5way tie by 5 beginners! Einstein forum
23 replies. Last post: 20060518
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Theo van der Storm at 20060501
Tournament table [einstein.mc.2006.mar.1.72]
einstein.mc.2006.mar.1.72
<!— tournament einstein.mc.2006.mar.1.72 >
Tournament:einstein.mc.2006.mar.1.72
Start date:20060313 13:08
Finish date:20060501 20:58N Name Rating 1 2 3 4 5 Points Son 1 Marius Hals?r info 1500(1598) 0 0 2 2 4 16 2 Eduard info 1500(1371) 2 2 0 0 4 16 3 Trevor Green info 1500(1549) 2 0 0 2 4 16 4 Matteo A. info 1500(1531) 0 2 2 0 4 16 5 Yann V info 1500(1564) 0 2 0 2 4 16
einstein.mc.2006.mar.1.72 – list of games
Game Player 1 Player 2 Result Moves #509183 Yann V Trevor Green 0 : 2 80 #509184 Trevor Green Eduard 0 : 2 64 #509185 Matteo A. Trevor Green 2 : 0 97 #509186 Trevor Green Marius Hals?r 2 : 0 73 #509187 Eduard Yann V 0 : 2 78 #509188 Yann V Matteo A. 2 : 0 69 #509189 Marius Hals?r Yann V 2 : 0 53 #509190 Matteo A. Eduard 2 : 0 51 #509191 Eduard Marius Hals?r 2 : 0 69 #509192 Marius Hals?r Matteo A. 2 : 0 63

Theo van der Storm at 20060501
Sorry about the blank space in the original posting.
I think a 5way tie is a very special result indeed! 
Ingo Althofer at 20060502
Theo, you probably mean “5way tie”
by 5 participants, right? At least
Marius Halsor has won already several
EinStein tournaments.
Greetings, Ingo. 
Theo van der Storm at 20060502
Ingo,
What you suggest is not what I meant.
I meant they were beginners at the start of this particular tournament.
Start date: 20060313 13:08. Note: 5 × 1500.
I agree “the Little Golems” have learned a lot,
eventhough I see that the top 5 of the rating list
are all experienced www.inetplay.de players :)
Player Rating
Ingo Althofer 1748
luiser 1743
Jonny 1707
Theo van der Storm 1682
YHW 1668
Kd Hoffmann 1646
Andy Olsen 1637
klaashaas 1625
caronte 1620
christopher 1612
Best,
Theo
PS: No offence to “original Little Golem” people intended
and I’m sure this is only a snapshot in time. 
Marius Halsor ★ at 20060502
No offence taken! :
) I must still be considered a beginner in this game. But just you wait – I’ll learn. I’ll get up to the top 5 – eventually.... ;) 
Ingo Althofer at 20060502
> Ingo,
>
> What you suggest is not what I meant.
> I meant they were beginners at the start
> of this particular tournament.
> Start date: 20060313 13:08. Note: 5 × 1500.
You are right. But this also shows the difference
between LittleGolem and live servers: A single
(best of 5) game can run over a long span of time;
and a player who was a novice at the beginning of
the game may be experienced when the game or
tournament is over.
By the way: I have thought about the possibility
having a choice between normal and quick tournaments
on LG. I see that most games are played quickly.
On the other hand it is a bit a pity to see that
ONE slow player can postpone completion of a
whole tournament for months – all others "waiting
only for him".
Has such a feature “quick tournaments” already been
discussed somewhere on LG?
Greetings, Ingo. 
Ingo Althofer at 20060502
Gregorio
> ingo, this feature has loooooong been discussed :)
Aha. That was also what my subconscience
told me all the time...
But it is not in the FAQ, when I read correctly.
Maybe, this point is the Achilles heel
of (all) servers for turnbased game play?!
Ingo. 
Andy Olsen at 20060505
I’d like to thank Richard and the random number generator. Richard for putting a game with a huge luck to skill ratio, and the RNG for giving me good rolls. Only this perfect combination of events could allow me to crack the top 10 list of an LG game. :
))
Street soccer was ok, but I feel there is a higher skill/luck ratio there, and my dice rolls were not enough to overcome this. : 
Hjallti at 20060509
The FAQ should be extended, but it would be best by a ntive English speaker rather then by me (the FAQ that is out now was written in the summer of 2003 or 2004 and sended to Richard as a gift :
) ) maybe someone could repeat this and make it much better :)
By the way it is FAQ and not FDR (Frequently demanded requests)... it just explains how the site works, not what people ask.
There have a lot of discussions on the time management and it seems though many are open to options most would like are happy with the 240/+36 rule as the standard (maybe championships and MC should stay like this, and RT could have different speeds: Fast RT’s and regular RT’s) 
Jonny ★ at 20060509
einstein.mc.2006.apr.1.104
“5way tie” by 5 participants too ;)))
Is that often? I dont know 
Ingo Althofer at 20060509
Jonny wrote:
> “5way tie” by 5 participants too ;)))
> Is that often? I dont know
When you have a 5player roundrobin, all
players of the same strength, and no advantage
of moving first in a game, then the chance of a
5way tie is exactly 3/128, which is approximately
2,34 percent.
Ingo. 
Marius Halsor ★ at 20060509
It seems to me it the chance is only 1/64. Did I calculate wrong? Are you sure about your numbers, Ingo?

Ingo Althofer at 20060509
On 31/128:
There are 1024 different outcomes.
The results in the first row may be "x 1 1 0 0"
or one of the other 5 arrangements.
When the first row is indeed “x 1 1 0 0”,
the second row may be either
(a) “0 x 1 1 0”
or
(b) "0 × 1 0 1"
or
© "0 × 0 1 1"
In cases (a) and (b) all remaining results are fixed.
In case © the lowest three players have 2 different
cycles for the internal “win direction”.
So, altogether there are 6 * (1 + 1 + 2) way to get a
5waytie. 24/1024 = 3 / 128.
Ingo.
By the way, it seems that different playing strengths will
only result in smaller probability for a fivewaytie. 
Marius Halsor ★ at 20060509
Thanks. I now found the missing 8 ways this can happen. One should think that when working only with 0 and 1, it would be easy to tell them apart, but then again... :)

Ingo Althofer at 20060510
One interesting thing is:
When we would NOT have ratings on LG, and when
the mixture of participants in tournaments would
be random, then the freqency of 5wayties (and
also the frequency of lowerranked ties) would
be an indication for the spreading of playing
strengths:
"the more 5wayties, the more similar
would the playing strengths be."
Ingo Althofer. 
Ingo Althofer at 20060518
SOme of my secondyear students in Jena were so kind
to compute the number of 7wayties for 7player
tournaments:
there are 2640 cases out of the 2tothe21.
So the quota is about 0,126 percent.
Open questions:
(i) exact number for 9wayties with 9 players
(should be computable exactly)
(ii) MonteCarlo approximations for (2n+1)ties
with (2n+1) players, n=5,6,7,8,...
Thanks in advance for all constructive feedback.
Ingo. 
ypercube ★ at 20060518
I meant 6way tie in 6player tournament. On second thought this is impossible in games like Einstein where there is no draw. No 4way ties in 4player tournaments either.

Stephen Silver at 20060518
Ingo: This is sequence A007079 in Sloane’s encyclopedia: 1, 2, 24, 2640, 3230080, 48251508480, 9307700611292160, 24061983498249428379648, 855847205541481495117975879680, ...

Ingo Althofer at 20060518
> This is sequence A007079 in Sloane’s encyclopedia:
> 1, 2, 24, 2640, 3230080, 48251508480, 9307700611292160,
> 24061983498249428379648, 855847205541481495117975879680, ...
Thanks, Stephen!
Ingo.