Clash of the Nations - matchday 4 (round of 16) [results]
Clément
- Thanks for all the entries!
- Please let me know if I got anything wrong - I have all your valid entries
saved in case we need to double check.
- Unfortunately, two players are prematurely eliminated from the tournament
after the round of 16.
* Matches
Mexico (milivella) (0) 1-2 (1) Argentina (Futbolmetrix)
USA (Joachim Parsch) (7) 8-7 (6) Germany (Mark V)
Ghana (Lleo) (3) 4-4 (4) Algeria (MH)
AET (1) 5-6 (2)
Korea Republic (Jesus Petry) (2) 3-0 (0) South Africa (Joachim Parsch)
Netherlands (Lleo) (4) 5-9 (8) Paraguay (milivella)
Brazil (Jesus Petry) (0) 1-2 (1) Spain (Abubakr)
New Zealand (Futbolmetrix) (0) 0-1 (0) Japan (Futbolmetrix)
Chile (MH) (6) 7-5 (4) Portugal (Joachim Parsch)
* Extra-goals left
Abubakr 24
Futbolmetrix 15
Jesus Petry 18
Joachim Parsch 7
Lleo 15
Mark V 17
MH 3
milivella 12
* Overall standings (after the round of 16)
1 Joachim Parsch 4 (+3)
Lleo 4
3 Futbolmetrix 2 (+6)
Jesus Petry 2 (+3)
Mark V 2
milivella 2 (+3)
7 Abubakr 0 (+3)
MH 0 (+6)
Abraço,
Luiz Mello
Mark V.
> Matchday 3 [results]
>
> - Thanks for all the entries!
> - Please let me know if I got anything wrong - I have all your valid entries
> saved in case we need to double check.
>
> - Unfortunately, two players are prematurely eliminated from the tournament
> after the round of 16.
>
> * Matches
>
> Mexico (milivella) (0) 1-2 (1) Argentina (Futbolmetrix)
>
> USA (Joachim Parsch) (7) 8-7 (6) Germany (Mark V)
Whoa! I'm gone! I switched from 7 to 6 goals at the last moment! I
still might have lost in ET.
I hope that this was worth it for you!
Clément
> On Nov 8, 6:35 pm, Clément wrote:
>> USA (Joachim Parsch) (7) 8-7 (6) Germany (Mark V)
>
> Whoa! I'm gone! I switched from 7 to 6 goals at the last moment! I
> still might have lost in ET.
I don't want to say anything that could reveal part of Joachim's strategy,
but I can say this much: you would have lost anyway with your original
entry, either on ET or PKs.
So no real harm done when you changed your mind, but it was close! =)
Abraço,
Luiz Mello
milivella
> Matchday 3 [results]
>
> - Thanks for all the entries!
Thanks to you, great gamemaster!
> - Unfortunately, two players are prematurely eliminated from the tournament
> after the round of 16.
Yeah, this obviously sucks in KO tournaments. Maybe avoiding this
could be a (secondary) aim in our reshaping of the rules?
I'm utterly emotionally devastated, but, trying to put together what
reamins of me, I can say this:
> Mexico (milivella) (0) 1-2 (1) Argentina (Futbolmetrix)
OK, the great feat was a 0-0 treaty to bring the match to PKs. I don't
know if lil' bastard breaking the treaty means that he's rotten or
it's me sticking to the metaphysical villain plan that makes me too
bad for this planet, but for sure the rivalry really has reached a new
stage... I just saw a ghost shouting to me: "milivella...
Revenge!!!" (copyright Shakespeare, or whoever wrote the Ur-Hamlet)
> USA (Joachim Parsch) (7) 8-7 (6) Germany (Mark V)
Holy sheet (used by Luiz to compute the results)!
> Ghana (Lleo) (3) 4-4 (4) Algeria (MH)
> AET (1) 5-6 (2)
As above.
> Korea Republic (Jesus Petry) (2) 3-0 (0) South Africa (Joachim Parsch)
>
> Netherlands (Lleo) (4) 5-9 (8) Paraguay (milivella)
The difference between making the results sure and wasting goals...
> Brazil (Jesus Petry) (0) 1-2 (1) Spain (Abubakr)
Compensation?
> New Zealand (Futbolmetrix) (0) 0-1 (0) Japan (Futbolmetrix)
Didn't see this coming...
> Chile (MH) (6) 7-5 (4) Portugal (Joachim Parsch)
So Michael manages to have two teams at the quarters... good, but he
has too few goals left.
--
Cheers
milivella
Abubakr
I simply played on the idea that Jesus will become rational once
again, hence play the game rationally, after his bout of paranoia.
Luckily, my hunch was right. :))
milivella
> On Nov 9, 1:59 pm, milivella <milive...@gmail.com> wrote:
>
>
>
> > Clément:
>
> > > Brazil (Jesus Petry) (0) 1-2 (1) Spain (Abubakr)
>
> > Compensation?
>
> I simply played on the idea that Jesus will become rational once
> again, hence play the game rationally, after his bout of paranoia.
> Luckily, my hunch was right. :))
Then it was a great display of strategic thinking and coolness: kudos
to you!
--
Cheers
milivella
Futbolmetrix
> reamins of me, I can say this:
>
> > Mexico (milivella) (0) 1-2 (1) Argentina (Futbolmetrix)
>
> OK, the great feat was a 0-0 treaty to bring the match to PKs. I don't
> know if lil' bastard breaking the treaty means that he's rotten or
> it's me sticking to the metaphysical villain plan that makes me too
> bad for this planet, but for sure the rivalry really has reached a new
> stage... I just saw a ghost shouting to me: "milivella...
> Revenge!!!" (copyright Shakespeare, or whoever wrote the Ur-Hamlet)
I have a number of reactions to this unexpected turn of events:
THE "DOG ATE MY HOMEWORK": I didn't do it on purpose, Sir. Just when I
was sending in my entry, the dog must have stepped on the keyboard and
changed the 0 into a 1!
THE "ABSENTMINDED PROFESSOR": Doh...I had already sent in my entry
when we sealed the deal, and I just forgot to amend it!
THE "YOU TOLD ME TO DO THIS" : Wasn't it you who said, "think of how
great it would be for RSS if we shocked them all and agreed to a deal,
and then you betrayed me? That would make our rivalry truly epic!"
Well, how could I deprive RSS of this entertainment value?
THE "JESUS PETRY" or THE PARANOIA ATTACK: I really wanted to stick by
the agreement, but at the last moment I was struck by an attack of
paranoia, thinking you would betray me, so I had to change my bet! [*]
THE "JOHN NASH": I really wanted to stick to the deal, but then an
angry John von Neumann appeared to me in a vision, accusing me of
betraying all the principles of game theory: choosing to cooperate in
a one-shot [**] prisoner's dilemma game could have had difficult to
predict (and potentially devastating) consequences for the equilibrium
of the cosmos. I couldn't do it, just couldn't...
THE "DORIAN GRAY": And he looked in the mirror, and his face was as
handsome and youthful as ever. But then, dreading, he lifted the veil
of the portrait. And there it was: a deep, unsightly gash right
through the middle of the face.
THE "RASKOLNIKOV": How will I ever live with the consequences of this?
I ask, I beg for forgiveness! I am repentant, I swear. I am even ready
to give up Thomas Mueller if only you will forgive my sins! [***]
THE "EMPEROR PALPATINE": (grinning, shoulders curved, rubbing his
hands) Did you really think that you could unseat the Dark Lord so
easily? You have much still to learn in the ways of the dark side,
young apprentice! [****]
D
[*] This one not completely untrue. But see also [****]
[**] But is this really a one-shot game?
[***] OK, I may have stretched this a bit...But maybe I won't dump
Thiago Neves on you if I win the Use-The-NT challenge.
[****] But this one more true :-)
PS: Still friends like before?
Mark V.
> >> USA (Joachim Parsch) (7) 8-7 (6) Germany (Mark V)
>
> > Whoa! I'm gone! I switched from 7 to 6 goals at the last moment! I
> > still might have lost in ET.
>
> I don't want to say anything that could reveal part of Joachim's strategy,
> but I can say this much: you would have lost anyway with your original
> entry, either on ET or PKs.
>
> So no real harm done when you changed your mind, but it was close! =)
It would have been ridiculous for me to commit 8 to beating him with
Abubakr lurking around the corner. I don't feel so bad. My number was
up!
MH
Maximum of 14 points
> Lleo 4
Maximum of 4 points
> 3 Futbolmetrix 2 (+6)
Maximum of 19 points
> Jesus Petry 2 (+3)
Maximum of 12 points
> Mark V 2
Maximum of 2 points
> milivella 2 (+3)
Maximum of 12 points
> 7 Abubakr 0 (+3)
Maximum of 10 points
> MH 0 (+6)
Maximum (laughable though it may seem) of 15 points
I think I got those right based on the matchups.
>
>
> Abra�o,
>
> Luiz Mello
Joachim Parsch
"Mark V." schrieb:
Oh well. At least I'm not completely out. Who would have thought,
that MH uses up all his remaining goals in the otofinals? As a matter
of fact, I had almost no chance of winning the clash before the
otofinals, the draw worked out badly for me.
BTW, I was first thinking about scoring only six, but then made
up my mind towards seven (I'm telling this just to annoy you ;-))
We'll meet again in the next clash...
Joachim
Joachim Parsch
> THE "YOU TOLD ME TO DO THIS" : Wasn't it you who said, "think of how
> great it would be for RSS if we shocked them all and agreed to a deal,
> and then you betrayed me? That would make our rivalry truly epic!"
> Well, how could I deprive RSS of this entertainment value?
As I said: the real lesson of this game is to learn, why Macchiavelli
was an Italian.
> THE "JOHN NASH": I really wanted to stick to the deal, but then an
> angry John von Neumann appeared to me in a vision, accusing me of
> betraying all the principles of game theory: choosing to cooperate in
> a one-shot [**] prisoner's dilemma game could have had difficult to
> predict (and potentially devastating) consequences for the equilibrium
> of the cosmos. I couldn't do it, just couldn't...
It's not a one-shot game, but it's a very pure prisoner's dilemma.
If millivella had also chosen to add a goal for safety (*g*), you
had both be in the same situation as before, only with one goal less left.
[...]
THE "SCHWARZENEGGER 1": "Do you remember, when I told you, that you'll
be the last to die? Yes? Ok - I lied."
THE "SCHWARZENEGGER 2": "I'll be back."
THE "COURT JESTER": I became confused, I swear! You told me, that the
the Dutch vs. the Paras was the duel with the fuel, while the Mexicans vs.
the Gauchos was the match with a scratch. When I sent my entry, the
Paras had the scratch and the duel with the Dutch had the match with the
Argies...
THE "NOSFERATU": To deceive and overcome the evil prince of Darkness,
Nosvellatu himself, you have to lure him by a beautiful suggestion until
he forgets the crow of the rooster and misses the deadline...
> PS: Still friends like before?
Friends? Oh, that ancient concept. I quite forgot that while playing the
game :-)
Joachim
milivella
> On Nov 8, 9:59 pm, milivella <milive...@gmail.com> wrote:
>
> > Clément:
>
> > I'm utterly emotionally devastated, but, trying to put together what
> > reamins of me, I can say this:
>
> > > Mexico (milivella) (0) 1-2 (1) Argentina (Futbolmetrix)
>
> > OK, the great feat was a 0-0 treaty to bring the match to PKs. I don't
> > know if lil' bastard breaking the treaty means that he's rotten or
> > it's me sticking to the metaphysical villain plan that makes me too
> > bad for this planet, but for sure the rivalry really has reached a new
> > stage... I just saw a ghost shouting to me: "milivella...
> > Revenge!!!" (copyright Shakespeare, or whoever wrote the Ur-Hamlet)
>
> I have a number of reactions to this unexpected turn of events:
While I enjoyed all of them, you still have to pay for your betrayal!
> [***] OK, I may have stretched this a bit...But maybe I won't dump
> Thiago Neves on you if I win the Use-The-NT challenge.
Nah... I want you to get what you'll win.
> PS: Still friends like before?
Even more, even more... everything that makes a backstabbing easier is
OK to me!
(kidding: still friends! and fierce rivals!)
--
Cheers
milivella
milivella
> THE "SCHWARZENEGGER 1": "Do you remember, when I told you, that you'll
> be the last to die? Yes? Ok - I lied."
>
> THE "SCHWARZENEGGER 2": "I'll be back."
>
> THE "COURT JESTER": I became confused, I swear! You told me, that the
> the Dutch vs. the Paras was the duel with the fuel, while the Mexicans vs.
> the Gauchos was the match with a scratch. When I sent my entry, the
> Paras had the scratch and the duel with the Dutch had the match with the
> Argies...
>
> THE "NOSFERATU": To deceive and overcome the evil prince of Darkness,
> Nosvellatu himself, you have to lure him by a beautiful suggestion until
> he forgets the crow of the rooster and misses the deadline...
I must say that the players who backstab me are the ones whose
writings I enjoy more... I should learn something from this.
--
Cheers
milivella
Futbolmetrix
news:4CD8FCC7...@bunuel.franken.de...
> THE "SCHWARZENEGGER 1": "Do you remember, when I told you, that you'll
> be the last to die? Yes? Ok - I lied."
>
> THE "SCHWARZENEGGER 2": "I'll be back."
>
> THE "COURT JESTER": I became confused, I swear! You told me, that the
> the Dutch vs. the Paras was the duel with the fuel, while the Mexicans vs.
> the Gauchos was the match with a scratch. When I sent my entry, the
> Paras had the scratch and the duel with the Dutch had the match with the
> Argies...
>
> THE "NOSFERATU": To deceive and overcome the evil prince of Darkness,
> Nosvellatu himself, you have to lure him by a beautiful suggestion until
> he forgets the crow of the rooster and misses the deadline...
>
THE "JESSICA RABBIT": I'm not bad, I'm just drawn that way!
THE "TUCO": When you have to shoot, shoot! Don't talk!
milivella
THE "BART SIMPSON": I didn't do it! [variant: THE "SHAGGY": It wasn't
me!]
--
Cheers
milivella
Lleo
> Ghana (Lleo) (3) 4-4 (4) Algeria (MH)
> AET (1) 5-6 (2)
> Netherlands (Lleo) (4) 5-9 (8) Paraguay (milivella)
Ouch! And here was I wondering whether I had spent too many goals in
this round... Too bad to go out with 15 goals still remaining.
Congrats and good luck to MH and milivella.
Btw, Paraguay scoring NINE goals? milivella will deserve a statue in
Asunción for that :-)
--
Lléo
milivella
> Btw, Paraguay scoring NINE goals? milivella will deserve a statue in
> Asunción for that :-)
Of course. Actually Ciudad de Mexico kindly offered to provide it:
it's 1:1 and it's made of a flesh-like substance that looks like the
real thing. What a pity it has heavy brushes here and there! (you
know, the long trip...)
--
Cheers
milivella
Jesus Petry
I think the standings can be better viewed this way:
Guaranteed Potential
1 Futbolmetrix 8 +11
2 Joachim Parsch 7 +7
3 MH 6 +9
4 Jesus Petry 5 +7
milivella 5 +7
6 Lléo 4 0
7 Abubakr 3 +7
8 Mark V 2 0
Tchau!
Jesus Petry
Mark V.
>
> BTW, I was first thinking about scoring only six, but then made
> up my mind towards seven (I'm telling this just to annoy you ;-))
> We'll meet again in the next clash...
YOU may find it annoying to know that I forced my opponents to score
29 goals to my 15, though to your credit you were both effective and
relatively efficient against my teams. But if you, Jesus, or
Futbolmetrix fail to win this thing, I'll take some small consolation
from my poison pill role.
milivella
> YOU may find it annoying to know that I forced my opponents to score
> 29 goals to my 15
Awesome statistics! The Master of Dark Diplomacy (I mean Daniele!) has
some 3 goals against in the whole tournament...
--
Cheers
milivella
Mark V.
Didn't I alone score 3 Danish goals against Japan? Do you mean he's
had nobody else commit goals to their teams against him? Impressive!
Clément
>
> I think the standings can be better viewed this way:
>
> Guaranteed Potential
> 1 Futbolmetrix 8 +11
> 2 Joachim Parsch 7 +7
> 3 MH 6 +9
> 4 Jesus Petry 5 +7
> milivella 5 +7
> 7 Abubakr 3 +7
> 8 Mark V 2 0
Absolutely. Thank you!
Abra�o,
Luiz Mello
milivella
Oh no, three was just an overstatement (actually and _under_statement
in this case), I just wanted to stress how he has managed to have
always helpful opponents. It would be interesting to see the exact
numbers of goals against for each of us.
--
Cheers
milivella
Clément
- Thanks for all the entries!
- Please let me know if I got anything wrong - I have all your valid entries
saved in case we need to double check.
- Unfortunately, another two players are eliminated from the tournament
after the quarterfinals.
- I owe an apology to the Universe because I thought the game would be
totally predictable at this point. What did I know.
- Now this is AFC's best World Cup ever. =)
* Matches
Paraguay (milivella) (9) 10-1 (0) Spain (Abubakr)
Argentina (Futbolmetrix) (0) 1-2 (1) USA (Joachim Parsch)
Korea Republic (Jesus Petry) (2) 3-3 (3) Algeria (MH)
AET (1) 4-3 (0)
Japan (Futbolmetrix) (3) 4-1 (0) Chile (MH)
* Extra-goals left
Abubakr 24
Futbolmetrix 12
Jesus Petry 15
Joachim Parsch 6
MH 0
milivella 3
* Overall standings (after the quarterfinals)
current guaranteed potential
1 Futbolmetrix 5 10 +5
2 Joachim Parsch 4 9 +5
3 Jesus Petry 2 7 +5
milivella 2 7 +5
5 MH 6 6 0
6 Ll�o 4 4 0
7 Abubakr 3 3 0
8 Mark V 2 2 0
Abra�o,
Luiz Mello
milivella
> Matchday 5 [results]
>
> - Thanks for all the entries!
Thank you!
> - I owe an apology to the Universe because I thought the game would be
> totally predictable at this point. What did I know.
Indeed!
> Paraguay (milivella) (9) 10-1 (0) Spain (Abubakr)
Abu told me that he was going to do this. I didn't trust him. How
different my situation would be!
So I'll leave this game not having betrayed nobody and having been
betrayed twice, and yet my own evilness will be the cause of my loss!
Sorry, Abubakr: it's not my fault, these ruthless RSSers stole my
faith in humanity... Of course part of the problem was that I didn't
understand why you wanted to give up, and indeed you could have your
hands on the cup right now, had you tried.
--
Cheers
milivella
Abubakr
I told you why: had Futbolmetrix played correctly he'd be on 12 pts
and I'd have no chance of winning. I didn't expect him to make a
blunder (or become fun loving?) at this point.
milivella
> On Nov 12, 10:40 am, milivella <milive...@gmail.com> wrote:
[snip]
> > Sorry, Abubakr: it's not my fault, these ruthless RSSers stole my
> > faith in humanity... Of course part of the problem was that I didn't
> > understand why you wanted to give up, and indeed you could have your
> > hands on the cup right now, had you tried.
>
> I told you why: had Futbolmetrix played correctly he'd be on 12 pts
> and I'd have no chance of winning. I didn't expect him to make a
> blunder (or become fun loving?) at this point.
On the other hand, you had two options:
1. try, and win only if somebody makes a blunder / becomes fun loving
2. don't try, and *never* win
What advantages have #2 over #1?!
However, I am the last one that has the right to ask about other
players' strategies! My playing has been *full* of non-sense...
Now I can't wait for CotN 2! :)
--
Cheers
milivella
milivella
> Sorry, Abubakr: it's not my fault, these ruthless RSSers stole my
> faith in humanity... Of course part of the problem was that I didn't
> understand why you wanted to give up, and indeed you could have your
> hands on the cup right now, had you tried.
And obviously persuading me that you were using 0 goals -> that I
should use only 1 goal (and save the rest for the last 2 rounds) would
have been the perfect diplomatic strategy for someone who needed to
get through the quarters spending little goals... e.g. 2.
--
Cheers
milivella
Abubakr
> Abubakr:
>
> > On Nov 12, 10:40 am, milivella <milive...@gmail.com> wrote:
>
> [snip]
>
> > > Sorry, Abubakr: it's not my fault, these ruthless RSSers stole my
> > > faith in humanity... Of course part of the problem was that I didn't
> > > understand why you wanted to give up, and indeed you could have your
> > > hands on the cup right now, had you tried.
>
> > I told you why: had Futbolmetrix played correctly he'd be on 12 pts
> > and I'd have no chance of winning. I didn't expect him to make a
> > blunder (or become fun loving?) at this point.
>
> On the other hand, you had two options:
> 1. try, and win only if somebody makes a blunder / becomes fun loving
> 2. don't try, and *never* win
> What advantages have #2 over #1?!
You are correct, there's no 'advantage', per se. I thought about
playing on for that very reason then realised I had already given Luiz
my submission for the round.
> However, I am the last one that has the right to ask about other
> players' strategies! My playing has been *full* of non-sense...
>
> Now I can't wait for CotN 2! :)
It's been lots of fun, so me neither!
> --
> Cheers
> milivella
Abubakr
I was wondering why you were cross examining me so much! LOL The
dreaded paranoia strikes again.
milivella
> I was wondering why you were cross examining me so much! LOL The
> dreaded paranoia strikes again.
Indeed for the first time I sent more than one submission to Luiz
(each one overwriting the previous one), and the series was:
4 goals (1 extra time)
3 goals (0 extra time)
9 goals (0 extra time)
!
--
Cheers
milivella
MH
> Matchday 5 [results]
>
> - Thanks for all the entries!
> - Please let me know if I got anything wrong - I have all your valid
> entries saved in case we need to double check.
>
> - Unfortunately, another two players are eliminated from the tournament
> after the quarterfinals.
>
> - I owe an apology to the Universe because I thought the game would be
> totally predictable at this point. What did I know.
>
> - Now this is AFC's best World Cup ever. =)
>
>
> * Matches
>
> Paraguay (milivella) (9) 10-1 (0) Spain (Abubakr)
>
> Argentina (Futbolmetrix) (0) 1-2 (1) USA (Joachim Parsch)
>
> Korea Republic (Jesus Petry) (2) 3-3 (3) Algeria (MH)
> AET (1) 4-3 (0)
>
> Japan (Futbolmetrix) (3) 4-1 (0) Chile (MH)
>
>
> * Extra-goals left
>
> Abubakr 24
> Futbolmetrix 12
> Jesus Petry 15
> Joachim Parsch 6
> MH 0
> milivella 3
Well if one has to go out, doing so with no goals left seems like the
right way to do it.
In a rational world this will now be a S. Korea - USA final.
USA will only have two goals left to spend, but then, maybe, so will S.
Korea......
Joachim Parsch
Abubakr schrieb:
Yes, but you could have fought for second place (after a semifinal exit
I would have been stuck at 9 points...)
As for Daniele, well, that has been my fault, as I convinced him to try
a scheme, that would leave him a chance to win the final as well as the
tournament. Of course he saw through it, that he might lose first place
this way, but as a game theorist he must agree, that the constellation now
is much more interesting than in the other scenario.
Now all 4 contenders still can win it (theoretically), and 3 of us (Futbolmetrix,
Jesus and me) have a real chance. It's all psychology and (maybe) penalties ;-)
Joachim
Mark
> * Matches
>
> Paraguay (milivella) (9) 10-1 (0) Spain (Abubakr)
>
Oscar Cardozo was on form! (And maybe Iker Casillas and Carles Puyol
injured?)
> Argentina (Futbolmetrix) (0) 1-2 (1) USA (Joachim Parsch)
>
After this World Cup, the contract of Argentina coach Diego Maradona
was not renewed.
Jesus Petry
This was crazy!
Now both of us JPs have basically the same strategies to consider.
Let's assume for simplicity that both Daniele and Andrea use all
their goals in the semis.
Each JP has two choices:
A - using 1 goal more to guarantee a place in the finals, having
only two left for the final;
B - using the same amount as the opponent, risking on PKs and saving
three goals for the final.
Assuming each of us gives a 50% preference to each option, strategy A
has 25% chance of guaranteeing an overall win before the final
(opponent picks strategy B AND loses semi on PKs) and another 25%
chance of giving the win on PKs (opponent picks A too, loses the final
on PKs). Total: 50%.
In the same case, strategy B gives 37.5% chance of winning it all
before the final (win on PKs in the semi, opponent picks A or picks B
and loses semi on PKs) and 6.25% of winning the final on PKs (win semi
on PKs, opponent picks B and also wins semi on PKs, then loses final
on PKs). Total: 43.75%.
But that difference makes it less attractive to use strategy B, which
leads to reevaluation of the chances for the opponent picking each
strategy, making it all fuzzy.
Tchau!
Jesus Petry
milivella
> Now both of us JPs have basically the same strategies to consider.
> Let's assume for simplicity that both Daniele and Andrea use all
> their goals in the semis.
> Each JP has two choices:
> A - using 1 goal more to guarantee a place in the finals, having
> only two left for the final;
> B - using the same amount as the opponent, risking on PKs and saving
> three goals for the final.
>
> Assuming each of us gives a 50% preference to each option, strategy A
> has 25% chance of guaranteeing an overall win before the final
> (opponent picks strategy B AND loses semi on PKs) and another 25%
> chance of giving the win on PKs (opponent picks A too, loses the final
> on PKs). Total: 50%.
> In the same case, strategy B gives 37.5% chance of winning it all
> before the final (win on PKs in the semi, opponent picks A or picks B
> and loses semi on PKs) and 6.25% of winning the final on PKs (win semi
> on PKs, opponent picks B and also wins semi on PKs, then loses final
> on PKs). Total: 43.75%.
> But that difference makes it less attractive to use strategy B, which
> leads to reevaluation of the chances for the opponent picking each
> strategy, making it all fuzzy.
Awesome! So now you're supposed to repeat it all changing the
assumption ("Assuming each of us gives a 50% preference to each
option")? And then you should repeat until you find a stable state?
I'm learning more game theory here (I know, basic stuff, and yet very
interesting for the layman) than I can hope to grasp anywhere else!
--
Cheers
milivella
Futbolmetrix
news:e0b7ea07-6ee2-4541...@z20g2000pra.googlegroups.com...
> Now both of us JPs have basically the same strategies to consider.
> Let's assume for simplicity that both Daniele and Andrea use all
> their goals in the semis.
That's a reasonable assumption.
> Each JP has two choices:
> A - using 1 goal more to guarantee a place in the finals, having
> only two left for the final;
> B - using the same amount as the opponent, risking on PKs and saving
> three goals for the final.
Nice analysis. I'll try a slightly different approach, that doesn't make any
assumptions about any player's beliefs about what the others do. The usual
assumption is that every player only cares about winning the whole thing.
The strategies will be listed as S = (JO, MI, JE, FU)
Equilibrium 1: The straightforward one: S = (4,3,13,12). This leaves JO and
JE to fight it out at Odds and Evens for the final title. Nobody has an
incentive to deviate: if either JO or JE play one goal less in the semi,
they are guaranteed to win the final, but it leaves them open to losing the
semi on PKs, so their probability of winning the whole thing remains 50%.
Equilibrium 2: Joachim takes a gamble in the semi: S = (3,3,13,12). In terms
of outcomes, the only difference here is that milivella has a chance to make
the final, but still the probabilities of winning the whole thing remain
(0.5,0,0.5,0). Jesus is better off hoping that milivella wins his semifinal,
than trying to leave himself enough points for the final.
That's because if the strategies are: (3,3,12,12), the winning probabilities
become: (3/8, 1/8, 3/8, 1/8) [Actually, that's not entirely correct,
because there is a 1/8 probability that milivella and I will finish tied on
12 points. But I'm assuming that that outcome is considered a full victory
by milivella, and a full defeat by myself]
Equilibrium 3: Jesus takes a gamble in the semi: S = (4,3,12,12). Same logic
as above. Unfortunately, this doesn't do me any good, because even if I
reach the final, I will lose to Joachim, who will then reach 14 points.
I don't think that any collusive strategies will work here, because JE and
JO will always have an incentive to deviate and secure passage to the final
with enough goals to spare to win the whole thing.
D