Modified Pot value experiment

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Modified Pot value experiment

Post by maglor » Thu Feb 08, 2018 9:25 pm

This thread is to explain, discuss, and perhaps gather new input and analysis on the open project discussed in the following post : http://www.internationalsaimoe.com/foru ... 61#p413961" onclick="window.open(this.href);return false;

Let's start with 2017 with character that was most talked about for the entire year, REM ( Megumi, the tiara winner, received lion-size of attention during elimination period, which, surprisingly, is typical of most Tiara winners. It actually is uncommon for #1 or 2 seed to win the elimination period )

Going into the 1st match of 2017, REM would have 100 points, just like everyone else. Her opponent Saten Ruiko also would have 100 points in her pot.

Now, since we are dealing with 3 separate percentages for the "betting amount" it may be easier to consider that every one has actually 3 pots, one titled N=0.1, another titled N=0.2, and the last titled N=0.5. All 3 pots have 100 points for both characters.

For the match Rem and Ruiko both pulls out appropriate percentage of what's inside the pot as their bets.

from N=0.1 pot, they pull out 10 on to the betting table, leaving 90 behind. N=0.1 table would have total of 10+10 = 20 points
from N=0.2 pot, they pull out 20 on to the betting table, leaving 80 behind. N=0.2 table would have total of 20+20 = 40 points
from N=0.5 pot, they pull out 50 on to the betting table, leaving 50 behind. N=0.5 table would have total of 50+50 = 100 points

The result of Aquamarine 1 match was 709 votes for Saten Ruiko and 1173 votes for Rem . Since Rem's VF% is 62.327%, she would receive 62.327% of the values on the table, while Ruiko will take the remaining 37.673%

The amount they take back is as follows

Rem take N=0.1 : 12.46546227
Rem take N=0.2 : 24.93092455
Rem take N=0.5 : 62.32731137
Ruiko take N=0.1 : 7.534537726
Ruiko take N=0.2 : 15.06907545
Ruiko take N=0.5 : 37.67268863

Note that while they contributed the same amount into the pot, they take back different amount. After they split the pot, Rem and Ruiko would both have new values for each of their three pots

Rem's new pot N=0.1 : 102.4654623
Rem's new pot N=0.2 : 104.9309245
Rem's new pot N=0.3 : 112.3273114
Ruiko's new pot N=0.1 : 97.53453773
Ruiko's new pot N=0.2 : 95.06907545
Ruiko's new pot N=0.3 : 87.67268863


Thus ended the first round.

Now, in the 2nd round Rem meets Sento Isuzu. Isuzu lost to Kōsaka Reina with VF of 49.22%. Her pot entering into Round 1 is as follows

Sento Isuzu New Pot N=0.1 : 99.84343091
Sento Isuzu New Pot N=0.2 : 99.68686181
Sento Isuzu New Pot N=0.5 : 99.21715453


We start the process again, but now, note that they contribute different amount into each pot

Into N=0.1 pot, Rem contributes 10.247, Isuzu contributes 9.984. The total for the pot is 20.23088932
Into N= 0.2 pot Rem contributes 20.986. Isuzu contributes 19.937. The total for the pot is 40.92355727
Into N=0.5 pot Rem contributes 56.164. Isuzu contributes 49.609. The total for the pot is 105.7722329

The match was 1601 to 874 in favor of Rem. Thus Rem takes 64.69% of the pot

The amount they take back is as follows

Rem take N=0.1 : 13.08672881
Rem take N=0.2 : 26.47216775
Rem take N=0.5 : 68.42074543
Isuzu take N=0.1 : 7.144160511
Isuzu take N=0.2 : 14.45138952
Isuzu take N=0.5 : 37.35148751

Their new pot values are now as follows

Rem's new pot N=0.1 : 105.3056449
Rem's new pot N=0.2 : 110.4169074
Rem's new pot N=0.3 : 124.5844011
Sento Isuzu New Pot N=0.1 : 97.00324833
Sento Isuzu New Pot N=0.2 : 94.20087897
Sento Isuzu New Pot N=0.5 : 86.96006478


Thus ends Round 2

Now in Round 3, Rem meets Kasugano Sora. Kasugano Sora enters into the match with pot values as follows

Kasugano Sora new pot n=0.1 : 101.627352
Kasugano Sora new pot n=0.2 : 103.2188397
Kasugano Sora new pot n=0.5 : 107.7781175


We do the process again


Into N=0.1 pot, Rem contributes 10.531, Isuzu contributes10.163. The total for the pot is 20.69329968
Into N= 0.2 pot Rem contributes 22.083. Isuzu contributes 20.644. The total for the pot is 42.72714943
Into N=0.5 pot Rem contributes 62.292. Isuzu contributes 53.889. The total for the pot is 116.1812593

The match was 1031 to 577 in favor of Rem. Thus Rem takes 64.12% of the pot



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Re: Modified Pot value experiment

Post by IGNITE » Sat Feb 10, 2018 4:20 am

maglor wrote:It actually is uncommon for #1 or 2 seed to win the elimination period.
I went and had a look after reading this, the result is 5/10 tiara winners having #1 or #2 seed for elimination period, it's not really uncommon.
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maglor
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Re: Modified Pot value experiment

Post by maglor » Sat Feb 10, 2018 4:48 pm

IGNITE wrote:
maglor wrote:It actually is uncommon for #1 or 2 seed to win the elimination period.
I went and had a look after reading this, the result is 5/10 tiara winners having #1 or #2 seed for elimination period, it's not really uncommon.
SpoilerShow
2008 Fate Testarossa RS 1st
2009 Katsura Hinagiku RS 11th
2010 Akiyama Mio RS 3rd
2011 Misaka Mikoto RS 2nd
2012 Tachibana Kanade Nova PS1 1st
2013 Gokō Ruri (Kuroneko) Stella PS1 2nd
2014 Itsuka Kotori Nova PS1 6th
2015 Chitanda Eru Stella PS1 3rd
2016 Shana Female CVP 2nd
2017 Katō Megumi Female CVP 7th
Nice analysis. So, chance of #1 or 2 winning is a coin toss
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Re: Modified Pot value experiment

Post by Homura » Sat Feb 10, 2018 6:09 pm

The time for #4 or #5 seed winning the Tiara lies ahead, possibly in the near future~
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Re: Modified Pot value experiment

Post by ~Baumkuchen-kun~ » Thu Feb 22, 2018 4:50 am

Gaaaah, this feels so weird to look at after all these years on this forum
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