths for a living uses the obelus. 

And many of those Facebook arguments could be quelled with a properly notated fraction, but then that doesn't generate traffic.
Children like pictures.  An obelus is a picture of a fraction, you imagine the top dot being replaced with a numerator number, and the bottom dot being replaced with a denominator number.  The "/" is a metaphor for that as well, of course, but it's not quite as clear, it has that twist of perspective to it. It's particularly tricky to imagine the left number is somehow above the right number when you're roughly 8.
It is very useful for expressing the idea that division can be treated both like a function/operand where the operator and the divisor mutate the the first term to become a different, lesser tem, but it can also be treated like a representation, where the numerator and denominator are peacefully existing on the appropriate sides of the dividing bar, each playing their role in representing some value, and both values are part of how that value is represented.  And use of the obelus emphasizes that these are both actually the same thing.  This smooths to transition to algebra.

I don't think I realized that is like a fraction until high school.  I always had treated it as an entirely separate symbol, like +, -, or .

As a kid, I always thought it was a visual representation of division: a group of two dots being divided in half by a line.
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Kuildeous

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Re: Random Stuff Part IV
« Reply #505 on: September 18, 2019, 09:00:50 am »
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It makes me wonder if there is a benefit to teaching with the obelus as a representation of a fraction instead of teaching the fraction itself.

But Im not in elementary education, so I dont have a lot of firsthand experience on that.

It just feels like the obelus is still being used because its whats already in use.
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jonts26

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Re: Random Stuff Part IV
« Reply #506 on: September 18, 2019, 09:09:25 am »
0

If you stopped using the obelus this is what you get

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Maxford

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Re: Random Stuff Part IV
« Reply #507 on: October 05, 2019, 05:54:51 pm »
0

Experiment: Can I post here to make the Verification thing go away?
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Re: Random Stuff Part IV
« Reply #508 on: October 05, 2019, 06:08:57 pm »
+1

Experiment: Can I post here to make the Verification thing go away?

People do it all the time.

By which I mean, like, you're maybe the 5th in the several years these random stuff threads have been up. All the time.
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
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Kuildeous

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Re: Random Stuff Part IV
« Reply #509 on: October 11, 2019, 11:21:28 am »
0

Wow, the view counts are insane right now.
The maths thread has 103k views. The movies thread has 136k views. The random stuff 4 thread has 21k views. The roguelike games thread has 114k views.

I mean, I know were some fascinating motherfuckers out there, but this is silly. Those poor bots.
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Tables

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Re: Random Stuff Part IV
« Reply #510 on: October 11, 2019, 12:43:19 pm »
+1

Having finished both Pandemic Legacy games I got thinking about what game or genre could be awesome with a legacy style game. And I feel like a Civilisation style game is the ideal fit. Through the Ages Legacy could work, I'm certain - each game advances through a few ages, starting very early with like ancient and classical era stuff but based on what people research, everyone starts with more and more techs until you're playing a modern era game. You could have civilisations who have special abilities, and the civilisations that win (not the players) gain bonuses each game, but also some civs die out every now and then so there's no super monster Rome with 10 win bonuses in the late game.

Anyway, just my random thought. I feel like a civ builder is the ideal format for a legacy game and I'm kind of surprised there isn't one (at least there isn't one that's well known)
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
I hereby declare myself the best dominion player in the world. Obviously.

faust

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Re: Random Stuff Part IV
« Reply #511 on: October 11, 2019, 03:05:53 pm »
+2

Having finished both Pandemic Legacy games I got thinking about what game or genre could be awesome with a legacy style game. And I feel like a Civilisation style game is the ideal fit. Through the Ages Legacy could work, I'm certain - each game advances through a few ages, starting very early with like ancient and classical era stuff but based on what people research, everyone starts with more and more techs until you're playing a modern era game. You could have civilisations who have special abilities, and the civilisations that win (not the players) gain bonuses each game, but also some civs die out every now and then so there's no super monster Rome with 10 win bonuses in the late game.

Anyway, just my random thought. I feel like a civ builder is the ideal format for a legacy game and I'm kind of surprised there isn't one (at least there isn't one that's well known)
I heard that there is work happening on a Terraforming Mars Legacy game, which kind of fits this description.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

silverspawn

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Re: Random Stuff Part IV
« Reply #512 on: January 15, 2020, 10:16:33 am »
+1

I believe that, at one point, the dominion rating system had the property that all information was contained in 1) the list of people you played against and 2) how many games you won. That is, if you play against X and then Y and win one of those games, it doesn't matter whether you win against X and lose to Y or vice-versa. This makes perfect sense to me; it's not clear why either one should be better, regardless of the ratings of X and Y. (Is it better to beat a low rated opponent and then lose to a high rated, or better to lose to the low rated one but then beat the high rated one?)

Or differently put, for each opponent, the game just computes a number between 0 and 1 which says what win% you have against that opponent. So if I play three people and have 0.2 and 0.3 and 0.4 respectively, I can just add them up and conclude that I'm supposed to win 0.9 of those games. So if I win 1 and lose 2, that's slightly good for me.

(Maybe with the caveat that your rating changes after each match and that's how order matters a bit after all.)

Does anyone know whether the current rating system works like this? Also, does anyone dislike this system?

I think most systems don't work like this, but maybe they should. Old dominion definitely didn't. Starcraft remastered (not that I play it, but I watch streams sometimes) also doesn't. One property which this system has is that every loss can be repaired by at most 2 wins against equal oppoents. Because at worst, you have 99.9% win chance or something, so if you lose that and then win against 2 people with 0.5 chance, you have 1.999 expected wins against 2 real wins. But in sc remastered, you can win or lose at least 45 points in extreme cases, while an equal opponent gives you something between 15 and 20. Pretty sure old dominion also violated this rule.
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faust

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Re: Random Stuff Part IV
« Reply #513 on: January 15, 2020, 11:10:38 am »
0

I believe that, at one point, the dominion rating system had the property that all information was contained in 1) the list of people you played against and 2) how many games you won. That is, if you play against X and then Y and win one of those games, it doesn't matter whether you win against X and lose to Y or vice-versa. This makes perfect sense to me; it's not clear why either one should be better, regardless of the ratings of X and Y. (Is it better to beat a low rated opponent and then lose to a high rated, or better to lose to the low rated one but then beat the high rated one?)

Or differently put, for each opponent, the game just computes a number between 0 and 1 which says what win% you have against that opponent. So if I play three people and have 0.2 and 0.3 and 0.4 respectively, I can just add them up and conclude that I'm supposed to win 0.9 of those games. So if I win 1 and lose 2, that's slightly good for me.

(Maybe with the caveat that your rating changes after each match and that's how order matters a bit after all.)

Does anyone know whether the current rating system works like this? Also, does anyone dislike this system?

I think most systems don't work like this, but maybe they should. Old dominion definitely didn't. Starcraft remastered (not that I play it, but I watch streams sometimes) also doesn't. One property which this system has is that every loss can be repaired by at most 2 wins against equal oppoents. Because at worst, you have 99.9% win chance or something, so if you lose that and then win against 2 people with 0.5 chance, you have 1.999 expected wins against 2 real wins. But in sc remastered, you can win or lose at least 45 points in extreme cases, while an equal opponent gives you something between 15 and 20. Pretty sure old dominion also violated this rule.
I'm pretty sure the rating system is explained somewhere on the ShuffleIT forums.

I feel like the system you propose would not be computationally efficient. It seems that every match would basically influence the rating of every player within the system, and that is a computational nightmare.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

silverspawn

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Re: Random Stuff Part IV
« Reply #514 on: January 15, 2020, 01:42:14 pm »
0

It seems that every match would basically influence the rating of every player within the system

Uh, why?
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Titandrake

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Re: Random Stuff Part IV
« Reply #515 on: January 16, 2020, 11:55:24 am »
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It seems that every match would basically influence the rating of every player within the system

Uh, why?

In the current system, we treat games as a stream of information of the form "Player A just beat Player B", and that gets updated into the existing skill estimates. The entire stream of games so far is summarized into the (mu, phi) that each player has, or in other words, after N games, the only information we need to care about is the rating system's current (mu, phi) estimate for each player.

In your proposed system, you want game order to not matter. So suppose Player A just beat Player B. This affects the skill estimate for A and B. However, consider all the people Player A has played against in the past. Like X1, X2, X3, X4, ..., X1000, for example. If game order doesn't matter, then these two orders should give equivalent rating.

(1000 games between A and Xi)
(game bewteen A and B)

vs

(game between A and B)
(1000 games between A and Xi)

In order to do this, we need to retroactively update the skill estimate of every player X1, ..., X1000, to account for the information "A just beat B", because this indirectly influences how much we care about the information "A beat X1, lost to X2, beat X3, beat X4, ..."

Game order also matters because player skill isn't static, it changes over time. If the skill changes over time then it makes sense to consider the chronological order. I don't think you want to say something like, "Magnus Carlsen's rating should go down because he lost to a 1600 player when he was 5 years old". This is an absurd example because in reality such a rating system would probably not look back that far, but if you want to assume player skill is static over the time window used, using "time window = 1 game" seems reasonable enough, and even if you used a slightly larger time window, I would expect your ratings to be almost identical to using a time window of 1 game.
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silverspawn

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Re: Random Stuff Part IV
« Reply #516 on: January 16, 2020, 12:16:32 pm »
0

I think you've misunderstood me. I don't literally want player order not to matter, I want player order not to matter except insofar as it changes your rating. Hence the line

(Maybe with the caveat that your rating changes after each match and that's how order matters a bit after all.)

This is still an important property. If we look at just two consecutive games, then the amount your rating changes is minimal, so the difference between (Lose -> Win) and (Win -> Lose) is going to be nonzero (losing first is better) but extremely small. The other property I mentioned (1 loss can only be as bad as 2 wins vs equally strong opponents are good) is also only slightly violated by your rating change.

I think this system is compatible with just having two (or one) parameters per player. Whenever two players are matched, compute the win% of player A and B based on those parameters, then compute (1_{game was won} - win%) for each player and update their rating based on that number.

I also agree that it's correct for order to matter, but in proportion to distance. So the difference between L->W and W->L is minimal, but the difference between {1000 games with 400 wins}->{1000 games with 600 wins} and {1000 games with 600 wins}->{1000 games with 400 wins} is much larger; the former indicates higher current skill. Which is exactly what the proposed system does.

Also, like I said I think this was actually how it used to be at some point, at least the match history was presented to suggest that it worked like that. I didn't make it up.
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Titandrake

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Re: Random Stuff Part IV
« Reply #517 on: January 16, 2020, 01:58:35 pm »
0

Okay, so you asked

"Does the current system work this way?"

And I believe the answer is yes, it combines the games for the past day into the single update. I'm not 100% sure of this, but DomBot on the Discord gives you estimates of what your next rating will be, and I believe it's always been accurate to the hundredths place. So if it does process 1 game at a time, then the difference between doing that and 1 day worth of update at once is negligible.

As for whether 1 loss should be repairable by at most 2 wins against an evenly matched opponent - that definitely seems more game dependent. From what I heard, in StarCraft, the gap in win rates between tiers is really big due to less inherent luck. So, if you lose to a low ranked player, it could be fair to say that you genuinely don't belong in your current skill tier, even if you perform well in games at your skill level.
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Mic Qsenoch

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Re: Random Stuff Part IV
« Reply #518 on: January 16, 2020, 03:39:00 pm »
0

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silverspawn

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Re: Random Stuff Part IV
« Reply #519 on: January 16, 2020, 03:51:58 pm »
0

As for whether 1 loss should be repairable by at most 2 wins against an evenly matched opponent - that definitely seems more game dependent. From what I heard, in StarCraft, the gap in win rates between tiers is really big due to less inherent luck. So, if you lose to a low ranked player, it could be fair to say that you genuinely don't belong in your current skill tier, even if you perform well in games at your skill level.

It's funny because that's what I always thought about sc1, but watching artosis' stream convinced me that it's not really true.

I think the "you need to win 0.9 games against this opponent, so if you lose you're 0.9 short" model just makes so much sense to me that I don't yet see a reason to do this differently (again, with the caveat that your own rating changes). Definitely I think most strong people in sc don't want to play against low rated players. Unlike in dominion, you can't set any preferences.
« Last Edit: January 16, 2020, 03:53:50 pm by silverspawn »
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ConMan

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Re: Random Stuff Part IV
« Reply #520 on: February 06, 2020, 05:04:51 pm »
+1

I was approximately today years old when I discovered that dougz, of Isotropic fame, was also the author of the seminal computer science paper Chicken Chicken Chicken: Chicken Chicken. Also available as one of the best presentations I've ever seen here.
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pacovf

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Re: Random Stuff Part IV
« Reply #521 on: February 06, 2020, 07:32:48 pm »
0

Shame of the low quality of the video. It's just as hilarious now as the first time I saw it, but 240p is not as acceptable anymore :p
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Kuildeous

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Re: Random Stuff Part IV
« Reply #522 on: February 07, 2020, 03:57:51 pm »
0

I was today years old when I realized that the sign for 100 and 1000 utilize the sign for C and M, respectively. Blew my mind that I never picked up on it before.
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markusin

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Re: Random Stuff Part IV
« Reply #523 on: February 07, 2020, 05:35:08 pm »
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I was approximately today years old when I discovered that dougz, of Isotropic fame, was also the author of the seminal computer science paper Chicken Chicken Chicken: Chicken Chicken. Also available as one of the best presentations I've ever seen here.

A lab mate had showed the paper to me, and then I was like, wait I recognize that author. I then tried my best to explain how I was a fan of the author's work on Isotropic.
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Re: Random Stuff Part IV
« Reply #524 on: February 23, 2020, 02:39:42 pm »
0

I have an important question.

Why does the recruiter produce villagers? Wouldn't he rather require you to provide him with villagers?
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