In math 15x > 10x for all positive x.

Not a question of opinion really.

With the current movement and many maps played, there's no real problem at doing 10 mins games though. It's more favorable than 15 mins with the current settings imho.

Is 0.99999... a positive number?

Is 0.999... even a number?

Is 0.999... actually 1?


Anyway apart from nostalgia, I don't think 15 min duels have a place in today's ql duel - for me personally it would feel too exhausting.

It would be nice to see some top players on a roll in 15 min duels and see if they can come up with more comebacks.

Yes.

Yes.

Yes, although not necessarily in infinitesimal math.

That's because of the faster overall gameplay.

It's not so much if top players can come up with that... As long as the game is not a blowout for either player a lot of changes will occur just because of a changed timelimit.
Not so much due to the player being top or not... just because it increases tactical options.

Infinitesimal math changes nothing regarding .(9) being equal to 1. 0.(9) is a finite number and not a sequence. The infinite amounts of 9's are not ongoing.

fuck it I won't argue again I'll just paste wikipedia rather than show it.

The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a sequence. It was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz.[2] Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object which is smaller than any feasible measurement, but not zero in size; or, so small that it cannot be distinguished from zero by any available means.

So one can say that 0.(9) is "not necessarily" 1. As you can write it as 1 - infinitesimal. Or you can say 0.(9) = SUM(9/10^x) where x goes from 1 to inf.

Heck the wikipedia page even has on it:
Students easily relate to the intuitive notion of an infinitesimal difference 1-"0.999...", where "0.999..." differs from its standard meaning as the real number 1, and is reinterpreted as an infinite terminating extended decimal that is strictly less than 1

(not that I am a great fan of the "students can easily relate to...." as it seems that on esr NOBODY can.

Hit 'em with logic and reason. Zing!

ZING!

Only problem is that all you did was c/p'ing the definition of infinitesimal objects but not that 0.(9) is in fact infinitesimally small, which it is not. You could just as well have defined any other concept (mathematical or not), unrelated to the subject :D… And regarding your last part; you just mentioned that students can relate to the idea of 0.99... < 1, which I know for a fact since I teach myself, but not that it in fact is true, heh.

Anyways, let's drop it. I don't really care =).

in most views on infinitesimal math 1-0.(9) is 'the infinitesimal'.
There are a shitloads of side notes to make with that... but I really cba to discuss them here.
Not unless you actually "do math" rather than "learned how other people did math". Which is one of the worst problems in teaching imho.

"But teacher why is a circumference of a circle related to Pi which is related to the sinus which is related to triangles?" -> "Just fill in those numbers into this equation and you'll get an answer!"

Well I'm not entirely sure that is correct, as that the infinite amount of 9's are, as I said, not ongoing. We are not talking about a limit here. There is nothing getting closer and closer to anything, it’s just that. But whatever, I don't really care and as you said, it has been discussed countless of times and I, just as you, cba to go further into it.

Teaching does not equal learning, that's for sure, and I agree that math in (Danish) high schools is way too focused on how to produce results and learn a number of methods to solve the same type of assignments over and over… But that’s an entirely different talk.

The focus on how to produce results is a much more relevant talk though...
Imho education on math is ridiculously poor. Even on the university the way math was taught to me was so bad... There is no "insight" taught as to how or why things are the way they are and thus everyone finds math dull.
While in fact it's one of the most fascinating things how one can reason about problems in an abstract way and still get valuable results.

0.999... = 0.9 + 0.09 + 0.009 + ... = 9*10^-1 + 9*10^-2 + 9*10^-3 + ... = (sum[k = 1 to inf] 9*10^-k) = 9/10 * (sum[k = 0 to inf] 10^-k) = 9/(10-10/10) = 9/9 = 1

Wiki ain't proof.

0.999... is even eh?

Another amazing insight by Weird

The question was:
"Is 0.999... even a number?"
and not:
"Is 0.999... an even number?"

Another amazing insight into obi.

You aren't even able to read.

You are odd.

fair enough

15x > 10x
15 * 1/a > 10 * 1/a, with 1/a being positive
now let a go to infinity so that 1/a becomes 0
15 * 0 > 10 * 0
0 > 0 ????

https://simple.wikipedia.org/wiki/Positive_number

edit:
Just realized that this is esr.... So I'd need to explain...
assuming that 1/inf = 0 then it falsifies the premise that x is positive.
If you'd say that 1/inf = infinitesimal then it is positive but then it should still hold that 15*infinitesimal > 10*infinitesimal.
But it is a somewhat gray area where a lot of stupid people have voiced even more stupid views about.

So when does 1/a stop being positive and become 0?

up for debate really... Chances are it has something to do with -1/12.
But Euler was so misunderstood in his time.

In general you can say that IF 1/a at some point does become 0 that it then also stops being positive.
But you can then also show that 1/(a+1) can't really exist (at least I would think that one can show that quite easily... There are sometimes some unexpected things though, like -1/12)

lmao you just reference random things from maths that have nothing to do with what youre talking about. it's extra funny because the thing you are talking about is total nonsense as well

it has to do with the question asyyy asked though... Which is not very related to what I posted earlier.
But hey I'm not nearly as lame as you are so I actually reply.

The -1/12 part is a bit far fetched, that's true. But if there is any way to answer the question where a >= inf and a+1 = a.... Then chances are it's related.

I give the answer to his question mainly in the 2nd paragraph though which starts with "In general you can say that".
Which is much more indicative of an answer than "it's up for debate really.... chances are it has something to do with"

plz learn how to read, then learn math, then learn how to write and THEN come back to me with a sane post.... And maybe I'll reply as if you're not an annoying little troll.
Deal?

I give the answer to his question mainly in the 2nd paragraph though which starts with "In general you can say that".

Yes, and as usual its bullshit because you don't define or understand anything you write in a rigorous way. Because you don't know how to define things, or why it would be important. It would also remove all your wiggle room to redefine and make things up on the fly.
I'd tell you to try and get a real math education somewhere but that would require some amount of humility on your part which is unlikely.

You clearly do not have any clue.
My response in the 2nd paragraph is perfectly understandable and well defined.

I note that
1) IF 1/a = 0 that it means that it is not anymore a positive number. (This is obviously because 0 is not positive, as positive is defined as * > 0 and NOT as * >= 0)

2) That if there would be an 'a' such that 1/a = 0 that one could show that 1/(a+1) cannot exist because it either must be the same as 'a' or give a result which is closer to 0 than 0. Which in itself cannot happen. (a != a+1 by definition and 0 cannot get closer to 0)

Quod erat demonstrandum you little trolling idiot.

Since when is multiplying both sides of an equation/unequation with 0 considered as an equivalent transformation? If you got no clue, don't pretend the opposite.

It was meant as a not so serious math troll.. obviously it is complete nonsense for at least 3 reasons.

how can a number "go" to infinity?

like that

I think on smaller maps like aero or tox no.
Maybe on the larger maps though, yes.

Id say its exactly the other way around. Small fast maps produce longer chain reactions of spawn-rape, thats why a longer time limit would balance that out.

possibly but I believe on the laundromat displayed correctly it would take longer together Friday so that I made it to accumulate more would be more.

Edit: that was voice recognition lol.

meant to say that the larger the map the longer it should take to get frags accumulating together so give it a little longer And more action will happen

wat

Check it out boys




Do you think that something can be destroyed and rebuilt with the same material and creating two entities?

Yes, for certain definitions of the words "destroyed", "rebuilt" and "material".

I'd like to hear the opinion of the greatest thunderstruck hero of all time.

i played my friend the other day's 125fps with madball vs. garpy and he liked it. 5 matches... but when i told him they used to be 15 minutes, he thought 8 would be better than 10!

I watched some of Rapha's games, first duels I have watched in a long time. Yes, the 10 minutes left me "wanting more." Felt extremely short. Keep in mind though, I played during the era of 20 minute duels. I thought 15 minutes was short. You have more time to mount a serious comeback in longer games as well. Forces consistent play over a longer period, adding to mental and physical stress.

That being said, what a final against Evil. Rapha really plays smart. I was extremely impressed. Great decision making.

did you watch the games at qcon 2015?
dont miss qcon 2013 evil vs rapha, those were even better by him IMO, evil played smarter than in 2015 so the challenge was greater

The first thing would be the weapon respawn time would have to change from 5 seconds to a full 10 seconds. No one would want to get raped 60-70 - 0 when first starting the game against an experienced player.

I started duel when they were 15 minutes and learned around that 10 minutes was a huge change because its a 30 percent reduction in gameplay time. Which means you have a 30 percent more chance to make a bad decision and not have an opportunity to make up for it. It utilizes a different competency entirely.

In makaveli's case 20 minute duels which would be a 50 percent reduction in time which is crazy. Althought 20-15 minute duels would still be a 25 percent in reduction for duel time. I think 15 minute is a great sweet spot. 10 minutes is great if you're trying to grind games but really I've seen many games that could have been turned with another 1-3 minutes on the clock. 15 minutes has the toughest mental challenge in my opinion.

Games with faster movement ala reflex, cpm and quake world 10 minutes feels just right. VQ3 games 15 feels amazing.

This is the main reason why I can't play or take duel that seriously in quakelive weapon control is a bigger aspect of the game and right now it doesn't exist you can only do damage to deny or bait weapons. Pretty stupid that you can only have a few tactics where with weapon control you can tell where your opponent is as well instead of just relying on sound cues.

I started duel when they were 15 minutes and learned around that 10 minutes was a huge change because its a 30 percent reduction in gameplay time

I think you've just murdered the local math club.

Someone quickly quote the Wikipedia article on infinitesimals!

DID I HEAR 0.9...?!

Yup you're right because I didn't state 33.33~% so my error was 3.33% of the original statement at 30% Oh well. Human error it happens.

What the actual fuck? Are you serious? Stop writing stupid bullshit.

Any time length will give exactly the same chances to win for anyone, because the player is just as likely to make a bad decision as to increase his lead with the extra time given.

There are no buts or whats here, this is not a debatable subject. Its just like that.

Any time length will give exactly the same chances to win for anyone

That's only true if you look at the outcome of the match as a whole, thus for example Probability(win match) = 70%. However, as you said yourself, it is about making decisions within a match.

In a very simplified model one could divide the match into sections of 1 minute each. And within each section, a crucial decision is made by both players. Each of your decisions can either be better or worse than your opponent's decision and to win the match, you need to "win" more decisions than your opponent (again, this is just hypothetical to illustrate the statistics).

Therefore you have a simple binomial distribution with either n = 10 decisions or n = 15 decisions.
Assuming that the better player on average has a 70% chance to make a better decision, the probability for the better player to win the match is as follows:

For 10 minute matches: Probability(at least 6 better decisions) = (10 choose 6) * 0.7^6 * 0.3^4 + (10 choose 7) * 0.7^7 * 0.3^3 + (10 choose 8) * 0.7^8 * 0.3^2 + (10 choose 9) * 0.7^9 * 0.3^1 + (10 choose 10) * 0.7^10 * 0.3^0 = 0.849 = 84.9%

For 15 minute matches: Probability(at least 8 better decisions) = (15 choose 8) * 0.7^8 * 0.3^7 + (15 choose 9) * 0.7^9 * 0.3^6 + (15 choose 10) * 0.7^10 * 0.3^5 + (15 choose 11) * 0.7^11 * 0.3^4 + (15 choose 12) * 0.7^12 * 0.3^3 + (15 choose 13) * 0.7^13 * 0.3^2 + (15 choose 14) * 0.7^14 * 0.3^1 + (15 choose 15) * 0.7^15 * 0.3^0 = 0.949 = 94.9%

The conclusion is that with more decisions, the player making better decisions on average has a higher chance to win in a 15 minute match compared to a 10 minute match.

Another example: in a bo1 the weaker player might win with luck, but he is very unlikely to win a full bo7 versus a significantly stronger player.

No.

The probability for both of the players to make more good decisions is going to increase proportionally and even out. Your calculation assumes that the probability to make more good decisions increases only for the winning player.

In other words, the player with the 70% match win is still going to win 70% of the time. Both of the players will still make the same amount of percentage of good decisions.

Both of the players will still make the same amount of percentage of good decisions.

Can't log in atm, but that's not how it works.

True, added up across all matches it is still 70% - 30% in decisions (or ingame events, whatever you want to call it), but that ratio can be produced in different ways when looking at individual matches.

For example there could be 10 matches and in each match the good player wins exactly 7 situations and the weaker player wins 3. So there you got a 10-0 wins in matches for the good player.

But that could also mean that in 7 matches the good player totally owns and wins all 10 situations, and in the other 3 matches the weaker player owns and wins all 10 situations. The result would be a 7-3 for the good player.

The longer the match, the less likely it is that the 30% player wins more situations and hence the match.

Maybe this example regarding chance helps: imagine you do not know how many females and males live in your town. So what would be a better way to determine the female/male ratio: (1) randomly selecting 10 people from your town and count the females or (2) do the same but randomly select 100 people? In which case you would expect chance to play a lesser role?

It's irrelevant to discuss the combinations and variations how the statistical values can form. The average values of 70% and 30% of win-rate across both players can form in infinitely many ways when analyzing the individual matches. There's even a chance the worse player is going to make infinitely more better decisions than the better player in a certain match (8 good decisions vs 0 as an example), but across a larger statistical base the above mentioned win-rates are going to form which already involve the chance and probabilities of their average decision making.

Longer amount of time can produce more accurate statistical values of players skill level, win-rates, their decision making and so on, but it's impossible to predict and assume which of the players are going to perform better or worse given any amount of time.

We often see players making great comebacks against supposedly superior players, but they fail due to lack of time. How can you assume that a worse player wouldn't, couldn't perform better with a longer amount of time given in a match? Perhaps they may need more time to adapt to the opponent, based on their play-style and unique traits which could possibly be more suitable to win more matches if they had more time to adapt their opponents and how they play a particular map at that day and time, just as an example. You cannot quantify, unify all the factors in any mathematical formula about the likeliness of how the players are going to perform.

The only safe assumption is that with any given amount of time any player is just as likely to perform better or worse.

Longer amount of time can produce more accurate statistical values of players skill level, win-rates, their decision making and so on,

And that's the point. You want less chance, and the win-loss rate to represent the skill difference between the players accurately (=more accurate ELO). Great, you finally got it.

but it's impossible to predict and assume which of the players are going to perform better or worse given any amount of time.

Oh god no why are you now saying that exact opposite as with which you started? I already showed that there is less uncertainty in longer matches (or in general, more trials if you talk in terms of a binomial distribution). Not going to do it again, unless I made a mistake in my calculations and someone points me towards it.

Perhaps they may need more time to adapt to the opponent, based on their play-style and unique traits which could possibly be more suitable to win more matches if they had more time to adapt their opponents and how they play a particular map at that day and time, just as an example.

That's your only good point here, namely that there might be a different ELO connected to 10 minute matches than to 15 minute matches as the result of individual differences. That's an entirely different story though and has little to do with probabilities. And so far it is only an assumption without any evidence whatsoever.

There could be cases in which the weaker player starts to shine from minute 11 on. Or the stronger player becomes even stronger over time as he reads his opponent like a book and also has a better stress management.

You can make all kind of hypothetical stuff up there, but no matter how complex and sophisticated your statistical model is, you still want to minimize the variation due to chance in the outcome.

Btw, while I myself would prefer 15 minute games with 10s weapon respawn time I understand perfectly that the current settings are a good tradeoff between fun, being viewer-friendly and chance.

Uncertainty or not, you can't predict which of the players are going to perform better or worse. Less uncertainty doesn't mean a certain player will ultimately do better or worse. So, it is safe to assume that every player has exactly the same chance to do better or worse as before.

Not sure you get the idea, so keep on yapping about your binomial calculations.

'Uncertainty or not, you can't predict which of the players are going to perform better or worse. Less uncertainty doesn't mean a certain player will ultimately do better or worse. So, it is safe to assume that every player has exactly the same chance to do better or worse as before.'

It is valid to say we don't know how exactly a longer timelimit will effect the chances of the stronger and the weaker players. Although i think asyyys model does capture the essential components of a duel quite well.

However, based on this there is no way you can then make the 'safe assumption' that it doesn't influence anything.

Well for a start, longer matches give the stronger player more opportunities to correct his errors. The disadvantage is that you see fewer surprising results with the underdog winning.

I mean it is the same in football, Barcelona can lose a single match 1-4 vs Celta Vigo, but if you let them play 10 matches you can expect Barcelona to win 7 or 8 times.

Or to get back to quake duel: everyone can beat rapha if the match takes only 1 minute. Have a good start, hit some lucky shots on the first confrontation, there you go. But as the match goes on he will correct the failed start and win the match.

The effect of going from 10 to 15 minutes is surely not that drastic, but the statistics are exactly the same when looking from that perspective.

As i said i do agree with your modeling approach. I agree with basically everything you said.

However, i also think it is a more or less legitimate, though nit-picky standpoint that a 5min longer timelimit might have more effects, which your model does not capture.

It's a somewhat futile standpoint though as the conclusion would be that you can't make any statement how it affects the outcome of the game.


Anyway, my point was, that neither standpoint justifies the assumption that it doesn't change anything.

Do you see players (on a decent skill level) regularly collapsing towards the end of the match? I don't. Which at least indicates strongly that fatigue does not play a role there yet.

Do you see players stabilizing towards the end of the match? Yes, that definitely happens. But that just shows that the match was too short to represent their true skill level.

In either case, increasing playtime just until fatigue kicks in would give the most accurate estimate of ELO.

But as I said, I am fine with 10 minutes. It's just people who do not believe in statistics because it is "against their logic" who annoy me.

What in the actual fuck is right. I broke it down and no any length of time will not do that. Try 2 minute duels 10 times then 5 minute duels 10 times and 10 minutes duels 10 times and tell me how the outcome of the game had changed every single time. How crucial certain decisions were over others because of time. Take for example chess vs speed chess. Entirely different but comparable in this instance. So in retrospect we learned you're a fucking retard.

if 15 minutes i think organizers should set up qualifiers for each region then in the main tournament it should be straight winners bracket ONLY then all matches should be played B03 only no b05
15 minutes is too much for the players to retain quality games up to the grand finals

When youre losing you sometimes wish it was more like 1min

somebody made the argument that in a quake duel, there is the start, the end and the middle part. The start is set in length, the end's length depends on the score, but doesn't get that much longer with 15 minute games.

Thus, 15 minute games have more of the middle part. Which is the interesting part. Both the start and the end are predictable in many ways. The middle part is where either player can win, make plays, come back and more.

Convinced me.

But nothing is changing I think.

Yes the mid game is probably the most important part. Most skilled players can run the clock with frag leads, put themselves into positions where they can disappear quick or evade nicely. It's what separates the pros from the hoes

what about fraglimit, first to 20 or 50?

10min fast maps
15min slow maps
=]

One of the main reasons people, myself included, thought that 10 mins was an improvement for QL was that it would be more appealing for new players, better for spectators, compatible with e-sports, etc... but I think we can safely say that shiterror murdered that dream so I wouldn't mind going back to 15 min duels like the good old daze.

Anyway fuck this shit thread, here's a baby hippo.

No.