Tournament Rules and Information

[_H2O]

For me, just because you can win on a counter pick doesn't mean it's right.

I think what you are trying to say, although I have never heard it said this way, Is that either way you must win the same number of winner picks games. The winner picks way simply allows more games to be played in a series.

The assumption being that each game is somewhat even and that somehow by having to mentality handle the emotions of a come back makes for a better player. And the somewhat fake comeback window created by the winner picks approach makes for more games and a better show.

[lesllamas]

For me, just because you can win on a counter pick doesn't mean it's right.

I think what you are trying to say, although I have never heard it said this way, Is that either way you must win the same number of winner picks games. The winner picks way simply allows more games to be played in a series.

The assumption being that each game is somewhat even and that somehow by having to mentality handle the emotions of a come back makes for a better player. And the somewhat fake comeback window created by the winner picks approach makes for more games and a better show.

No, and no. There was a whole thread where this was laid out, and I don't think you understand or want to understand. You cannot deny that your opinions are coming from the place of a player who almost always wins his series, often in 3-0 fashion, who loves to mirror people. Of course you don't want to play a 3-0 series without getting to counterpick at all yourself. But that doesn't make it any less bullshit.

You can take just about any major sport to see this same idea in action. Let's say the Lakers are playing the Celtics in an exhibition match--first to 5 baskets.


Scenario 1:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, but they turn it over, and the Lakers score. 2-0 Lakers
The Lakers now for some ungodly reason get to possess the ball from the inbound, and score. 3-0 Lakers

Scenario 2:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, and score on their possession. 1-1 tie
The Lakers inbound the ball, but the Celtics steal it and score. 2-1 Celtics
The Celtics now for some ungodly reason get to inbound the ball. 3-1 Celtics
--This scenario is even worse, because under alternating possession (pick), the Celtics get to inbound the ball twice while the Lakers get to inbound the ball once.



No competition with successive interactions (multiple possessions, multiple games in a series, etc), takes place in a vacuum. All rulesets are designed so that no team wins in such a way that they have an unfair number of their counterpicks before their opponent can have a chance at theirs. Even sports with fixed "counterpicks" due to scheduling lay their series out in such a way to maximize this. Take a look at the ordering of the NBA finals, Stanley Cup finals, World Series, anything. You simply have no logical leg to stand on, but TBH it doesn't really seem to matter. You're going to do what it is that you want to do, and that's just fine. It's not my business if you hold tournaments with incredibly fair or unfair rulesets, or something in between.

[_H2O]

For me, just because you can win on a counter pick doesn't mean it's right.

I think what you are trying to say, although I have never heard it said this way, Is that either way you must win the same number of winner picks games. The winner picks way simply allows more games to be played in a series.

The assumption being that each game is somewhat even and that somehow by having to mentality handle the emotions of a come back makes for a better player. And the somewhat fake comeback window created by the winner picks approach makes for more games and a better show.

No, and no. There was a whole thread where this was laid out, and I don't think you understand or want to understand. You cannot deny that your opinions are coming from the place of a player who almost always wins his series, often in 3-0 fashion, who loves to mirror people. Of course you don't want to play a 3-0 series without getting to counterpick at all yourself. But that doesn't make it any less bullshit.

You can take just about any major sport to see this same idea in action. Let's say the Lakers are playing the Celtics in an exhibition match--first to 5 baskets.


Scenario 1:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, but they turn it over, and the Lakers score. 2-0 Lakers
The Lakers now for some ungodly reason get to possess the ball from the inbound, and score. 3-0 Lakers

Scenario 2:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, and score on their possession. 1-1 tie
The Lakers inbound the ball, but the Celtics steal it and score. 2-1 Celtics
The Celtics now for some ungodly reason get to inbound the ball. 3-1 Celtics
--This scenario is even worse, because under alternating possession (pick), the Celtics get to inbound the ball twice while the Lakers get to inbound the ball once.



No competition with successive interactions (multiple possessions, multiple games in a series, etc), takes place in a vacuum. All rulesets are designed so that no team wins in such a way that they have an unfair number of their counterpicks before their opponent can have a chance at theirs. Even sports with fixed "counterpicks" due to scheduling lay their series out in such a way to maximize this. Take a look at the ordering of the NBA finals, Stanley Cup finals, World Series, anything. You simply have no logical leg to stand on, but TBH it doesn't really seem to matter. You're going to do what it is that you want to do, and that's just fine. It's not my business if you hold tournaments with incredibly fair or unfair rulesets, or something in between.

Thanks for the feedback. We will consider it again.

[lesllamas]

TBH I've been impressed with your rulesets in almost every other area. I don't think you guys haven't thought things through. One thing I'd be fascinated to know is how you come up with the map pool for each round? I know next to nothing about the top level meta, as I don't play at that level. So I don't have very good opinions on what maps allow for harder or weaker counterpicks. Do you guys take the "counterpick-ability" of the maps into consideration and try to distribute them in such a way that under alternating pick, one player does not get two super strong counterpicks while the other gets more neutral maps? I was thinking about this a couple weeks ago, and it struck me as one potential advantage (that I had not considered) of having a set system of counterpicks. But I don't really know how the community views the map pool with regards to how it affects counterpick strength.

[Jaeger]

For me, just because you can win on a counter pick doesn't mean it's right.

I think what you are trying to say, although I have never heard it said this way, Is that either way you must win the same number of winner picks games. The winner picks way simply allows more games to be played in a series.

The assumption being that each game is somewhat even and that somehow by having to mentality handle the emotions of a come back makes for a better player. And the somewhat fake comeback window created by the winner picks approach makes for more games and a better show.

No, and no. There was a whole thread where this was laid out, and I don't think you understand or want to understand. You cannot deny that your opinions are coming from the place of a player who almost always wins his series, often in 3-0 fashion, who loves to mirror people. Of course you don't want to play a 3-0 series without getting to counterpick at all yourself. But that doesn't make it any less bullshit.

You can take just about any major sport to see this same idea in action. Let's say the Lakers are playing the Celtics in an exhibition match--first to 5 baskets.


Scenario 1:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, but they turn it over, and the Lakers score. 2-0 Lakers
The Lakers now for some ungodly reason get to possess the ball from the inbound, and score. 3-0 Lakers

Scenario 2:
The Lakers win the tip, and score a basket on their possession. 1-0 Lakers
The Celtics inbound the ball, and score on their possession. 1-1 tie
The Lakers inbound the ball, but the Celtics steal it and score. 2-1 Celtics
The Celtics now for some ungodly reason get to inbound the ball. 3-1 Celtics
--This scenario is even worse, because under alternating possession (pick), the Celtics get to inbound the ball twice while the Lakers get to inbound the ball once.



No competition with successive interactions (multiple possessions, multiple games in a series, etc), takes place in a vacuum. All rulesets are designed so that no team wins in such a way that they have an unfair number of their counterpicks before their opponent can have a chance at theirs. Even sports with fixed "counterpicks" due to scheduling lay their series out in such a way to maximize this. Take a look at the ordering of the NBA finals, Stanley Cup finals, World Series, anything. You simply have no logical leg to stand on, but TBH it doesn't really seem to matter. You're going to do what it is that you want to do, and that's just fine. It's not my business if you hold tournaments with incredibly fair or unfair rulesets, or something in between.

Oh god bringing in fucking sports just made it confusing as hell

[Jaeger]

TBH I've been impressed with your rulesets in almost every other area. I don't think you guys haven't thought things through. One thing I'd be fascinated to know is how you come up with the map pool for each round? I know next to nothing about the top level meta, as I don't play at that level. So I don't have very good opinions on what maps allow for harder or weaker counterpicks. Do you guys take the "counterpick-ability" of the maps into consideration and try to distribute them in such a way that under alternating pick, one player does not get two super strong counterpicks while the other gets more neutral maps? I was thinking about this a couple weeks ago, and it struck me as one potential advantage (that I had not considered) of having a set system of counterpicks. But I don't really know how the community views the map pool with regards to how it affects counterpick strength.

I think there are too many civs and maps in AOE3 to take into account the stuff which you said when making map sets. I'm not sure how well I can explain this, but I'll try my best:

With a couple outliers (Indonesia) you can make 3 main categories:
a) Land TP maps
b) Land no TP maps
c) Water maps (I think all ESOC water maps except indonesia have a TP, so it isn't worth making a water non TP category)
(You can almost combine sets a and c because the majority of players just ignore water. and I think Indonesia is the only non TP water map)

Whoever wins a matchup doesn't usually change within a category; i.e. if civ A beats civ B on a map from set a, you can pretty much assume civ A beats civ B on all maps in set a
Each set has multiple top civs that are pretty balanced within themselves. If you know how to play any civ which is good for that set of maps, you can't really get counterpicked.

For example, let's say we are in category a. Civs that come to mind are Port, Spain, France, Germany(?). If you can play one of these, you can't really get counter-picked on any Land TP maps. In category b, if you know Aztec, India, British, (maybe some others, I don't want to think about it), you also can't really get counterpicked.

There are some exceptions of course (civs that are strong on a certain set of maps, but still have counterpicks on that set): Japan is good on non TP maps, but you don't want to pick it first since you can get counterpicked with Brit But as long as you don't pick civs with obvious counterpicks on a given set of maps, you should be fine. The main point is that if a player gets a bad matchup, it's mostly their fault for not knowing enough civs, or not planning ahead on which civs to save for when.

[doublehelix2569]

From what I can tell, the rulesets are just weird for this game overall. The reason these rules are so odd in my opinion is the set maps for each game. If there was a set map pool then it would be easier. I'm gonna agree with the melee example because it is also my primary game of choice even though I'm not great at it. The primary reason this counterpicking system works is not to make for the best show possible but to make sure the person on the back foot to have a chance to comeback. I'm fairly new here, but from what I can tell, previous tournaments had many mirrors because people would have to pick first after losing. In the mirror, my understanding is that the better mechanical player generally wins and gives less of an opportunity to take advantage of the strategic differences of the civs, taking out large portions of macro elements. This leads to the player who got behind early having no chance to get back in even if that player's macro is marginally better but mechanics are marginally worse.

Earlier, lesllamas brought a sports analogy that really makes sense in terms of counterpicking. The only reason this may be a reasonable argument is due to the quantity of games played. For example, if bracket matches started at best of 7 (dear lord) and then got bigger as the tournament progressed (again...why so many games?), then perhaps this alternating form of picking would be a great show of skill (not to mention we would get a higher sample size and a more strongly established meta) because it would be less comparable to basketball and more comparable to tennis. For example:

Nadal wins game 1 on serve 1-0 Nadal
Federer wins game 2 on serve 1-1
Federer breaks serve on game 3 2-1 Federer
etc.

The reason this model works is because not only is it a first to 6 and they win by two or there is a tiebreak (unless it's the US Open [I think]), but its also a best of 3 or 5 first to 6 sets.

TL;DR
If the quantity of games is to remain low, winner picks should be implemented possibly with a map pool existing.

[momuuu]

TBH I've been impressed with your rulesets in almost every other area. I don't think you guys haven't thought things through. One thing I'd be fascinated to know is how you come up with the map pool for each round? I know next to nothing about the top level meta, as I don't play at that level. So I don't have very good opinions on what maps allow for harder or weaker counterpicks. Do you guys take the "counterpick-ability" of the maps into consideration and try to distribute them in such a way that under alternating pick, one player does not get two super strong counterpicks while the other gets more neutral maps? I was thinking about this a couple weeks ago, and it struck me as one potential advantage (that I had not considered) of having a set system of counterpicks. But I don't really know how the community views the map pool with regards to how it affects counterpick strength.

I think thats the most unfair aspect of the rules. The winner pick or alternating pick stuff is indeed a bit messy, however at this point changing it (with people being used to it and stuff) would possibly have a more negative effect. I did argue for it though but I was ignored

Theres not someone with a lot of time to thoroughly think about the mappool and civ strats right now, so sometimes you get a map where a first pick is harder or easier.

[momuuu]

So me and ryan ran the maths with regards to this civ picking stuff. Taking a hypothetical scenario where one play goes up 1-0 (which happens 100% of the time) in a bo5 the chance of the player going up 1-0 at an estimated counterpick winrate of 2/3rds winning is:
- 70% for alternating pick
- 71% for winner picks
- 69% in the case there is no counterpicking (so then the winrate is 50%)

This mathematical analysis seems to imply that changing the rules people have gotten used to is not worth the effort.

[lesllamas]

So me and ryan ran the maths with regards to this civ picking stuff. Taking a hypothetical scenario where one play goes up 1-0 (which happens 100% of the time) in a bo5 the chance of the player going up 1-0 at an estimated counterpick winrate of 2/3rds winning is:
- 70% for alternating pick
- 71% for winner picks
- 69% in the case there is no counterpicking (so then the winrate is 50%)

This mathematical analysis seems to imply that changing the rules people have gotten used to is not worth the effort.

How could you possibly come up with a mathematical assumption for one player winning a game over another. Skill gaps maps and civ mus all play into this.

The entire logical flaw behind alternating pick is that its fairness is predicated on the expected result occurring. Projecting that with a mathematical model that makes the exact same assumption is just confirmation bias on the fundamental flaw.

[momuuu]

So me and ryan ran the maths with regards to this civ picking stuff. Taking a hypothetical scenario where one play goes up 1-0 (which happens 100% of the time) in a bo5 the chance of the player going up 1-0 at an estimated counterpick winrate of 2/3rds winning is:
- 70% for alternating pick
- 71% for winner picks
- 69% in the case there is no counterpicking (so then the winrate is 50%)

This mathematical analysis seems to imply that changing the rules people have gotten used to is not worth the effort.

How could you possibly come up with a mathematical assumption for one player winning a game over another. Skill gaps maps and civ mus all play into this.

The entire logical flaw behind alternating pick is that its fairness is predicated on the expected result occurring. Projecting that with a mathematical model that makes the exact same assumption is just confirmation bias on the fundamental flaw.

You eliminate other factors to look at the system of alternating counter picks vs winner picks first. It's the most natural way to look at it, and it's not confirmation bias because I was simply curious what was better. I dont think you fully understand what we did. The assumptions where the following: the winrate of a counterpick is 66%. This was taken based on experimental data gathered by h2o, but mostly because 2/3rds is easy for calculation. In general, the results won't change much when you change the counterpick rate, the difference in methods becomes smaller the closer it gets to 50%. If you want to argue more winrates have to be tried, that can be done even though it takes a little bit of extra effort.

Now what we did is draw a chance tree. Start out at one player going up 1-0 (the 0-1 result is insignificant since its statistically the same as 1-0, since 100% of the time a player goes up 1-0 and we don't care which player it is). Then, for every match 2 options arise: player A winning and player B winning. The chances depend on the counterpick method. For example, in the current alternating pick scenario, the chance that player A wins game 2 and then game 3 is 33% (in game 2 he picks first) * 66% (in game 3 he counterpicks) which results into a ... chance. Now doing this for all possible outcomes (so things ranging from player B wins 3 games in a row, to player A wins game 2 player B game 3 and 4 to whatever order of wins and losses is possible) and calculating the chance that an outcome happens results into a prediction for scores. Theres a certain chance that 3-0 happens, that 3-1 happens, that 3-2 happens, that 2-3 happens and that 1-3 happens (0-3 is not possible).

Now this results into a chance that player A (the winner of game 1) wins the series and a chance that player B (the loser of game 1) wins the series. Doing this for the method alternating pick and the method winner picks first gives the outcome that: With alternating pick, player A has about a 70% chance to win, while in the winner picks first scenario player B has about a 71% chance to win. This difference will only get smaller if the counterpick winrate gets smaller, but 2/3rds is already higher than what the emperical data seems to show. So yes, alternating pick is a little bit shittier for the winner of game one. We are however talking about 1% of the games, thats a very low amount. You mentioned it yourself, theres a ton of other factors that play a role here, which are much and much more relevant than this 1% thing. The map order, the civ reset, the skill level of players, even the mentality and the winstreak effect. Funnily enough, counterpicking actually favors the winner of game 1 compared to when it's free pick. In a scenario where there is no counterpicking (so 50% winrate regardless of game number) the expected winrate for player A is actually 69%, which is lower than 70-71%. In that sense you could see the counterpicking is already favoring the winner of game 1, however the alternating pick system we use is less so favoring the predicted result than the winner picks first system does. If a scenario where all matches are 50/50 is the most fair scenario, which I think isn't a stupid to say (although you can argue over it of course) then alternating pick would be better than winner picks first.

Based on these things I'd conclude that it's not worth it to change a system that people have gotten used to, since the effect of the different systems is basically nothing.

[lesllamas]

Not going to quote because on mobile and it's too long, but your methodology is still extremely and fundamentally flawed.

The probability that a single game in a series is won obviously does not depend on the prior and subsequent games' probabilities.

The only scenario you need to run is 3-1 for player B.

2/3 chance they win g2.
1/3 chance they win g3.
2/9 chance you arrive at g4 with player B up 2-1.

22% chance you end up in that scenario.

Now, the fundamental flaw in your logic is that player B has an equal chance of winning his counterpick game 4 (alternating pick) as he does in game 5 (winner picks first).

You can't mathematically project the likelihood so simply. Games in a set do not exist in a vacuum. Consequently, I also accept that player B arriving at g4 up 2-1 will probably occur less than 22% of the time.

Adaptation is a significant portion of this and other competitive games. Earlier in this thread I showed empirical proof of this 2-1g4 scenario in action, and how winner picks first gave player A enough time to finish adapting to new gameplay and barely squeeze out g5 on a very hard counterpick.

As we've brought up though, aoe3 is different, and I'm open to alternating pick because maps are so important and are currently planned ahead of time. However, the mathematical analysis is frankly bullshit and not indicative or reflective of how actual sets are played.

[momuuu]

I feel like you do not get it. If you isolate other variables (which is how you do an experiment) you reach the result I did. It's simple as that. This scenario applies for 2 players of equal skill playing eachother 5 times on the same map without civ resets. In that case you literally get this result, which gives the perfect indication of how much the picking system actually matters. If you'd combine that with how much external factors matter you can actually calculate a winrate. That winrate that is calculated is in no way a prediction of who is going to win in what score, it just shows how much the picking systems supposedly differ in how much they favor which player.

In practise and theory the picking system matters less than 1%.

[lesllamas]

Probabilities. In. Practice. Change. Depending. On. What. Has. Happened. In. The. Set.

You literally cannot make the assumptions your experiment is predicated on. The picking system affects the probability of A vs B winning in every game 4 2-1 case. Without fail and without question.

[lesllamas]

All other results are irrelevant.

[lesllamas]

TL;DR

This just happened yesterday. Two of the top 3 players in the game's history played a best of 5 set. Armada won game 1, won game 2 on Mango's counterpick, and game 3 was on Mango's counterpick again. Mango took about 2 and a half games to acclimate and adapt to Armada's peach, and barely squeezed out game 3. Had the set been alternating pick, Armada probably would have won 3-0. However, Mango won the next 3 games as he adapted and managed to figure out Armada's playstyle well enough to take the set 3-2. Armada did not deserve to win the set. But he probably would have if it were alternating pick. Winner picks first favors the better and more adaptive player, and is a test of perseverance and adaptation. Alternating pick greatly favors those who can cheese a single counterpick win.

This one makes a lot of sense

@jerom

notification

Practical results diverge from any mathematical model you can create.

[momuuu]

Probabilities. In. Practice. Change. Depending. On. What. Has. Happened. In. The. Set.

You literally cannot make the assumptions your experiment is predicated on. The picking system affects the probability of A vs B winning in every game 4 2-1 case. Without fail and without question.

Probabilities do change in practice, correct. Practice also has multiple factors contributing towards the outcome, making it impossible to asses how much what factor contributes. I feel like you just don't get the idea behind this at all tbh. It's basically science.

It's like when you theoretically calculate the electric force an electron exerts on another electron. In theory this gives a result which gives the amount of force this electron experiences. In practise theres huge amounts of charge in space all affecting the force that things experience so this calculation doesn't really tell you anything about whats going to happen. It does tell you the one electron pushes the other away though.

Like, the chance the winner of game one wins depends on a lot of factors. For example how good he is, what happens in the series, what the picking system is, what the maps are, mapscrews etc. All of those things have a quantifiable effect on the outcome. For example the picking system might kinda imply that its 70% winrate, but then the one player might be worse which means theres another factor reducing its winrate. The total average chance he wins is the product of all these little contributions, and this method I applied gives the contribution towards the winrate created by the counterpicking system. I do not think I have the ability to explain this more clearly, but I am 100% convinced this is correct.

[momuuu]

TL;DR

This just happened yesterday. Two of the top 3 players in the game's history played a best of 5 set. Armada won game 1, won game 2 on Mango's counterpick, and game 3 was on Mango's counterpick again. Mango took about 2 and a half games to acclimate and adapt to Armada's peach, and barely squeezed out game 3. Had the set been alternating pick, Armada probably would have won 3-0. However, Mango won the next 3 games as he adapted and managed to figure out Armada's playstyle well enough to take the set 3-2. Armada did not deserve to win the set. But he probably would have if it were alternating pick. Winner picks first favors the better and more adaptive player, and is a test of perseverance and adaptation. Alternating pick greatly favors those who can cheese a single counterpick win.

This one makes a lot of sense

@jerom

notification

Practical results diverge from any mathematical model you can create.

See my other post. These systems can be modeled perfectly, without errors, in isolation, so their contribution towards the winrate can be perfectly assessed. You don't seem to want to understand this at all.

[momuuu]

I have an example explaining the method used with every day things.

We're taking cards from two decks. Both players shuffle the cards back into their own deck. The one who gets the highest card wins a game, its a BO5. In game one both players have normal decks. Then using either alternating pick or winner picks first, one of the players gets a disadvantage because the highest cards are taken out of decks so that his chance to win is 1/3rd.

Now we can accurately compare alternating pick to winner pick. This gives is the result that the player that wins the first 50/50 game has a 70% chance to win using alternating pick and a 71% chance to win using winner picks first. This is a fact.

What I am desperately trying to explain here is that this is proof that the winner picks first system is actually indeed better for the winner of game one. It's also proof that this margin is very small (1% in this case). The lower the winrate is to win on what is in our tournament system a first pick, the more winner picks first starts to favor the winner of game one compared to alternating pick.

I want to know if you agree at all with this post before I can at all continue.

[lesllamas]

You cannot model momentum, tilt, or adaptation in competitive gaming. They are non trivial factors and they come into play consistently and to varying degrees. I know your 1% number to be bullshit because I've played and seen enough sets in these exact scenarios where those factors changed the outcome in a way they wouldn't under alternating pick. I do understand what you did, and it's just wrong in practice.

[lesllamas]

I have an example explaining the method used with every day things.

We're taking cards from two decks. Both players shuffle the cards back into their own deck. The one who gets the highest card wins a game, its a BO5. In game one both players have normal decks. Then using either alternating pick or winner picks first, one of the players gets a disadvantage because the highest cards are taken out of decks so that his chance to win is 1/3rd.

Now we can accurately compare alternating pick to winner pick. This gives is the result that the player that wins the first 50/50 game has a 70% chance to win using alternating pick and a 71% chance to win using winner picks first. This is a fact.

What I am desperately trying to explain here is that this is proof that the winner picks first system is actually indeed better for the winner of game one. It's also proof that this margin is very small (1% in this case). The lower the winrate is to win on what is in our tournament system a first pick, the more winner picks first starts to favor the winner of game one compared to alternating pick.

I want to know if you agree at all with this post before I can at all continue.

I disagree with the fundamental premise but agree with the math. Your math isn't wrong, it just has no practical application in competitive gaming.

[momuuu]

Sure we can argue about momentum and shit, but you originally claimed alternating pick was faulty regardless of things like momentum. Winner picks first creates more games and kinda takes momentum away from the better player from time to time. I'm not really sure thats an argument for winner picks first honestly.

It does have application in practise, it definitely does. Winner picks first on its own causes the player that wins game one to win 1% more often compared to alternating pick. That's a real thing in practise. We're almost had enough games for that 1% to be a real thing already. It of course also interacts with shit like momentum, although I really dislike the winner picks first in that sense too.

Here in this post you present winner picks first as relevant regardless of momentum, and seemingly imply that momentum is an argument against it even: viewtopic.php?f=111&t=4923
You mentioning the 1-3 scenario in this thread is basically also kinda advocating the system regardless of momentum. So I do kinda agree that the 1-3 scenario is more likely, I started wondering from which results it draws the chance that it gains from alternating pick, and then I wanted to know the whole story. I did the maths and found out that we're talking about like 1% and kinda felt like the importance was overstated and overestimated by myself.

[lesllamas]

Sure we can argue about momentum and shit, but you originally claimed alternating pick was faulty regardless of things like momentum. Winner picks first creates more games and kinda takes momentum away from the better player from time to time. I'm not really sure thats an argument for winner picks first honestly.

It does have application in practise, it definitely does. Winner picks first on its own causes the player that wins game one to win 1% more often compared to alternating pick. That's a real thing in practise. We're almost had enough games for that 1% to be a real thing already. It of course also interacts with shit like momentum, although I really dislike the winner picks first in that sense too.

Here in this post you present winner picks first as relevant regardless of momentum, and seemingly imply that momentum is an argument against it even: viewtopic.php?f=111&t=4923
You mentioning the 1-3 scenario in this thread is basically also kinda advocating the system regardless of momentum. So I do kinda agree that the 1-3 scenario is more likely, I started wondering from which results it draws the chance that it gains from alternating pick, and then I wanted to know the whole story. I did the maths and found out that we're talking about like 1% and kinda felt like the importance was overstated and overestimated by myself.

Was waiting until I had a spare set of time to reply to this on my computer instead of mobile.

I thought you had done something more complicated, but I went back and reread your deck of cards explanation. You have to realize the idiocy of this experiment, right? Like, under your experiment the order of the counterpicks LITERALLY does not matter. Order the counterpicks AA BB, A B A B, A BB A, and you get the exact same win rates for player A (winner of game 1) every time. In fact, the 1% part is what confused me. Where is this anomalous 1% coming from? The entire experiment is basically like a dice roll, with 4 six sided dice. Two of the dice have 4/6 painted red (winner of game 1), and 2/6 painted blue (loser of g1), while the other two dice are the inverse.

You roll the 4 dice. All scenarios with at least 2 red dice result in player A victory. All scenarios with at least 3 blue dice result in player B victory.

It's literally this simple:

4 dice trials, average probability of success 3/6 (4/6 4/6 2/6 2/6, also represented by the fact that of the four counterpick games, under your assumptions, each player has an equal chance of winning on their counterpick and winning on their opponent's as the other does of theirs, etc.)

success times m probability P
0 0.0625
1 0.25
2 0.375
3 0.25
4 0.0625

0=3-0 win for red
1=3-1 win for red
2=3-2 win for red
3=3-2 win for blue
4=3-1 win for blue

The distribution or order literally does not matter a single iota under your parameters. I have no fucking clue where you got a 1% variance from.


But the point is that OF COURSE the order matters! You wouldn't just give games 2 and 3 to the winner of game 1 as counterpicks, would you? You wouldn't set a system where the loser of game 1 automatically gets games 2 and 3 as counterpicks, regardless of game 2's result, either.


So here's the quotation from my post about momentum that you linked:

"But lesllamas, what about the momentum having two counterpicks in a row could give your opponent?"

If your opponent has two counterpicks in a row, it means you've won on their counterpick, and are either up 2-0 (in which case momentum should be entirely in your favor anyways) or 2-1 ( N L W W L) and should be in a position of counterpick advantage.

This still holds true. Momentum is not in that player's favor. They are, however, given the longest amount of time possible to adapt. Adaptation is incredibly important and it is non-trivial. The goal of a tournament series is to determine the better player at that particular time. The 3-1 example is so much more prevalent in practice than is statistically likely because cheese is especially powerful early in a series of nearly any competitive game. Winner picks first effectively allows players to ride out the cheese as long as possible until they adapt to it, and wipe the floor with their opponent. Of course, if it's not just cheese, then they'll still lose. Alternating pick is probably fine in BO9 and larger IMO. If you consider a BO51, ridiculous as it is, the practical difference between winner picks first and alternating pick is nil. In BO5 and to a lesser extent BO7, though, it is significant. By significant, I mean maybe 5-10% of competitive tournament sets, which is a fairly large number.

All of this is rendered fairly moot, as I said earlier, though, because of how maps and civ counterpicks interact in AoE3. The relative power of different counterpicks on different maps is too volatile, and alternating pick is probably better if you can plan the map pool ahead of time to be as fairly distributed as possible.

[lesllamas]

Also re: the dice, I understand that some of the 3-1 will in practice be 3-0 because not all counterpicks are played out, but the win probability is just folded over in the aggregate to the same player anyways.

[momuuu]

Draw the chance trees yourself if you dont believe me.

Actually I guess you didnt get that the chance being considered is the chance that the winner of the first game wins the series, in which case it obviously doesnt end up being 50/50.

Its a pretty pointless decision because you refuse maths really.