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On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket.
If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)?
That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
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On July 23 2013 06:25 Talin wrote:
It's bad either way. Tournaments are not meant to determine (let alone aid) better players, they're meant to determine winners. The format doesn't matter in that context.
Extended series is just a tunnel vision solution to the inherent ugliness of double elimination systems when it comes higher-lower bracket interaction. There's really no better alternative to extended series - they're all terrible, because the underlying format (double elimination) is terrible.
Wow, you sound like me. Talin am I your evil twin, or is it the other way around?
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On July 23 2013 05:59 wingpawn wrote:
Okay, so long story short, instead of no odds/1 game odds in Bo3 or Bo5, winner bracket guy gets 1 game/2 game odds in Bo7, depending on his previous performance against that rival, right? Strange, but might be acceptable for many, I guess.
Not exactly, which is why I gave the example in the way that I did.
In double elimination, there are two separate series with no scoring overlap and no influence from the previous meeting. If the winner's bracket player wins, it's over. If the loser's bracket player wins, the scores don't carry over and there is a second series where winner takes all. Think of it as the loser's bracket player has to eliminate the winner's bracket player twice, since he hasn't been eliminated at all yet.
Extended series has a starting score from their winner's bracket meeting and both players are playing to a set number of wins. One player starts down 1-2 games, but you can display the score and say they're playing to 4 and it makes sense. Whereas, if I put a 1-1 score up during a normal double elimination, you don't know if it's the first series or second series.
There are only really two important differences (aside from the clarity of showing the score):
1) If the Loser's bracket player lost 1-2 in the first meeting, that 1 win counts in the finals in extended series, but not in double elimination.
2) If the Loser's bracket player wins 2-1 in the first series of the finals, the 1 win for the Winner's bracket player counts in the second series in extended series, but not in the double elimination.
On July 23 2013 05:59 wingpawn wrote:It's largely a matter of taste, but I always felt that 'the underdog' shouldn't be punished with any point disadvantage at all. After all, he is so often punished for 1-2 defeat in super-close series that could've gone either way. Maybe the losers' brackets should merge with winners' at earlier stage of the tournament? Or, perhaps, to compensate for having 'weaker' players in their bracket, losers should make some sort of group stage between each other to increase the number of games and difficulty of getting through the bracket, so it could match the difficulty of winners?
Being the underdog and coming from the loser's bracket of a double elimination are two different things.
If you make it all the way through a tournament without losing a match, why should you be on an even playing field with someone who lost once already? That holds true whether the loser's bracket player is Goody or Innovation. It has nothing to do with weaker players vs stronger players and everything to do with having a bracket that rewards you for your performance.
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On July 23 2013 06:33 wingpawn wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket. If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)? That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
The one behind receives mental discomfort from the very knowledge that he or she is behind. Mental discomfort can lead to worse play, demoralization, etc. On the flip side, the one ahead gains mental comfort from knowing he or she is ahead, and in games where you accumulate points through various methods of scoring (e.g. soccer), the winner after scoring one point just has to sit back, defend, and let the clock run out.
This is why I've never agreed with double elimination brackets, nor the extended series, because it unnecessarily complicates determining who is the winner, and throws in factors other than player skill in determining the winner as well. IMO pool play based on seeding + single elimination brackets are the best way to go, but that could just be my bias talking.
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@TrippSC2 - Understood. Somehow, I screwed up the logic of double elimination format. Guess I'm just tired. Or dumb. 
My new proposition that just crossed my mind: losers bracket dude has no game disadvantage, but has to offrace in the exact number of games he previously lost to his winners' bracket opponent. Wouldn't this provide even more games and fun?
@Day[9] - ohhh, I see. Actually, I should've figured that out earlier lol (GOOD player can't beat BAD again, cause in your example, he was beaten by BAD before, so there's no point of saying again). By the way, I'm quite sure that in this case, psychology backs up pure statistics even more.
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On July 23 2013 06:33 wingpawn wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket. If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)? That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
Fuck!! I mistyped! I meant to type "meets" but I typed "beats"
Fixed!
[edit]
I completely understand where your confusion came from, but just in case anyone else is still a bit confused: there is literally 0 psychology in what I've typed. It's just straight statistics.
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I think Day[9] is onto what is happening here. Here is a simplified example with numbers. I made these simplifications: regular series are BO1. There is one Noob in the tournament, he has a 10% winning chance against all the pros. Suppose the brackets are such that he plays pro1 in WR2, and the only time they ever meet again is LR4. (I skipped WR1 because LR1 acts a little differently than other loser rounds).
WR2 pro1>noob 0.9
WR3 prox<pro1 0.5
LR2 noob>prox 0.1
LR3 noob>prox 0.1
LR4 pro1 vs noob 0.9*0.5*0.1*0.1 = 0.0045
No extended (BO1) : pro1 0.90 * 0.0045 = 0.004050
Extended (pro up 1-0): pro1 0.99 * 0.0045 = 0.004455
WR2 noob>pro1 0.1
WR3 prox>noob 0.9
LR2 pro1>prox 0.5
LR3 pro1>prox 0.5
LR4 noob vs pro1 P=0.1*0.9*0.5*0.5 = 0.0225
No extended (BO1) : pro1 0.90 * 0.0225 = 0.020250
Extended (noob up 1-0): pro1 0.81 * 0.0225 = 0.018225
No extended 0.004050 + 0.020250 = 0.02430
Extended 0.004455 + 0.018225 = 0.02268
No extended series gives pro1 a 0.02430 chance to advance.
Extended series gives pro1 a 0.02258 chance to advance.
The issue is that without considering the rest of the tournament, you would expect pro1 to be up 1-0 against noob with a probability 0.9. But since noob usually fails in the loser rounds:
If the players meet in LR4, probability pro1 will be up 1-0:
0.0045 / (0.0045+0.0225) = .167
In fact if they meet in LR4, it's overwhelmingly likely that this happened because noob got lucky in WR2 by beating pro1 1-0. And on top of that you extend the series. Pro1 also benefits from this in the reverse case, but that case is far less likely to actually happen.
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On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD.
The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around?
The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough).
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...or just forget it all and set up a rule that by shamefully dropping to the losers bracket through losing to BAD, GOOD himself becomes BAD and BAD becomes GOOD - as he just proved himself better than a GOOD player. Problem solved 
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The part I identify with in Day[9]'s idea is that I also want GOOD to win. But I don't think GOOD deserves any advantages against BAD if he/she already lost to BAD once. BAD took maps. BAD should get credit for those maps and GOOD should have to fight for them back. Hopefully GOOD took a map in series 1. That means GOOD has to deliver 3 maps to BAD's 1, which would prove that GOOD can win more maps.
Somewhere I saw it suggested that BAD should go to a Bo5 with a +1. That means GOOD has to win 3 maps to BAD's 1, which is exactly what happens if GOOD takes 1 map in series#1 and it goes to an Extended Bo7. All shortening the Extended series does is give the losing player an advantage by ignoring lost maps.
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On July 23 2013 07:15 wingpawn wrote:...or just forget it all and set up a rule that by shamefully dropping to the losers bracket through losing to BAD, GOOD himself becomes BAD and BAD becomes GOOD - as he just proved himself better than a GOOD player. Problem solved
I like you. Let's be friends.
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On July 23 2013 07:07 kingNothing42 wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD. The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough).
That usually happens if they're really, really good players with a strong playbook. You know who also came back in extended series? Leenock. He was on fire that time though. If someone gets red hot at a LAN good luck taking them out.
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On July 23 2013 07:07 kingNothing42 wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around?
BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4.
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On July 23 2013 07:04 KillerDucky wrote:I think Day[9] is onto what is happening here. Here is a simplified example with numbers. I made these simplifications: regular series are BO1. There is one Noob in the tournament, he has a 10% winning chance against all the pros. Suppose the brackets are such that he plays pro1 in WR2, and the only time they ever meet again is LR4. (I skipped WR1 because LR1 acts a little differently than other loser rounds).
WR2 pro1>noob 0.9
WR3 prox<pro1 0.5
LR2 noob>prox 0.1
LR3 noob>prox 0.1
LR4 pro1 vs noob 0.9*0.5*0.1*0.1 = 0.0045
No extended (BO1) : pro1 0.90 * 0.0045 = 0.004050
Extended (pro up 1-0): pro1 0.99 * 0.0045 = 0.004455
WR2 noob>pro1 0.1
WR3 prox>noob 0.9
LR2 pro1>prox 0.5
LR3 pro1>prox 0.5
LR4 noob vs pro1 P=0.1*0.9*0.5*0.5 = 0.0225
No extended (BO1) : pro1 0.90 * 0.0225 = 0.020250
Extended (noob up 1-0): pro1 0.81 * 0.0225 = 0.018225
No extended 0.004050 + 0.020250 = 0.02430
Extended 0.004455 + 0.018225 = 0.02268
No extended series gives pro1 a 0.02430 chance to advance. Extended series gives pro1 a 0.02258 chance to advance. The issue is that without considering the rest of the tournament, you would expect pro1 to be up 1-0 against noob with a probability 0.9. But since noob usually fails in the loser rounds: If the players meet in LR4, probability pro1 will be up 1-0: 0.0045 / (0.0045+0.0225) = .167 In fact if they meet in LR4, it's overwhelmingly likely that this happened because noob got lucky in WR2 by beating pro1 1-0. And on top of that you extend the series. Pro1 also benefits from this in the reverse case, but that case is far less likely to actually happen.
Yes! This exactly!
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On July 23 2013 07:27 Day[9] wrote:Show nested quote +On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4.
BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)?
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On July 23 2013 01:58 Alryk wrote:
You are ignoring the fact of # of series lost. One player, even with better map score, has lost two series. Player B has only lost one. We aren't looking for the best player vs player B, but the best player, which takes into account all of the matches. The same thing happens in GSL.
Player A 2-0 Player B
C 2-0 D
C > A
B > D
B 2-1 A
Does A still deserve to advance just because he has a better map score vs player B? He still lost one more series than B did, therefore as an overall player he is not as skilled on that day.
Yes, GSL groups have the same map score issue, and I think the 2nd advancement match isn't fair. In my opinion, GSL style groups should have extended series.
It's easy to see how GSL groups map directly to a 4 person double-elim bracket w/o a Grand Final (just draw it on paper really fast if you can't see it).
Player B won two series, but he/she has not beaten Player A.
Here is how I see it. Take all of the information prior to the last match. What do we know? We know Player C won the Winner's Bracket. Player D lost in the Loser's Bracket with no rematches. These two are removed from the problem. Player C advances from the group, and Player D is out.
Now consider A and B. They are meeting in the Loser's Bracket final. This match determines who 'deserves' to be in the Grand Final (i.e. advance from the group). If B bests A 2-1, then overall map scores are A: 3 maps, B: 2 maps. Why does B deserve to be in the Grand Final?
In my opinion, B doesn't deserve to be in the Grand Final until B proves he/she is better than A. Hence invoke the extended series rule so B can prove this to me. If B wins the extended series, then B will be 2:1 in group series and have the overall better map score 4:2 when compared to A.
TLDR: It's the same argument from my first post. If you think head to head map scores are important (like I do and I think MLG does) then you are in favor of extended series. If you don't care about map scores and order of series wins (some kind of argument like later rounds are more important) then you probably think extended series is a useless or hurtful rule.
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On July 23 2013 07:43 kingNothing42 wrote:Show nested quote +On July 23 2013 07:27 Day[9] wrote:On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4. BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)?
I have made no statements on whether the format is poor or good (or any opinions for that matter). I'm simply providing an explanation for the counter intuitive results that OP presented.
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On July 23 2013 08:11 Day[9] wrote:Show nested quote +On July 23 2013 07:43 kingNothing42 wrote:On July 23 2013 07:27 Day[9] wrote:On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4. BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)? I have made no statements on whether the format is poor or good (or any opinions for that matter). I'm simply providing an explanation for the counter intuitive results that OP presented.
That is fair. What you've stated could definitely explain the difference between a statistical calculation of the entire tournament vs a mathematical representation of the outcome of only the second match. Agreed!
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i already did the conditional probability stuff back on page 1, read the whole thread guys.
On July 23 2013 02:21 jalstar wrote:Imagine a tournament with double elimination Bo1, and another tournament with double elimination Bo1 extended into Bo3 in rematches. Now take two players who meet in the first round and will always meet each other in the loser's bracket regardless of who wins the initial game. In the first tournament, the better player will have x chance to advance, where x is his chance of winning a Bo1 against the worse player. In the second tournament, if the better player wins the first match, he has (1 - (1-x)^2) chance of advancing. (1 minus the chance of losing 2 Bo1s in a row) If the worse player wins the first match, the better player has x^2 chance of winning the extended series (2 Bo1s in a row) So for the second tournament, the better player has x*(1 - (1-x)^2) + (1-x)*x^2 chance to advance, based on simple conditional probability. This is larger than x for all x between 0.5 and 1, as seen here: http://www.wolframalpha.com/input/?i=x*(1 - (1-x)^2) + (1-x)*x^2 = xIt really looks like extended series benefits the better player to me, and I don't see why this would change with Bo3 extended to Bo7.
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On July 23 2013 08:52 jalstar wrote:i already did the conditional probability stuff back on page 1, read the whole thread guys. Show nested quote +On July 23 2013 02:21 jalstar wrote:Imagine a tournament with double elimination Bo1, and another tournament with double elimination Bo1 extended into Bo3 in rematches. Now take two players who meet in the first round and will always meet each other in the loser's bracket regardless of who wins the initial game. In the first tournament, the better player will have x chance to advance, where x is his chance of winning a Bo1 against the worse player. In the second tournament, if the better player wins the first match, he has (1 - (1-x)^2) chance of advancing. (1 minus the chance of losing 2 Bo1s in a row) If the worse player wins the first match, the better player has x^2 chance of winning the extended series (2 Bo1s in a row) So for the second tournament, the better player has x*(1 - (1-x)^2) + (1-x)*x^2 chance to advance, based on simple conditional probability. This is larger than x for all x between 0.5 and 1, as seen here: http://www.wolframalpha.com/input/?i=x*(1 - (1-x)^2) + (1-x)*x^2 = xIt really looks like extended series benefits the better player to me, and I don't see why this would change with Bo3 extended to Bo7.
This analysis is spot on if you assume that the extended series happens immediately following the first match. However, this analysis doesn't account for either player being eliminated from the tournament in other ways. This is what I posted about above: if the good player wins in the upper bracket, it's unlikely that the players will meet again. If the bad player wins in the upper bracket, it's more likely that the players will meet again.
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EPT
