population distribution problem

[telemann]

If we assume that 3d got a 18% chance of losing to 1d we get INDEPENDENT probability (so you can't add them). With every next game probability of losing is the same (not considering mental state after series of loses).

So when our statistic 3d play one 1d player he got 82% chance of winning
If he take another 1d player he still got 82% chance of winning

We got states:
our 3d could lose both games, win one or win both of them:
chance of 3d losing two games = 18% * 18% = 0.18 * 0.18 = 3%
chance of 3d losing one game of two = 18% * 82% = 16%
chance of 3d winning both games = 67%

If you take those six 1d players we got 0.82^6 chance of winning ALL SIX games = 30%
This is approximate simulation, because to get more accurate results we should use probably Bernoulli scheme, but the difference is clear

But we are still considering 3d who is merely a 3d (that means he is in lower part of win/lose ratio required to advance from 2d to 3d). If we consider "strong" 3d the chances are considerably higher.

So if you consider even an army of 8k-2k it would be VERY hard to overtake a 3dan player (statistically) )

[topazg]

We got states:
our 3d could lose both games, win one or win both of them:
chance of 3d losing two games = 18% * 18% = 0.18 * 0.18 = 3%
chance of 3d losing one game of two = 18% * 82% = 16%
chance of 3d winning both games = 67%

Actually, chance of winning one and losing one is 30% (ok, 29% rounded, but just making everything add up to 100%).

FWIW, getting one win against any opponent is the ASR holy grail. Going 0-3 against everyone gives you 22.75 points, going 3-0 gives you 45.5, but going 1-2 gives you 35.75, closer to 3-0 than 0-3. Reason being, 2-1 and 1-2 are both worth a total of 6 points (split between the players), whereas 3-0 and 0-3 are worth 5.25 split.

If you have lost twice to someone, you are at 1.5 points, but with 1.25 points at stake for being able to win that third game (instead of the 0.5 the opponent can get for racking up his third win against you). I'm not complaining about this being inbalanced in any way, but it's an important consideration for those after promotions

[Joaz Banbeck]

We got states:
our 3d could lose both games, win one or win both of them:
chance of 3d losing two games = 18% * 18% = 0.18 * 0.18 = 3%
chance of 3d losing one game of two = 18% * 82% = 16%
chance of 3d winning both games = 67%

Actually, chance of winning one and losing one is 30% (ok, 29% rounded, but just making everything add up to 100%).

Representing it graphicly, and ignoring rounding errors, it looks like this:

Code: Select all

              Game 1
            Win   Lose
G        +-------+------+
a  Win   |   67  |  15  |
m        +-------+------+
e  Lose  |   15  |   3  |
2        +-------+------+

Note that there are 2 ways to win one and lose one.

FWIW: The sum of any row or any column is 18 or 82; the total sum is 100.

[ChemBoy613]

If you guys want to crunch the math, you forget the meaning of the league to weaker players.

In a system where winning is rewarded, and where you get the chance to play stronger people, I've noticed the ASR kyus play their games much more sersiously, take their time, and do some actual reading. As someone who is in more of a "teacher" role, this is something i'm glad to see. However, sometimes I notice a 6k will all of a sudden look more like a 2k in game simply because he avoids dumb mistakes. I think the math fails to realize that the big reason kyus are kyus is not taking games seriously, playing to fast, playing without thinking, etc, which are all quickly solved in a league format.

I think, usagi, you and i have a similar time zone problem. When I was in the USA and had nothing to do for a month, i played 51 games, which is active, but not a realistic pace to keep up. The problem I'm having here in asia is that i can't play anyone before 9pm at night, and often times i am out/busy/tired/etc... so the games i do play are bad quality games. I, of course, find this very disappointing.

While it's true, sure, you have to play many games against kyu players to get into alpha, i don't think it's a bad thing... i actually find playing kyus relaxing and a nice thing to do when it's too late to give it 100%.

THat said, I think the real issue is a time zone issue, at least for us, not some sort of strengths issue. It's nice to be in alpha and play other 3ds/4ds, but I think the stronger players won't bother, because it will essentially become just an endless string of T games for them.