Mediocrity - Match 1 [Game Over!]

[Packbat]

Mediocrity - The Game Of Doing Well Enough, But Not Too Well

A bit of partially-accurate history

Once upon a time, in the ancient and wonderful world known as the Santa Clara Valley circa 1982, there was a university called Stanford. And in the Computer Science Department of this institution was a man named Douglas Hofstadter, who wrote many wild and wonderful things in a publication called

Scientific American

, a publication titled after the country in which man, university, and valley resided. One of these wonderful things was a column called

Metamagical Themas

, so called because it was an anagram of

Mathematical Games

, the title of the previous column occupying that space in the magazine. And one of the reasons why this column was so wonderful were the several extraordinary and unusual games which were first presented publicly there.

One of these games was called "Mediocrity", and it is this game which has brought together a number of contestants in this humble venue today.

Some Rules

Spoiler: Full text

(Note: these rules differ from Hofstadter's in certain minutiae, being in part inspired by the card game version. This particular event is what is known as a Level-3 game.)

1. The goal of Mediocrity is to be neither the greatest nor the least, but rather the middlemost. This occurs on each level - the winner of the match is the one with the middlemost number of won sets, with the winner of each set being the middlemost winner of games in that set, each game being won by posting the middlemost number.
   
   
   
2. Each game will proceed as follows:
   1. The moderator (currently, Packbat) will post a message indicating that the game has begun, indicating a deadline.
      
   2. Each player will PM a positive integer in decimal form to the moderator. Players not submitting a PM with such a number before the deadline will each be assigned a random number in the range from 1 to 10 inclusive. If multiple such PMs are sent, the last PM arriving before the deadline shall be used.
      
   3. After the deadline, the moderator will post all players' numbers and give one game point to the player with the middlemost number. In the case of draws, points shall be divided evenly.
3. Each set will proceed as follows:
   1. The moderator will run a series of games, keeping track of game points, until one or more players reaches or exceeds four game points.
      
   2. When these games are complete, one set point shall be awarded to the player with the middlemost number of game points. In the case of draws, points shall be divided evenly.
4. The match will proceed as follows:
   1. The moderator will run a series of sets, keeping track of set points, until one or more players reaches or exceeds three set points.
      
   2. When these sets are complete, the winner shall be the player with the middlemost number of set points. In the case of a draw, the match will go to Sudden Death, as described in Rule 5.
5. Sudden Death, should it occur, shall proceed as follows:
   1. While Sudden Death continues, the moderator shall begin games as normal, save that at the conclusion of each game set points shall be awarded, rather than game points.
      
   2. Sudden Death will end when, after any game, there is a single player with the middlemost number of set points. That player shall be the winner.
6. The term "middlemost", when referring to a set of numbers, shall be defined as follows.
   1. If there is any single number such that an equal number of numbers are greater and lesser than that number, that number shall be the middlemost. For example, in the set (5, 10, 16), 10 is the middlemost, and in the set (2, 2, 3, 6, 98), 3 is the middlemost.
      
   2. If 6a does not hold, but there exists a pair of numbers such that (i) no other number lies within the range of those two numbers (inclusive), (ii) an equal number of numbers are greater and less than both numbers, and (iii) one number in that pair is closer to the mean of all the numbers than the other, that number shall be middlemost. For example, in the set (3, 4, 7, 10), between 4 and 7, 7 is closer to 6, so 7 is the middlemost, and in the set (1, 14, 18, 19), between 14 and 18, 14 is closer to 13, so 14 is the middlemost.
      
   3. If neither 6a nor 6b hold, if there is any number such that an equal number of
      unique
      numbers are greater and lesser than that number, that number shall be the middlemost. For example, in the set (4, 4, 12, 20), 12 shall be middlemost, and in the set (5, 6, 20, 20, 20), 6 shall be middlemost.
      
   4. If none of the above hold, all numbers closest to the median shall draw. For example, in the set (1, 2, 3, 4), 2 and 3 shall draw, and in the set (8, 10, 11, 11, 13), 11 and 11 shall draw.

Edit: Clarified Rules 1 and 6 slightly.
Edit 2: Clarification on 6b,c,d.
Edit 3: Clarification on 2b, spoiler tag.
Edit 4: Reformatting using list tags.
Edit 5: Correcting 6b.

[Packbat]

Players, Match 1

• gandalf5166 - 1/2 set point
  
• Hoppster - 3 set points
  
• Twistedspoon - 1+1/2 set points - WINNER

Set 1

Start - End

Game #	gandalf5166	Hoppster	Twistedspoon
Game 1 - Start, End	0	0 +1/2	0 +1/2
Game 2 - Start, End	0	1/2	1/2 +1
Game 3 - Start, End	0	1/2 +1/2	1+1/2 +1/2
Game 4 - Start, End	0 +1	1	2
Game 5 - Start, End	1	1 +1	2
Game 6 - Start, End	1	2	2 +1
Game 7 - Start, End	1	2	3 +1 = 4

Score:

• gandalf5166 - 0 set points
  
• Hoppster - 0
  +1
  set points
  
• Twistedspoon - 0 set points

Set 2

Start - End

Game #	gandalf5166	Hoppster	Twistedspoon
Game 8 - Start, End	0	0 +1	0
Game 9 - Start, End	0 +1	1	0
Game 10 - Start, End	1	1	0 +1
Game 11 - Start, End	1	1	1 +1
Game 12 - Start, End	1	1 +1	2
Game 13 - Start, End	1	2	2 +1
Game 14 - Start, End	1	2 +1	3
Game 15 - Start, End	1 +1	3	3
Game 16 - Start, End	2 +1	3	3
Game 17 - Start, End	3 +1/2	3 +1/2	3
Game 18 - Start, End	3+1/2 +1=4+1/2	3+1/2	3

Score:

• gandalf5166 - 0 set points
  
• Hoppster - 1
  +1
  set points
  
• Twistedspoon - 0 set points

Set 3

Start -End

Game #	gandalf5166	Hoppster	Twistedspoon
Game 19 - Start, End	0 +1	0	0
Game 20 - Start, End	1	0 +1/2	0 +1/2
Game 21 - Start, End	1	1/2 +1	1/2
Game 22 - Start, End	1	1+1/2	1/2 +1
Game 23 - Start, End	1	1+1/2	1+1/2 +1
Game 24 - Start, End	1 +1/2	1+1/2 +1/2	2+1/2
Game 25 - Start, End	1+1/2 +1/2	2 +1/2	2+1/2
Game 26 - Start, End	2	2+1/2	2+1/2 +1
Game 27 - Start, End	2	2+1/2 +1	3+1/2
Game 28 - Start, End	2 +1/2	3+1/2 +1/2 = 4	3+1/2

• gandalf5166 - 0 set points
  
• Hoppster - 2 set points
  
• Twistedspoon - 0
  +1
  set points

Set 4

Start - End

Game #	gandalf5166	Hoppster	Twistedspoon
Game 29 - Start, End	0 +1	0	0
Game 30 - Start, End	1	0 +1/2	0 +1/2
Game 31 - Start, End	1	1/2 +1/2	1/2 +1/2
Game 32 - Start, End	1	1	1 +1
Game 33 - Start, End	1	1	2 +1
Game 34 - Start, End	1	1 +1	3
Game 35 - Start, End	1 +1/2	2 +1/2	3
Game 36 - Start, End	1+1/2 +1	2+1/2	3
Game 37 - Start, End	2+1/2 +1	2+1/2	3
Game 38 - Start, End	3+1/2	2+1/2 +1/2	3 +1/2
Game 39 - Start, End	3+1/2	3 +1/2	3+1/2 +1/2=4

• gandalf5166 - 0
  + 1/2
  set points
  
• Hoppster - 2
  + 1/2
  set points
  
• Twistedspoon - 1 set point

Set 5

Start - End

Game #	gandalf5166	Hoppster	Twistedspoon
Game 40 - Start, End	0 +1/2	0	0 +1/2
Game 41 - Start, End	1/2	0	1/2 +1
Game 42 - Start, End	1/2	0	1+1/2 +1
Game 43 - Start, End	1/2	0 +1	2+1/2
Game 44 - Start, End	1/2	2 +1/2	2+1/2 +1/2
Game 45 - Start, End	1/2 +1/2	2+1/2 +1/2	3
Game 46 - Start, End	1 +1	3	3
Game 47 - Start, End	2	3 +1/2	3 +1/2
Game 48 - Start, End	2 +1/3	3+1/2 +1/3	3+1/2 +1/3
Game 49 - Start, End	2+1/3 +1	3+5/6	3+5/6
Game 50 - Start, End	3+1/3 +1=4+1/3	3+5/6	3+5/6

• gandalf5166 - 1/2 set point
  
• Hoppster - 2+1/2
  +1/2 = 3 set points
  
  
• Twistedspoon - 1
  +1/2
  set points

---

Players, Match 2:

• Acronach
  theplague42
  
• Robotnick2
  
• Tragedy

Players in queue:

• animorpherv1
  
• JDGA
  
• Hoppster

[Packbat]

Question: 24-hour deadlines, 48-hour deadlines, or longer?

[gandalf5166]

48 hours plz.

[Hoppster]

Eh, 48 works.

[Packbat]

Going with 48, then! Player list is closed!

Game 1 Begins

- Deadline: March 25, 9 p.m. EDT.

Discussion in thread freely allowed, by players and spectators.

[Hoppster]

I'm picking 5. That's in the middle.

[Packbat]

I'm picking 5. That's in the middle.

...of the range that a player who forgets to send in a number will be assigned. You're allowed to PM any positive integer in decimal form: 1, 2, 5, 10, 50, 8675309,

any

.

[Twistedspoon]

oh, lol


not 1 to 10

that complicates things =|

[Hoppster]

I'm picking 5. That's in the middle.

...of the range that a player who forgets to send in a number will be assigned. You're allowed to PM any positive integer in decimal form: 1, 2, 5, 10, 50, 8675309,

any

.

That's the genius of my plan.

[gandalf5166]

I chose 23000067.

I don't want to win too much.

[Packbat]

The numbers picked for Game 1 are:

• gandalf5166:
  5
  
  
• Hoppster:
  7
  
  
• Twistedspoon:
  7

Hoppster and Twistedspoon tie, each receiving 1/2 game point.

Game 2 Begins

- Deadline March 27, 9 p.m. E.D.T.

[theplague42]

/in for next match.

[Packbat]

/in for next match.

Noted!

[Hoppster]

Interesting. If I pick 6, and the two of you both stick with your numbers...

[Packbat]

Quick rules clarification, while I'm thinking of it: if multiple legitimate PMs are received, the last PM before the deadline is the one that counts.

[Packbat]

The numbers picked for Game 2 are:

• gandalf5166:
  8
  
  
• Hoppster:
  6
  
  
• Twistedspoon:
  7

Twistedspoon wins 1 game point.

Game 3 Begins

- Deadline March 29, 9 p.m. E.D.T.

[Twistedspoon]

yes

Advantage Spoon

Question: how many sets and how many games in each set will we be playing?

[Packbat]

Each set goes until someone reaches 4 game points, and the match ends when someone reaches 3 set points.

[Acronach]

/in please

[Packbat]

/in please

Added to queue!

[animorpherv1]

Um, the deadline was 2 days ago. No results?

[Packbat]

*headdesk*

My bad - I simply forgot. The numbers picked for Game 3 are:

• gandalf5166:
  6
  
  
• Hoppster:
  7
  
  
• Twistedspoon:
  7

Twistedspoon and Hoppster each win 1/2 game point.

Game 4 Begins

- Deadline April 2, 9 p.m. E.D.T.

[Twistedspoon]

Twistedspoon and Happster each win 1/2 game point.

Curse you Happster

[Packbat]

Twistedspoon and Happster each win 1/2 game point.

Curse you Happster

What can I say, he's a happstening dude! Fixed.