Are the A-sides and B-sides of the wonder boards really balanced?

Question

I know the rules claim the sides are balanced and can be mixed in the same game, but I have my doubts. In general, the B-sides feel a little stronger to me, but it's sometimes hard to compare because they are so different. In most cases, it probably comes down to style of play and strategy to be used in a particular game. However at least in the case of Rhodes, the B-side seems to have an advantage. Here's a comparison:

Completing all wonders of A-side yields:

• 10 Victory points
• 2 Shields

Completing all wonders of B-side yields:

• 7 Victory points
• 2 Shields
• 7 Coins

Just looking at this alone, there is little difference between the benefits of the two sides. Since the 7 coins can be converted to 2.33 victory points, the A-side has only a very slight edge. However, there are some other things to consider which tip the scales in favor of the B-side:

• 3 coins are worth more than a victory point. At a minimum 3 coins equal a victory point, but coins are the tie-breaker, so 3 coins is greater than one victory point. Also, coins have more utility as they can be used to purchase other things, if desired.
• The B-side gets a Shield bonus and 3 coins after building the first wonder, making it much easier to get a military victory at the end of the first Age, and the coins are very helpful early on. The A-side doesn't give any benefit for the first wonder (aside from the victory points, which don't help until the end of the game).
• The A-side requires 2 Wood, 3 Clay and 4 Ore to build its three wonders, respectively. The B-side only requires 3 Stone and 4 Ore. The 3 Clay and 3 Stone are basically equivalent, so the B-side avoids needing two of a third resource (Wood).
• The B-side only requires two turns to build all wonders, while the A-side requires three. With the extra action a B-side player could simply discard a card for three coins, giving it a total of 10 coins, which then puts its rewards ahead of the A-side as the 10 coins would give 3.33 victory points. But the B-side player also has the option to put an additional card into play, which could be worth much more than 3 coins.

All of this makes a strong case that the B-side of Rhodes is not balanced with the A-side. About the only advantage I can think of that the A-side has is for cards that count number of wonders built: Arena and Builder's Guild. Depending on the setup, Builder's Guild may not even be in the game. And, the B-side has the advantage of weakening that card for your neighbors. Arena is a nice card, but it's not a big loss, IMO. Does the A-side have some other advantage I'm missing?

I'm not sure if the A-side of Rhodes is underpowered or the B-side is overpowered, compared to other boards. When using the wonder cards to randomly determine which wonder board each player will play, we've taken to letting players choose the side they want to play because the consensus is some sides are just weaker than others.

Do any of the other boards exhibit similar imbalance? I haven't examined the others that closely.

Answer 1

From what my friends and I can ascertain, the board sides are not designed to be strictly balanced per se, but are instead designed to work best with different play strategies, or at least different skill levels.

In my experience, the "A" sides provide fewer opportunities for specialization than their "B" side couterparts. For example, if a player is playing with Rhodes, but fails to take advantage of the early military points and never plays a military card, that player would have probably been better off with side "A", which provides a few extra victory points and more closely matches the costs and benefits of the other wonders.

That said, it doesn't take much more than a basic working knowledge of the game to make the "B" sides more than pay for themselves, especially with a wonder as unbalanced as Rhodes (other wonders' "B" sides aren't quite as obviously better). In our games, even novice gamers rarely select side "A" after their first couple run-throughs, and when they do, it is rarely a winning strategy.

Answer 2

No, they are not strictly balanced. It's impossible for such a thing to be true. Still, the degree of imbalance in a global objective sense is not as great as a the perceived imbalance of the boards given any particular set of players.

7 Wonders is highly interactive, so your choices affect your opponents and vice-versa. Due to a particular set of player's strategies, some boards will certainly provide an advantage over other boards. If you are finding one side wins more than another try adjusting your strategy (and getting other players to do so as well) to compensate, and you'll see a significant change in winning stats.

Even if a large number of games, with a wide and varying number of players with different skills in different groupings is played and collected (e.g. on BSW) differences in wins for different sides of the board could be due to the skill-level/complexity of playing that side of the board, and not an intrinsic imbalance.

Answer 3

[EDIT]
As promised I'm getting back with more stats.
TL;DR: You can view an interactive version of the stats in this js fiddle
There are 3 tables. One for sides only, one for wonders only and one for wonders and sides.
Long version200 games played.
Taking into account sides only (ignoring wonders) results into a pretty good balance in points average. Side A wins by 0.1 points, but side B has a better winning percentage.

Looking at wonders only, ignoring sides, there are differences.
The stats contain also some extension packs and the funny thing is that the wonders from the extension packs are at the top or bottom of the list.
For the standard wonders the difference in points average between the "best" (Ephesos) and the "worst" (Rhodos) is a bit below 4 points.

Combining both wonders and sides the results are all over the place.
Some wonders look balanced, some don't.
But, again, one funny thing. Contrary to the OP's example, Rhodos looks like the most balanced one. The points average are the same up to the second decimal point 62.94, though nobody in our group has ever won with Rhodos A. (this has been debunked 100 games later.)

most balanced wonder seems to be Alexandria with 0.34 points in favor of B.

Most unbalanced one is: Halikarnassus with a difference in average of 4.5 points in favor of B.

Disclaimer: My answer should not be taken as proof of anything. The values are based on the games we played in the same group of 12 people. Almost all games were played with leaders and cities extension (3 were played with standard game only) and the wonders were assigned randomly and in most of the games the sides were random as well
[/EDIT]

Original answer:
I know this is an old question, but I wanted to add my input on this.
We play 7w occasionally at the office and I've built an app to keep scores (because we ran out of score papers).
We don't have a lot of games recorded, so this may not be conclusive, but the equilibrium has been there since the beginning.
The numbers are not exactly the same, but they are really close.
All of the games have been played with the standard game plus extensions for leaders and cities and wonders pack.
The wonders were assigned randomly, but in some of the games the sides were chosen and in others were assigned randomly.

Here is the text version:

Side    Games Played    Games Won   Win %      Total Points     Average     Max Points  Min Points
A       127             21          16.54%     8121             63.94       91          36    
B       131             24          18.32%     8507             64.94       90          34

What "scares" me the most is the points average.
It differs by 1 point.
If I choose only the games played in 3 to 7 people (exclude the ones in 8) so they all have 7 rounds per age the average is this:

A: 66.25  
B: 66.72  

This means less than 0.5 points in difference.

Answer 4

The two sides are not designed to be balanced. On 6 out of 7 wonders in the base game, side A has been in fact created to ease new players in the game, by providing a common pattern among them:

1. 3 Victory Points
2. Variable power
3. 7 Victory Points

Side B is almost always strictly better than side A. Here's a detailed approach, from my point of view.

Alexandria

Probably the most versatile wonder in the base game, you can seldom get locked out of resources with this one. Side B gives you:

• The wild raw material in the first stage, which is extremely important to have in the early game. When constructing stage #2 of side A it's usually too late to take full advantage of it.
• Gives you a wild advanced material, which is usually welcome, especially in 4-player games, where you can easily get locked out of one.
• 3 Victory Points less, in exchange for aforementioned infrastructure. Is it worth it? I'd say yes.

Furthermore, side A is really weak, as you need double Glass for the final stage. There is no card or other Wonder stage in the base game that needs a double glass and your neighbors, if playing smart, will refuse to take one for you. So, unless you come across a Forum in Age II, you're forced to lose an action to take a second Glass, so that you can take 7 Points, making it 3.5 points per move in the late game, which is very suboptimal. Ephesos and Halikarnassós suffer from a similar problem.

Babylon

Overall, the weakest Wonder in the base game, from my point of view, and side A makes things worse as it forces you to get science cards, by placing the wildcard science symbol in the middle. Side B gives you:

• The ability to play the last card of each Age, so up to 3 more cards than other players.
• The wildcard symbol is placed at the last stage, so you may opt out from science completely.
• 7 Victory points less, in exchange.

Is it worth it? Well, both are weak.

Ephesos

Nothing to discuss here. Side B also gives you 10 points, more money, 12 coins in total instead of 9, and the money is distributed over the 3 stages, making Ephesos more versatile. Furthermore, side A suffers from Alexandria's side A problem, by requiring a double Paper for the final stage. Therefore, side B is strictly better than side A, no arguments about that. This is probably my second favorite Wonder in the base game, following Alexandria B.

Gizah

That's probably the only wonder with almost equally balanced sides. Side B gives you 5 more points in exchange for one more wonder stage. However, I would still claim that side B is more useful as:

• It tends to increase the value of the Arena from 6 Victory Points to 8 Victory Points, including money, and the value of Builders' Guild, if you get it.
• Makes it a perfect anti-science Wonder, as you can tuck 4 green cards underneath it!

Therefore, having an equal choice, I'd still choose side B.

Halikarnassós

It probably has the biggest strength difference between side A and side B. Side B offers:

• 3 "take from discard pile" actions, instead of 1, on every wonder stage.
• 7 Victory Points less, in exchange for that.

Is it worth it? You bet it is! The 2 extra cards you'll pick from the discard pile will usually make up the difference, but you'll have more flexibility. Side A's ability is right in the middle, which is really bad, as you'd want to construct your Wonder at the last round of the game, after everybody has discarded their cards. However, you'd lose the final 7 Points if you do, with side A.

Furthermore, side A suffers from Alexandria's side A problem, by requiring a double Loom for the final stage.

Olympia

This is different. Side B gives you:

• The ability to copy a neighbor's Guild.
• A double trading post.
• 5 Victory Points less and stripes you of the ability to construct a card for free on each Age.

Is it worth it? Eh, kinda. The double trading post on the first stage is always welcome. However, the "copy a Guild" is usually pointless: a Guild giving lots of points to a neighbor will usually be worthless for you, so the final stage won't give you more than 3-4 points. Even the double trading post won't be always useful, as maybe the player across you has been hoarding all the resources, making your neighbors reluctant to take any brown cards. Furthermore, the ability to construct a building for free is a good one to have and gets very useful in Ages II and III.

3 player games are an exception, the double trading post is much more powerful, as you are able to buy resources from all your opponents and the final stage tends to give out more points. You can safely pass the Builders' Guild there!

Consequently, when I have a choice, I pick side B if I'm playing a 3-player game and side A otherwise.

Rhodes

Side B gives you:

• 7 coins
• Only 2 stages and the two shields distributed over them.
• 3 Victory Points less.

Is it worth it? Definitely. Taking money into account, side B gives you 9.33 points, but 3 coins are strictly better than 1 Victory Point, as you can spend them to get a valuable card which otherwise you'd have to pass up and they count towards the tiebreaker. Therefore, the 7 Victory Points && 7 coins are borderline "strictly" better than 10 Victory Points. This money comes very handy in the game.

Furthermore, taking one shield at a time is much more useful, as you can sometimes have your first shield in Age I, which might make the difference. Not to mention that you have one wonder stage less to build, although this decreases the value of the Arena or Builder's Guild and makes Rhodes a bad anti-science Wonder.

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To sum up, side B is almost always much more useful and flexible than its side A counterpart. For this very reason, in my groups I always let people chose their favorite side, than just rotating the card as suggested by the rules. Even if the group's rules are to randomly choose the sides, I'd definitely defend anyone who ended up with side A of Alexandria, Ephesos or Halikarnassós, as they are clearly underpowered.