7WD in Numbers

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Le007n
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Joined: 30 March 2020, 22:47

7WD in Numbers

Post by Le007n »

For a while now I have wanted to try providing more insight to the questions in this forum with some more data other than my experience. The below is my attempt to do just that.

Hopefully this will be of some interest and help to provide some insight or at the very least, generate some interesting discussions based on my findings and thoughts (which may or may not be correct!)

Hopefully I’ve linked all the right images, if not and something looks out of place, please let me know

The Data

Over a couple of weeks in February to March 2022 I collected data covering:
  • A cross section of the top 500 players (3,8,13,18,23)
  • High level data for their last 50 ‘ranked’ games (removing anything which was conceded, abandoned etc)
  • Low level data for their last 10 games (players starting ages, wonders selection / construction etc)
This gave me a data set of 5000 games with most of the stats you see on the game completion screen, and just over 1000 games with more in depth game data
Just for reference, the average winners rating was 406.6 and the average losers rating 301.6 so just over 100 points difference however this would be expected when looking at the top players who would likely have a higher rating than the majority of their opponents

Key
Where I refer to ‘Pantheon’ or ‘Agora’ I am referencing games with ONLY the one expansion added. Standard is self explanatory, and ‘Both’ refers to a game with Agora and Pantheon enabled.

#1 Games Played

The distribution of games over the 5000 analyzed was:
  • Standard : 3049 (61%)
  • Pantheon : 225 (4.5%)
  • Agora : 596 (11.9%)
  • Both : 1130 (22.6%)
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#1.1 What game type are the most played?
Most players play standard (vanilla) 7wd on BGA. This was the expected outcome since this is the most accessible version
There is however a fair amount of play using both expansions (better than I expected), with approx. 1 in 4 games involves all expansions. This may be higher than the overall average if preferred by the top players, this is the reason however why I took a cross section to try shy away from just looking at the top 10 so it is hopefully more balanced and gives a true reflection
Pantheon alone is very seldom played (which was a little bit of a surprise)

#1.2 Should the arena have alternative formats?
Either expansion alone would have little player base
Just agora has a strong enough player based but would not cover the majority of players
Two stand alone arenas would likely be the best solution > standard & both

#1.3 Do players play different game types?
When looking at the top 10 games played for each player the distribution was within +/- 1%. This leads me to believe that players general play a fixed game type and don’t jump between the formats too often

#2 Win Type

In the games analyzed, the win ratios were as follows:

Standard
  • Civilian: 58%
  • Science: 25.6%
  • Military: 16.4%
Pantheon
  • Civilian: 44%
  • Science: 38.7%
  • Military: 17.3%
Agora
  • Civilian: 37.6%
  • Science: 10.2%
  • Military: 22.7%
  • Political: 29.5%
Both
  • Civilian: 33.8%
  • Science: 16.0%
  • Military: 19.2%
  • Political: 31%
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#2.1 Military is slightly lower than I would have expected for standard but this win type is definitely the least utilized for the majority of players I believe with science and civilian being slightly more frequent in the standard game

#2.2 Pantheon is more unbalanced to science wins. I have seen many games where both players are waiting for one token at the start of age three, so this comes as no surprise.

When the science token is in play in the standard game this put a whole new dynamic on the game due to the increased likelihood of a science win. The Pantheon gods make it much more likely this token is available and gives other ways to copy token making science much easier to achieve and unbalancing the game in my opinion

#2.3 The rate of political wins is slightly lower than I expected so I will fall on my sword here a bit. Political is nearly the dominant win type and is much stronger than military and science, but with both expansions it balances ok with a civilian victory so its not too game breaking

#2.4 With agora alone, science is less impactful. Adding Pantheon gives back that science advantage and helps to balance it out

#3 Turns vs Wins

Next I looked at the number of turns taken between the two players to see the trends
This value is based on the player I was collecting the stats for and their +/- turns vs their opponent and whether they won or lost. On average, the top players would win just under 70% of the time in a game with an equal number of turns, increasing the more extra goes they had

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#3.1 Not too much to say here. As expected, the more turns a player has, generally, higher their win percentage as this gives more chance to gain cards for more points or other effects
There are a couple of outliers in agora only with a few games being won with 4 less turns but this seems like an exception
Last edited by Le007n on 26 April 2022, 11:22, edited 1 time in total.
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Le007n
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Re: 7WD in Numbers - Part 1/3

Post by Le007n »

#4 Card Selection

Another area I was interested in was the card types taken. The overall BGA stats don’t really paint a clear picture since it involves every game played so I again split this down by type


Yellow
#4.1 There is no real difference between the number of yellow cards taken by the winners and the losers in most cases. The exception been games with Pantheon where having more yellow (likely earlier on) is highly beneficial to affording the gods which are like mini wonders in their power
There are quite a few yellow cards in Age III which are generally less sought after and probably balance out this across both players
Experience says that you would ideally want one or two yellow cards early on to help with coins. Possible one or two in Age II for refined resources / coins or resource. Then in Age III there are generally better cards with the odd one being worth while for coins and VP which supports the average of 4 or 5 yellows over the game. Where these are taken in the key

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Brown
#4.2 Nothing too interesting here again. Players average about 3 brown cards, win or lose. The exception being when playing with both expansions where the number of brown cards drops slightly for the winning player

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Grey
#4.3 Much like brown, very little difference in card counts of this color. Yellow refined resource cards are often much more useful along with the Piraeus wonder and take away some of the need for these cards. With less grey cards on offer, these are likely split when available
Games with Agora again have a slightly lower take of resource cards for both sides

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Blue
#4.4 The average number of blue cards between players is standard again with blue being slightly favored in Agora games (as expected).
Looking at the average number of blue cards for the winner, there is a wide range which spans from 0 right up the scale. In a game where the player is going for a science or military victory only, blue cards are mostly discarded for coins, so the value of these cards is variable
There is a similar trend across all game types where either none, a few (possibly for a late points grab or early, keeping options open) or many blues are taken
For all the other card colours mentioned so far, the charts for all game formats are nearly identical in distribution. Blue cards are the only one with any real variation. The value increases in Agora due to the political gain and somewhat diminishes with Pantheon as the battle to get more coins for the gods is a bigger priority which likely reducing the age II selection for the more likely science win which requires no blue

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Green
#4.5 Both red and green cards are situational based on the game state. That being said, across standard and Pantheon (where science is stronger), the winner player has on average 1+ more green cards than his opponent.
Regardless of win type, green cards often combine to gain a token to provide an advantage which with the right tokens would increase a players win chances - Theology, law or strategy tokens would increase the value and selection rate of green cards in most games
In games including Agora (stand alone and both expansions) the number of green cards drops dramatically. The mode number of green cards taken is 0 in both instances.
This ties in with the reduce science win rate though I would have expected the tokens still have been of value. Maybe someone with a deeper understanding of Agora can expand upon the reason for this complete disposal of green cards which would have to happen right from Age I?

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Red
#4.6 In all game types excluding Pantheon (the race for science), the winning player has a slightly higher average number of red cards
In Agora, military is advanced much more with 4 military cards being the mode value and an average of 3.5 cards, 1 higher than the losing player
Like science, the timing and selection of cards played is the key. With military, you don’t want to give up first turn for no good reason but taken some cards can add pressure forcing opponents to make different plays. A few well-placed shields in Age II and then control of the structure in Age III can soon open the doors for a Military win

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Divinities

# 4.7 Continuing the theme of selection numbers, I next looked at the effect on the number of divinities taken vs a players win rate.
As expected, the winning player plays more divinities on average across the game. This isn’t a massive difference which would indicate the divinities offer an advantage, but this isn’t too significant across all the cards (+0.5). Benefits here are obvious that they offer extra powers and are also used to change the turn order, so taking more divinities would help swings the game
Ra is to my mind the most unbalanced divinity which I will look at shortly
There were a number using games with Both expansions where no divinities were activated. I presume these games have finished very early with a political victory (age I or early age II)

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Conspiracies

# 4.8 The number of conspiracies played seems very low across both Agora variants with many games having none triggered. In Agora alone, the losing player triggered marginally more conspiracies on average, so this doesn’t seem to push a player towards a victory on average and seems like an under powered element of the game which may be advantageous in isolated situations but is less utilized due to the set up required

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Influence

#4.9 On the other hand, influence is strongly tied to winning (political). The average winning player had nearly 2 more points of influence with a mode value of 7 influence points across the games making the cards (and wonders) which help grant influence high priorities

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That’s probably enough stats on the card selection so lets move on to the wonders!


#5 Wonders Selections

I next wanted to see which wonder was the most selected and if this roughly matched my own opinions. I don’t expect any surprise here and I think most players could guess the outcome, but let’s check just to be sure
For choice of pick I weighted the first set of wonders and the second set as the same so wonders shown can picked in place 1 (favorite) to 4 (drafted by default)

#5.1 Standard

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Thoughts:
  • The 5 wonders with replay ability are the first choices (for good reason)
  • The Pyramids are the least selected wonder which matches the common perception that this is the worst wonder
  • The 3 military wonders are also at the bottom of the pick order with the colossus often left as left pick along with the Pyramids
  • The Piraeus wonder was left for 4th pick only once
It is probably worth saying that second and third selections are likely interchangeable. In my experience, if there is one obvious choice I’ll pick that first then decide on the other. If there are two obvious choices, I’ll likely pick them in any order which is what I presume may occur here.

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Looking at the percentages:
  • The great library is favored as pick two or three and is seldom selected over a replay wonder
  • The sphinx is least likely to be picked if any other replay wonders are available

#5.2 Pantheon

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  • The replay wonders are still the favored choice with the inclusion of the Sanctuary
  • The sanctuary is preferred over the sphinx and the apian way but not the other replay wonders
  • The divine theatre is also in the top selection tier with ability to get a strong god card but is seldom selected ahead of the top 3 replay wonders
  • Someone picked the Pyramids as their first choice! This player was 475 rated against a 300+ player so I can only presume a mis-click 😊 There were 2 games in all the data where the Pyramids were a first pick. These players both lost!

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#5.3 Agora

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  • The Curia Julia wonder immediately goes to first pick. The benefit of a replay, coins and conspiracy make this very strong
  • Knossos also features highly ahead of the hanging gardens with its political advantage
  • The other wonders move down the ranks in a similar order as the other game types

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#5.4 Both

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  • No real surprises when the wonders of Agora and Pantheon are combined
  • Agora wonders are the top choices with their political advantage and Pantheon wonders come in behind the top 2 standard replay wonders
  • The mausoleum and statue of Zeus again sit low down the selection with the Pyramids last selection again

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#5.5 All

Just to round things off we’ll look at the break down of all wonders and game modes ordered by selection percentage

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  • 9 out of 10 games Curia Julia appears it is the first pick for Agora based games
  • Military wonders are the last picks
  • Replay wonders are only left for the expansion wonders

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Le007n
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Re: 7WD in Numbers - Part 1/3

Post by Le007n »

#6 Wonder Win Rate

We obviously have favorite wonders to select but do these wonders equate to a higher win?
If you had to guess now, which would be your top 5?

Image

#1 - The answer is not too surprising. For Agora based games, the Curia Julia is ahead of the pack with a 59.3% win rate
#2 - Second in terms of win rate is Knossos at 58.6%
The inclusion of both these wonders in the high win rate positions again points to the strength of Political influence in these games which is much stronger than other areas

#3 Removing the Agora wonders the top standard wonder is Piraeus at 54.1% win rate. The replay ability combined with the additional refined resource often removes the pressure of gathering these resources allowing players to concentrate on other areas

#4 The first surprise is the Sphinx at place 4 with 53.1%. The sphinx is often the last selected of the replay wonders but its 6pts seemingly makes it a strong end game wonder for collecting extra points. This is much more so than the Pyramids which warrants its last pick with just 3 extra pts and no additional abilities

#5 At number 5 is the Mausoleum. This is an underrated wonder in my opinion and it is very versatility to assist in a science, military or other win type. The ability to take a previously discarded card means it can open the door for some surprise victories and it is in my opinion a great second or third pick and an amazing fourth pick if you are left this wonder after the top picks have been taken

Surprisingly, 2 of the 3 military wonders make up the only other to have a better than 50% win rate
Since the military win rate is the lowest of all types, these wonders are probably more likely to be used for victory points or not constructed. That being said, I do think the Statue of Zeus is another underrated wonder which can be very strong removing a resource in the right situation and should not be taken lightly



#7 Ra

#7.1 Whenever I play Pantheon it always feels like the race for Ra. The ability to take an opponent’s wonder always seems game changing to either get the advantage in replay wonders or to use as a threat to force wonders to be quickly made
I therefore wanted to see what the win % was when Ra was in play
The results were somewhat expected

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In Pantheon alone, constructing Ra led to a massive 86.7% win rate. This is game changing. In a game with Both expansions, the influence of Ra is reduce but still gives the player a 68% win percent so I think I can safely say that Ra is as powerful as I though!

#7.2 Of the games analyzed, Ra appears in over half (59.4%). This is likely due to Ra appearing from the initial card turns and then players searching for him using the Divine Theatre or the Gate giving Ra a higher appearance percentage


#8 Starting Player

The question which I see the most is ‘first player has a big advantage’.
In my experience, do I want to be first player, yes! I like having control of the first Age to get good resources. Does it matter if I don’t get it, no! The better resources are in Age II. Top players know how to work the card structure and to be good at the game it is key to win as either first or second player. That sometimes mean adjusting your strategy but is a article for another day
So is there an Age or combination of Ages which increase your chance to win? Lets see…

#8.1.1 Standard

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As expected, if you start all the ages you have the highest chance of winning – 74%. This would likely occur with a less experienced opponent who gives up turn position early or for a player with many replay wonders who can take two cards at the end of Age I to benefit from starting Age II. Starting all 3 Ages would give first pick for many cards and a very strong control over the card structure so is rightly linked to a high win percent

#8.1.2 - Start Multiple Ages
A combination of starting Ages 1 & 2 or Ages 2 & 3 give the next best win rate at 66.4-67.3%.
Starting Ages 2 & 3 is the strongest combination for the second player and they can control these Ages (presuming they have equal or an advantage of replay wonders) where the stronger selection of cards are available
Starting Age I and III in comparison has a much lower win rate which is surprising but may indicate a player which has not applied any military pressure giving their opponent the pick of cards

#8.1.3 - Start Only One Age
If you were to only start one age, the Age II is the one to go for.
Players starting the second age often have first pick of science cards to make pairs and can start collecting resources missed from Age I. Obviously, the only way a player could only start Age 2 is if they weren’t the first player, so this is Player 2’s chance to shine!

#8.1.4 - Start An Age
The main question we want to answer, what advantage does the first player have?
For player one, starting Age I in the standard game, (regardless of starting any of age) has a 55.7% win rate. This is only just over half so by no means broken, overpowered or any other words used.
Age II is the most beneficial to start. Players starting Age II have a 64.5% chance of winning.
An Age III start gives a much lower 53.8% win rate so Age II seems to be the more pivotal Age



#8.2 Pantheon

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  • Pantheon follows a very similar pattern to Standard. Starting all Ages increases the win chance to a huge 88.2%
  • Age II is again the best age to start when taking away any other combinations – 74%
  • Starting just Age II is also very strong at 77.8%.
  • Age II is likely even stronger in Pantheon thanks to the first pick of the divinities. As a direct effect of this, starting Ages 1 & 3 (not Age 2) gives the worst win percent at 22.2%. Getting first pick of the divinities is key



#8.3 Agora

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  • Age II is again the top performer in Agora
  • Starting all three ages is no longer quite as high, possibly due to the additional cards available changing the flow of the game or possible this is just the case in the games analyzed?
  • Starting Ages 1 & 3 or just Age 3 has the worst win %
  • Starting just Age 1 increases back to a 55.9% win rate without the presence of the divinities




#8.4 Both

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  • Starting all ages returns to the top spot
  • All combinations with Age II appear next, again showing its importance
  • There are fewer extreme values then with either of the expansions on their own making it more akin to the Standard game
  • First player has a 56.1% win rate so above average but again, only slightly



#8.5 All

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  • Across all game modes, the first player has a 55.1% win rate
  • Starting Age II is the most important – Starting Age II give a 60% + win rate rising to 65%+ when starting any other Age also
  • Players starting just Age 3 have the lowest win rate. By this point in the game, the opponent has likely had their pick of the best resources, science and political cards creating a strong (but not unbeatable) position


Conclusion

First player has a 55% win rate. Ra is very broken and Age II is the best age to start.
I have some more areas I looked at, most / least constructed wonders etc but I think that will do for now.
Some of this may be rushed and I’ll no doubt tidy things up at some stage but I’ve sat on it for a while and wanted to share.
Hopefully it will provide some areas of interest to allow others to expand on this understanding to enjoy this beautiful game!
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sorryimlikethis
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Re: 7WD in Numbers

Post by sorryimlikethis »

I don't have the most experience with 7WD, it's not one of my favourite games. But I saw this thread and clicked out of curiosity. I'm blown away by the amount of detail you've gone into! Seriously impressive. You should share this on Board Game Geek where it will reach a larger audience.

The format of everything looks fine after a few refreshes. Not sure if it was my browser or these forums that had trouble loading everything, the posts kept getting cut off.

As for the data itself I'll need a while to go through everything properly. It looks great though well done.
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Pistol Star
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Re: 7WD in Numbers

Post by Pistol Star »

Awesome, awesome work, my friend! :)

It's really interesting. The sample size is still too small I think but that's a really good start and definitely shows clear tendencies at the very least.

How did you do this analysis btw.? Where did you get the data from?

I do not agree about 1st player being only a slight advantage. Around 56% is really much and that is really sad that there is no balancing in terms of starting money or something else. It's also a shame because the starting player is always randomly chosen. If at least it would be possible to always switch between being first player and 2nd player..But if you are unlucky you have a pretty long streak of being 2nd player in the worst possible moments :D

It is roughly a 56% vs 44% advantage. Each percentage point you deviate from the perfect 50/50 scenario is in reality a 2% deviation. So here we do have a 12% deviation, which is just insane.
I do think it should be at the very least below 52% vs 48% to pay tribute to this fantastic game. If this could be achieved it would be such a colossus improvement to the game.

For me it's also not understandable how the designers could add such overpowered wonders and gods into the expansion. At the very latest when an expansion is being planned they should understand the balance of the game and there was their chance to add a handicap to the 1st player advantage/2nd player disadvantage but they missed it and added even more overpowered wonders and gods to the game.

This game is fantastic but it could be even waaaaay more fantastic if they could improve on these things :)
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Jellby
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Re: 7WD in Numbers

Post by Jellby »

Pistol Star wrote: 26 April 2022, 14:37It is roughly a 56% vs 44% advantage. Each percentage point you deviate from the perfect 50/50 scenario is in reality a 2% deviation. So here we do have a 12% deviation, which is just insane.
You could also say that if 1st player wins 56 games, and 2nd player wins 44 games, 1st player is winning 27% more games than 2nd (56/44 = 1.27).
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Pistol Star
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Re: 7WD in Numbers

Post by Pistol Star »

Jellby wrote: 26 April 2022, 14:56
Pistol Star wrote: 26 April 2022, 14:37It is roughly a 56% vs 44% advantage. Each percentage point you deviate from the perfect 50/50 scenario is in reality a 2% deviation. So here we do have a 12% deviation, which is just insane.
You could also say that if 1st player wins 56 games, and 2nd player wins 44 games, 1st player is winning 27% more games than 2nd (56/44 = 1.27).
Good point! This is just way too much. When we just compare these numbers with how often the casino wins in no skill games like roulette vs a perfect playing person then we see that the casino's win far less frequently then the first player in 7 Wonders Duel and the casino's are making insane amounts of money with these "slight" edges. In reality these house edges are really large over a large sample size and it's a shame for a board game to have such imbalances because this flaw could be so easily eradicated.
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Silene
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Re: 7WD in Numbers

Post by Silene »

Pistol Star wrote: 26 April 2022, 15:09 Good point! This is just way too much. When we just compare these numbers with how often the casino wins in no skill games like roulette vs a perfect playing person then we see that the casino's win far less frequently then the first player in 7 Wonders Duel and the casino's are making insane amounts of money with these "slight" edges.
But in a casino, you will always have the slightly lower odds vs. the bank while here in 7WD, the odds are sometimes for and sometimes against you, which means you'll get your fair share over time. I think 56% is not a big deal. But if it can be fixed easily, then it sould.
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exoone
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Re: 7WD in Numbers

Post by exoone »

Excellent work!
Maybe there will be more statsitics on divinity cards? Like win rate, seletction rate or something else?
And for some situational Gods, like Ishtar or Nisaba, will the player who plays them lose more with no science victory achieved later or no green cards to put Nisaba token on? Or more genereally, will a player lose more if he plays God only to "skip" turns?
The analysis about Wonders is awesome. I might ignore this part and I wonder will a player with more replay Wonders drafted win more?
Another question is about advatange in starting Age 2. In most cases, players fight for starting Age 2 and the loser gain 0 shield advantage. I have no idea but kind of wonder if becoming the second player in Age 2 with shields advantage could impact the win rate?
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Pistol Star
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Re: 7WD in Numbers

Post by Pistol Star »

Silene wrote: 26 April 2022, 15:32
Pistol Star wrote: 26 April 2022, 15:09 Good point! This is just way too much. When we just compare these numbers with how often the casino wins in no skill games like roulette vs a perfect playing person then we see that the casino's win far less frequently then the first player in 7 Wonders Duel and the casino's are making insane amounts of money with these "slight" edges.
But in a casino, you will always have the slightly lower odds vs. the bank while here in 7WD, the odds are sometimes for and sometimes against you, which means you'll get your fair share over time. I think 56% is not a big deal. But if it can be fixed easily, then it sould.
That's true of course, except for Poker ;) But the odds aren't that slightly off. It adds up really quickly in casino games. That's why I wrote "slightly".
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