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Subject: Data on the massive start player advantage rss

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Andrew Drummond
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Last month I ran the 7 Wonders Duel tournament at the World Boardgaming Championships in Seven Springs, PA.

We had 86 players compete in a 4-round Swiss tournament breaking to an 8 player single elimination playoff. This resulted in 156 competitive games worth of data. Of these games the start player had a 62% advantage (97-59).

While it would take a lot of analysis to explain exactly why the advantage is so big, the game is clearly unbalanced towards the start player.
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Erik Webb
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Your sample size is not nearly big enough to say the start player has a massive advantage.

62% in a single tournament is not that much. Those players may just have been better.
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ardrummo wrote:
Last month I ran the 7 Wonders Duel tournament at the World Boardgaming Championships in Seven Springs, PA.

We had 86 players compete in a 4-round Swiss tournament breaking to an 8 player single elimination playoff. This resulted in 156 competitive games worth of data. Of these games the start player had a 62% advantage (97-59).

While it would take a lot of analysis to explain exactly why the advantage is so big, the game is clearly unbalanced towards the start player.


156 games and 62% is not much. This means that just 32 more games were won more by first player in a tournament of 86 players, playing Swiss tournament style. EIGHTY SIX PLAYERS. What\s more, 32 is just 16 more games above the 50-50 split.

This statistic would be worrysome if based on games of 2 or 4 players. But not 86.

It would be more interesting to see what the split is based on top 4 players played games, but sample size would still be way too small.
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Zaphod Beeblebrox
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Yep, as the first responder said, I'd like to see some attempt to control for player quality. Also:

ardrummo wrote:
Of these games the start player had a 62% advantage (97-59).

This gives the wrong impression. "The start player won 62% of the games" doesn't mean "the start player had a 62% advantage."
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nbread wrote:
Also:

ardrummo wrote:
Of these games the start player had a 62% advantage (97-59).

This gives the wrong impression. "The start player won 62% of the games" doesn't mean "the start player had a 62% advantage."


Do the math...they're actually pretty close (it's actually a 64.4% advantage, with the 1st player winning 62.2% of the games).
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Rick Teverbaugh
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I can not shed any light on this hypothesis. I have only played 2 games and both players had never played before. The start player won both games and in one case went first in two ages and in one case went first in 3 ages. I personally don't find the tourney results troubling at all. First player could have drafted a better set of wonders for instance. I would like to know what percentage of the players who won as first player also won as second player in other rounds of the tournament.
 
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Zaphod Beeblebrox
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fnord23 wrote:
nbread wrote:
Also:

ardrummo wrote:
Of these games the start player had a 62% advantage (97-59).

This gives the wrong impression. "The start player won 62% of the games" doesn't mean "the start player had a 62% advantage."


Do the math...they're actually pretty close (it's actually a 64.4% advantage, with the 1st player winning 62.2% of the games).

That's true, but I was thinking that the best way to define start-player advantage is relative to if there were no advantage (i.e., a 50% win probability). By that calculation, the start-player advantage here is 24% (97 / 78 - 1).
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M. B. Downey
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What was the point spread for each game?

Did the first player lose by less than the second player?

Were any of the games cut short because of a military or science victory?

How many of the top eight players won games as the second player?
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Jean-Philippe Thériault
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That's enough data to suggest there is an advantage for first player with a 99% confidence interval.

(The real r-value is within the interval 51% and 73%, 99% of the time.
The 95% interval is between 57% and 69%, but I don't usually put a lot of faith in those.)

It's not enough to suggest it's a *huge* advantage. It could as well be 55/45 as 70/30.
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Zaphod Beeblebrox
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XDarkAngelX wrote:
That's enough data to suggest there is an advantage for first player with a 99% confidence interval.

(The real r-value is within the interval 51% and 73%, 99% of the time.
The 95% interval is between 57% and 69%, but I don't usually put a lot of faith in those.)

It's not enough to suggest it's a *huge* advantage. It could as well be 55/45 as 70/30.

Your implicit assumption here is that the quality of first and second players was the same, on average.

That may or may not be true.
 
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M. B. Downey
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nbread wrote:
fnord23 wrote:
nbread wrote:
Also:

ardrummo wrote:
Of these games the start player had a 62% advantage (97-59).

This gives the wrong impression. "The start player won 62% of the games" doesn't mean "the start player had a 62% advantage."


Do the math...they're actually pretty close (it's actually a 64.4% advantage, with the 1st player winning 62.2% of the games).

That's true, but I was thinking that the best way to define start-player advantage is relative to if there were no advantage (i.e., a 50% win probability). By that calculation, the start-player advantage here is 24% (97 / 78 - 1).


A better way would involve a general point advantage. Much easier to determine and easier to quantify.
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M. B. Downey
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nbread wrote:
XDarkAngelX wrote:
That's enough data to suggest there is an advantage for first player with a 99% confidence interval.

(The real r-value is within the interval 51% and 73%, 99% of the time.
The 95% interval is between 57% and 69%, but I don't usually put a lot of faith in those.)

It's not enough to suggest it's a *huge* advantage. It could as well be 55/45 as 70/30.

Your implicit assumption here is that the quality of first and second players was the same, on average.

That may or may not be true.


We really need to know the scores of each game for this data to be useful.
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Also there is no 62% advantage but merly 62% games won by starting players. The actual relative advantage (if any) could be considerably smaller.

For example, if we consider that hypothesis that there is in fact an advantage, this could be a 0.1% relative advantage for the starting player. What the championship would.have shown in that case would be that of all the games that were played, 62% of the starting players had managed to take advantage of it.

It takes a lot more gaming though to determine whether there is or not any type of advantage.
 
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Stats is certainly NOT my area of expertise but one that stands oit to me is you said there were games played by people who have never played Duel before. I dont think these kinds of games would provide accurate results. Gamer or not, if you have two people playing a game for the first time, both people are figuring things out, and the likelihood of mistakes being made is pretty high. When i play games with people who have never played the game before and they have to be taught i dont consider these a win/loss game. The second game we play, fine, as they are familiar with it at that point and can concentrate on actually playing the game but certainly not the first game.
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downeymb wrote:
A better way would involve a general point advantage. Much easier to determine and easier to quantify.


No, that's a horrible measure in any game but even more-so in games like this with alternate victory conditions. It is completely irrelevant whether I win by 2 points, 20 points, by science, or by military. If I hate draft my opponent -- hurting both of our scores but his more than mine -- I could still win easily but have a smaller point gap than a hard-fought victory with less hate drafting.
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Phil Mechanic
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nbread wrote:
Your implicit assumption here is that the quality of first and second players was the same, on average.

That may or may not be true.


Absolutely, but with sample size n>50, it's a reasonable assumption to make.
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Russ Williams
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dicemechanic wrote:
nbread wrote:
Your implicit assumption here is that the quality of first and second players was the same, on average.

That may or may not be true.


Absolutely, but with sample size n>50, it's a reasonable assumption to make.


With a large sample size, I'd rather expect that in most games, the first and second players were NOT of similar strength. The more players, the bigger the spread from weakest to strongest!

It seems more reasonable to assume that the number of games in which the first player was stronger was roughly equal to the number of games in which the second player was stronger. (Assuming that players were randomly paired and first players were randomly selected.)

(Which of course works out either way to the same implication, i.e. that the observed higher frequency of first-player wins was not merely due to the first players being stronger.)
 
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Phil Mechanic
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If Duel was perfectly balanced, wins would follow a binomial distribution with win probability 0.5. The probability of achieving 97 or more wins out of 156 games on that basis is 1.47*10^-3, or 0.15%
[Edit: correct probability, I'd put the wrong value P into my spreadsheet!)

So we certainly can't say for certain that going first gives you a X% advantage. But we can say that on the basis of this sample, it is highly like that there is a *clear* advantage to going first.

As with any experiment, you'd want to repeat it, look for bias in the distribution, etc. (e.g. if you allow players to choose whether to start & the best players identify that going first gives you a small advantage, the size of that advantage will become statistically over-represented)

What would be interesting is to collect more data and see if the advantage lies in both point scoring AND insta-wins. I can see how it might help Scientific. With that high win rate, it almost certainly impacts on points-wins. I suspect it has least impact on Military.

And THEN comes the handicapping. Is going first worth 1 point? 2? 3? If so, then it's a quick fix to give player 2 a bonus point or two, but that could have knock-on impact in other areas. E.g. if you start with 2 extra points, would that inherent advantage mean a player is more likely to ignore insta-win strategies? That's when behavioural economics and psychology comes into play.

Cmon someone, there's at least a couple of PhDs in this I reckon


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Phil Mechanic
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Quick question: how were wonders selected? Did First Player get both first wonder pick and first card pick?

In terms of analysing the "why" of this distribution, separating out advantage of first Wonder pick from first Card pick would be potentially very important.
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dicemechanic wrote:
Quick question: how were wonders selected? Did First Player get both first wonder pick and first card pick?

In terms of analysing the "why" of this distribution, separating out advantage of first Wonder pick from first Card pick would be potentially very important.


Well, that would be just following the rules. First player gets first fourth, sixth and seventh pick. Then he gets first card pick.
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dicemechanic wrote:
How were wonders selected? Did First Player get both first wonder pick and first card pick?


I think this could probably be the reason for the first player bias. Picking wonders first and going first could be rather substantial.
 
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Russ Williams
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emptyset wrote:
dicemechanic wrote:
How were wonders selected? Did First Player get both first wonder pick and first card pick?


I think this could probably be reason for the first player bias. Picking wonders first and going first could be rather substantial.


"Could be"? As pinoeppel noted, the game rules say that the "first player" chooses the first wonder and begins Age I. Why are you guys talking as if it "could be" otherwise, as if one player could pick the first wonder and the other player could start Age I?

Am I missing something?
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russ wrote:
"Could be"? As pinoeppel noted, the game rules say that the "first player" chooses the first wonder and begins Age I. Why are you guys talking as if it "could be" otherwise, as if one player could pick the first wonder and the other player could start Age I?

Am I missing something?


The start player does choose the wonder first and play first. And the data indicates that there is indeed a first player advantage. This is very likely because of the first point. But there could be soemthing else at work regarding pairings and choosing the first player.

Maybe good players were always paired with bad players, maybe the better players also got first player.
 
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golden_cow2 wrote:
downeymb wrote:
A better way would involve a general point advantage. Much easier to determine and easier to quantify.


No, that's a horrible measure in any game but even more-so in games like this with alternate victory conditions. It is completely irrelevant whether I win by 2 points, 20 points, by science, or by military. If I hate draft my opponent -- hurting both of our scores but his more than mine -- I could still win easily but have a smaller point gap than a hard-fought victory with less hate drafting.


Hence why I asked for all the scores of each game and whether any games were won by military or science. Plenty of games give handicap points or starting money to players after the first, it's a completely reasonable means of determining advantage.

What we really need is someone to run AI players against each other using various strategies several thousand times. Then we could compare similar strengths and various strategies and see what the advantage would be and decide if and how to give a handicap to the second player.
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Hey.

Wonder selection does NOT matter. There are two rounds of wonder selection, not one. And in the second round of selection the other player goes first. Board state does not change one bit between these two rounds.

In fact, second player may even have an edge with wonder selection, since they get to do it while already knowing what were the wonders that were selected in first round.
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