Life In 19x19

4/9/15 - 8th game;

Choi Jeong defeated Cao Youyin by resign.

Players;
Korea:Kim Hyemin, Choi Jeong, Kim Chaeyoung, Oh Yoojin, Oh Jungah
China:Yu Zhiying, Cao Youyin, Song Ronghui, Li He, Wang Chenxing
Japan:Xie Yimin, Okuda Aya, Kibe Natsuki, Fujisawa Rina, Hoshiai Shio

Bold = remaining players

A question for game theory specialists:

In win & continue team events like this, is it best to keep your best player as the last player up as a sort of "iron goalkeeper" (a phrase used of Nie Weiping and Yi Ch'ang-ho in such events), as seems to be the general case.

I would have thought there was a case for keeping the weakest player till the end, on the assumption he/she may not even be needed.

John Fairbairn wrote:A question for game theory specialists:

In win & continue team events like this, is it best to keep your best player as the last player up as a sort of "iron goalkeeper" (a phrase used of Nie Weiping and Yi Ch'ang-ho in such events), as seems to be the general case.

I would have thought there was a case for keeping the weakest player till the end, on the assumption he/she may not even be needed.

The same question arises in penalty kicks in soccer, though the dynamics are different. In that sport, if you save your best kicker for late, you might have already lost before they get a chance.

At least with win and continue tourneys, one is assured all of your players will get a shot before elimination.

The psychology of assigning an iron goalkeeper versus striving for a crushing sweep is interesting. Maybe there is less pressure early, so less-proven players might perform better then than later.

If we take a simple case of two teams of 3, one of three middling strength players (call them 5p) and another of one middle (5p), one strong (9p) and one weak (1p) then assuming 5p vs 5p is 50:50 and 9p vs 5p is the same as 5p vs 1p, for example 70:30, then whether the mixed team goes in increasing or decreasing order of strength doesn't actually change the overall probability of win (it's 59.7% for the mixed team with those numbers). Probably there is some neat argument to show that but I just crunched the numbers as my brain has atrophied from years of disuse What would happen with two mixed teams in either same or opposite order I don't know but my gut feeling is it would similarly have the same probability. Of course in real life probabilities of wins are not independent, some players are particularly good or weak against others etc so it all gets rather complex.

Simple example: 2 player teams, where player A beats each opponent with probability a and player B beats each opponent with probability b. Player A is the first player.

The team wins the match if Player A beats both opponents, with probability, a*a, or if Player A loses the second game and player B wins the next game, with probability, a*(1-a)*b, or if Player A loses the first game and Player B wins both games, with probability, (1-a)*b*b. The total probability of winning is a*a*(1-b) + a*b + b*b*(1-a). Obviously, it does not matter which player plays first.

OTOH, there are physical and psychological questions to consider. The probability of winning a game may depend upon circumstances. Suppose that it goes down with physical fatigue. Then you want to start with the most physically fit player, who may well be younger and less skilled, because the less fit player will probably play fewer games. Suppose that it goes down with pressure. If Player A loses, then Player B will have the pressure of winning both games. Usually the better player will stand up better under pressure. Again, this argues for starting with the less skilled player. Also, there is the question of the future of the team. If the first player is less skilled, then if he wins the match by himself, it will provide a psychological boost which may help him to advance in the future. It may also lower the confidence of the other team, since the winning team beat them "with one hand tied behind our back".

In general, the player order does matter. As an extreme example, for two teams with players {A1,A2} and {B1,B2}, if P(A1>B1)=1, P(A1>B2)=0, P(A2>B1)=0, p(A2>B2)=1, either team can arrange a win if they get to pick the player order after the other team first announces their order. The winning strategy is to set the lineup so that you win-lose-win in that order.

4/10/15 - 8th game;


Choi Jeong defeated :Yu Zhiying by resign.

5th Huanglongshi Cup goes to Korea !!!!!!!!!!!!!!

Players;
Korea:Kim Hyemin, Choi Jeong, Kim Chaeyoung, Oh Yoojin, Oh Jungah
China:Yu Zhiying, Cao Youyin, Song Ronghui, Li He, Wang Chenxing
Japan:Xie Yimin, Okuda Aya, Kibe Natsuki, Fujisawa Rina, Hoshiai Shio

Bold = remaining players