EPTYou're playing WarCraft II Orcs and Humans, and playing as Humans. What are the odds of a mirror opponent? 1 in 2, or 50%
What are the odds in StarCraft which has an extra race? Clearly not 50%.
[PL] October Imbalance - Page 5
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siv00
261 Posts
You're playing WarCraft II Orcs and Humans, and playing as Humans. What are the odds of a mirror opponent? 1 in 2, or 50% What are the odds in StarCraft which has an extra race? Clearly not 50%. | ||
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diehilde
Germany1596 Posts
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okum
France5777 Posts
You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? | ||
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QuakerOats
United States1024 Posts
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ZeaL.
United States5955 Posts
On October 28 2009 03:22 okum wrote: Let's consider a slightly modified problem. You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? Far too much effort for an obscure joke lol. | ||
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okum
France5777 Posts
On October 28 2009 03:39 ZeaL. wrote: This is what the internet is all about.Far too much effort for an obscure joke lol. | ||
TheYango
United States47024 Posts
On October 28 2009 03:22 okum wrote: Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? The real question is why you played Hyuk on Monty Hall in the first place, given it's anti-zerg statistics slant.  + Show Spoiler + Yes I get the reference. | ||
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Keniji
Netherlands2569 Posts
On October 28 2009 03:22 okum wrote: Let's consider a slightly modified problem. You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? did you just put the monty hall problem(paradox - i love your second map choice) in a starcraft scenario? awesome! In school it would be much easier to understand it this way. | ||
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OpticalShot
Canada6330 Posts
STA101 The difference between 33% and 50%. Includes: 20 different examples for the same problem. | ||
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Drakonis
Canada97 Posts
Player A / Player B 1) T ---- vs---- T 2) T ----vs---- P 3) T ----vs---- Z 4) P ----vs---- T 5) P ----vs---- P 6) P ----vs---- Z 7) Z ----vs---- T 8) Z ----vs---- P 9) Z ----vs---- Z As you can see, there are 9 different matchup possibilities, 3 of which are mirrors. Therefore, 3/9 = 1/3 = 33.33333333333% chance of a mirror matchup. | ||
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Signet
United States1718 Posts
On October 28 2009 00:18 ]343[ wrote: and to address the "more of some race" issue: say team 1 has T1 terrans, P1 protosses, Z1 zergs, and let X1 = T1+P1+Z1 then the total # of ways is say team 2 has T2 terrans, P2 protosses, Z2 zergs, and let X2 = T2+P2+Z2 PROBABILITY = TOTAL # OF DESIRABLE / TOTAL # (but if permutations matter on top, they must matter on the bottom!... using combinations is the same; you just cancel) Total #: X1*X2 Total # desirable (i.e. mirror): T1T2 + P1P2 + Z1Z2 So the probability of a mirror in this match is (T1T2+P1P2+Z1Z2)/[ (T1+P1+Z1)(T2+P2+Z2) ] in the case where T1=T2=P1=P2=Z1=Z2 (i.e., the ideal world where every team has equal numbers of T/P/Z and equal number of players), this evaluates to (1+1+1)/[ (1+1+1)(1+1+1) ] = 1/3 Nicely written, this is the right way to do the calculation of this real-world scenario. I think it still needs to account for the 1 player of each race rule. I would make each team a vector of [1 1 1] + [(Ti-1)/(Xi-3) (Pi-1)/(Xi-3) (Zi-1)/(Xi-3)] to represent the expected number of players of each race that that team will send out for its first 4 matches. Then do vector cross for teams i=1 and i=2. It would end up being exactly 1/3, like you said, if Ti=Pi=Zi and the 4th player is equally likely to be any race (ie, the races have the same skill distribution). | ||
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