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First of all thanks to

Johan Koitka
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Lille
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He is an (the?) admin on boite-a-jeux, coded their excellent Castles of Burgundy implementation and kindly provided me with essential database-dumps. Without these I wouldn't have been able to analyze a few thousand games that quickly. Unfortunately board numbers have only been recorded for some weeks (since 10x boards went live) so I could use only about 40% of all CoB games played on boite-a-jeux up to May 23rd.

Please pay attention to the absolute numbers given in the second column. These should indicate that the sample just can't be representative especially for 3 and 4 player games. But the results shown in the tables/diagrams below are interesting nonetheless. I elected not to clutter up the post with quartiles, quantiles, averages (=arithmetic means) for each starting position and placement, max/min scores and some other more obscure stats as the ones given below paint a nice enough picture. I also didn't invest time to check if better players (by Elo points) fare better on specific boards or if board x really shines against board y. There's just not enough data (yet) to get significant results. But if you want more just let me know what you'd like to see explored.

A few tidbits:
- about 1-2% of games were decided by tiebreaker (2p 1.01%, 3p 1.67%, 4p 1.96%)
- starting the game seems to be an advantage with 2p (51% win%), but not with 3 or 4 (32.66%, 22.64%) - it's more extreme with some boards of course
- per extra player the average score goes up by about 17 points (2p 184.6, 3p 201.7, 4p 218.2 - for games with at least one expert board)
- board 8 is by far the best one (who would've guessed that? )
- board 7 is obviously better than people think (a 7 space city isn't that hard to complete)
- 10a/e/f/h are even worse than the standard board
- 10g really shines with more people (likely due to the 6 space meadow)
- the more players contend the closer the fight for 1st place (yeah, another astonishing discovery )

A few explanations:
- The 1vs1 row contains only games where all players used board 1. Therefore there are no win% and differences for these.
- diffW = 1st place points - 2nd place points
- diffL = 1st place points - (2nd|3rd|4th) place points [= point difference between 1st and achieved place]
- boards 10a to 10h are ordered so one can compare front and back easier

4p games

brd n avg sd 1st 2nd 3rd 4th diffW diffL

1vs1 193 204.7 25.6
1 214 206.9 25.3 15.3% 22.7% 24.1% 38.0% 12.8 43.8
2 151 215.9 27.2 22.2% 25.9% 21.5% 30.4% 18.2 37.5
3 167 220.6 23.7 25.7% 27.5% 24.6% 22.2% 17.1 34.4
4 174 210.8 22.5 11.2% 28.7% 30.9% 29.2% 15.8 39.1
5 166 222.3 21.8 23.4% 28.1% 30.4% 18.1% 19.7 29.5
6 159 220.9 24.8 29.7% 24.2% 24.8% 21.2% 20.1 35.6
7 53 224.0 21.9 29.1% 32.7% 27.3% 10.9% 22.2 29.6
8 167 245.4 25.8 59.4% 21.1% 13.7% 5.7% 28.1 22.2
9 51 210.4 25.2 18.5% 22.2% 18.5% 40.7% 13.9 41.1
10a 117 202.3 23.6 7.4% 17.2% 30.3% 45.1% 11.0 46.0
10e 100 205.6 24.9 11.5% 19.2% 28.8% 40.4% 15.9 46.5
10b 157 227.2 22.4 34.2% 29.8% 23.0% 13.0% 21.1 29.2
10f 43 204.5 20.5 6.7% 22.2% 37.8% 33.3% 35.3 41.9
10c 133 225.4 22.5 32.4% 31.7% 17.6% 18.3% 16.2 30.1
10g 102 227.7 26.0 37.1% 27.6% 22.9% 12.4% 22.0 35.5
10d 108 221.0 23.8 26.3% 30.7% 26.3% 16.7% 13.8 34.1
10h 108 202.2 20.9 8.2% 18.2% 32.7% 40.9% 12.1 44.1


3p games

brd n avg sd 1st 2nd 3rd 4th diffW diffL

1vs1 220 187.3 22.5
1 197 193.8 22.8 26.3% 36.3% 37.4% 16.2 34.0
2 128 197.7 28.2 24.8% 39.8% 35.3% 23.8 35.8
3 149 206.0 23.0 40.0% 29.3% 30.7% 20.5 30.7
4 168 199.3 24.0 25.1% 32.2% 42.7% 18.4 34.1
5 168 208.5 18.6 34.9% 41.9% 23.3% 17.2 26.1
6 161 197.0 24.7 30.2% 29.0% 40.7% 19.6 33.4
7 54 203.4 23.8 32.1% 32.1% 35.7% 29.3 29.6
8 159 226.1 22.8 68.8% 25.6% 5.6% 29.2 20.0
9 55 194.7 25.1 21.4% 37.5% 41.1% 27.0 39.5
10a 129 188.7 20.1 16.2% 33.8% 50.0% 20.9 37.8
10e 75 193.9 23.9 16.9% 36.4% 46.8% 19.4 37.7
10b 154 207.2 21.1 44.9% 31.4% 23.7% 23.0 29.2
10f 62 184.0 26.2 25.8% 17.7% 56.5% 15.1 49.0
10c 109 213.7 23.2 46.4% 33.9% 19.6% 25.5 28.8
10g 85 207.6 24.1 39.3% 38.2% 22.5% 19.3 29.4
10d 107 204.8 21.8 30.9% 41.8% 27.3% 18.1 27.5
10h 101 184.6 19.7 18.4% 35.0% 46.6% 15.7 38.1


2p games

brd n avg sd 1st 2nd 3rd 4th diffW diffL

1vs1 2091 169.4 21.5
1 1317 174.2 21.4 39.0% 61.0% 23.1 29.8
2 713 178.7 25.0 42.9% 57.1% 26.5 32.3
3 901 188.8 23.0 52.7% 47.3% 29.5 25.5
4 927 182.0 21.8 45.7% 54.3% 24.4 27.2
5 1124 191.4 19.1 58.0% 42.0% 28.0 22.3
6 906 185.3 23.9 53.3% 46.7% 29.1 27.4
7 343 190.3 22.8 58.9% 41.1% 28.7 26.1
8 1027 205.5 22.8 74.4% 25.6% 35.7 18.2
9 273 179.5 24.1 48.0% 52.0% 32.0 31.2
10a 830 173.6 21.1 34.9% 65.1% 20.0 31.4
10e 446 169.4 26.4 29.4% 70.6% 21.1 32.9
10b 954 191.8 20.6 61.5% 38.5% 27.4 23.8
10f 295 174.5 22.0 40.3% 59.7% 24.4 32.3
10c 714 191.7 23.1 57.8% 42.2% 30.6 24.3
10g 543 187.2 21.9 53.6% 46.4% 26.8 26.3
10d 759 188.9 20.2 48.0% 52.0% 26.7 23.5
10h 529 164.1 22.4 29.5% 70.5% 21.7 35.6


Or in a nutshell:

avg pts per board per player count

win% - expected win%
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Were the 10x boards only played against each other using the altered rules?

Does this simulation take back to back boards into account (i.e. with the physical copy, someone with board 8 can never play against board 9 since they are back to back, same with 10a and 10e)?
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Matt Sargent
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DoomTurtle wrote:
Were the 10x boards only played against each other using the altered rules?

Does this simulation take back to back boards into account (i.e. with the physical copy, someone with board 8 can never play against board 9 since they are back to back, same with 10a and 10e)?


The rule about having to connect all your areas to a castle was not used.

At the start of the game, you are given one of the boards at random and choose which side of it to use. So yes.
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DoomTurtle wrote:
Were the 10x boards only played against each other using the altered rules?

Does this simulation take back to back boards into account (i.e. with the physical copy, someone with board 8 can never play against board 9 since they are back to back, same with 10a and 10e)?
What Matt said.

It's even slightly visible in the numbers. Adding n for 2+1*1/4, 3+1*1/4, 4+1*1/4, 5+1*1/4, 6+7, 8+9, 10a+e, 10b+f, 10c+g, 10d+h should result in the same range.
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Patrick Fournier
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Great stuff, very interesting. Thanks for sharing!

I'm a bit surprised by the performance of board 7. People have to choose between board 6 and 7, and they pick #6 about 3 times more often, when board 7 is giving a better result (approx. +5 points). I'll know what to do next time... whistle

I'm also surprised by the standard deviation of board 2, I expected the 36-point 8-tile city to generate more variance, it's usually hit or miss with this high-risk board.

I hope you'll be able to update your stats with a bigger sample in a few months. I'd be very interested, if it's not too much trouble.

Btw, congratulations on your ranking on boiteajeux, most impressive. cool
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David Debien
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Pretty much shows me what I have been saying all along. Board 8 should be removed or given to noobs.
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Patrick Fournier
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casualgod wrote:
Pretty much shows me what I have been saying all along. Board 8 should be removed or given to noobs.


+1. Based on this sample, assuming normal distributions, in a 2p game, if someone draws board #8 and the other player draws board 10a/10e (picking the 'good' 10a side), that player has about a 15% probability of winning (assuming equal skill)...

Sure, there's some luck involved in CoB, but that's a bit too much...
 
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Josh Chen
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Next time when I pick my board I should stick to odd numbers:

3, 5, 7...and the only even number I should pick is 8. whistle

(Just kidding, in reality, when I play it with gf, we roll a d8 dice for it)

Thanks for sharing!
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DoomTurtle wrote:
Were the 10x boards only played against each other using the altered rules?
Sorry, misinterpreted your question. The draw is random (like Matt said) and there's mix and match. So you could play with 10x against 1-9.

I've just checked for games with only 10x boards (2p only), the results are slightly different but the trend isn't broken:

10a 245 170.7 21.0 31.4% 68.6% 20.0 31.2
10e 145 170.3 29.5 26.2% 73.8% 25.4 30.8
10b 324 193.3 20.6 68.5% 31.5% 29.4 23.8
10f 98 175.4 19.6 44.9% 55.1% 26.4 32.4
10c 257 192.3 24.3 62.6% 37.4% 35.3 24.3
10g 158 187.6 22.5 60.1% 39.9% 25.3 25.2
10d 252 188.8 21.0 49.6% 50.4% 30.8 23.3
10h 163 163.2 24.6 36.2% 63.8% 20.9 36.2



Falzir wrote:
Great stuff, very interesting. Thanks for sharing!

I'm a bit surprised by the performance of board 7. People have to choose between board 6 and 7, and they pick #6 about 3 times more often, when board 7 is giving a better result (approx. +5 points). I'll know what to do next time... whistle

I'm also surprised by the standard deviation of board 2, I expected the 36-point 8-tile city to generate more variance, it's usually hit or miss with this high-risk board.

I hope you'll be able to update your stats with a bigger sample in a few months. I'd be very interested, if it's not too much trouble.

Btw, congratulations on your ranking on boiteajeux, most impressive. cool

Thanks for the feedback.
I'll chose board 7 more often as well ^^
The sd of board 2 is slightly higher. But even in "normal" games results will vary heavily due to the different mix of knowledge tiles, let alone the dice I hadn't expected the sd to be that high across the board as well, but it seems to be correct.
I'd like to update the stats in some months. diplojak might be nice enough
 
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Cool! Looking forward to seeing results with more data!

For those of us who don't know which board is which (surely there are better pictures? I'll update this if/when I find them):

1

2
3
4
5

6 7
8 9

10a
10e

10b
10f

10c
10g

10d
10h
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Frédéric MOULIS
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noon wrote:
The rule about having to connect all your areas to a castle was not used.


Either I don't understand what you mean, or you are wrong.

In BoiteAJeux's implementation, you play with the real rules : you can chose your side of the board, and the place for your first castle. Then, the tiles you place must always lie directly adjacent to at least one previously-placed tile.
So all your areas are connected to a castle.
 
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bretonducalvados wrote:
Either I don't understand what you mean, or you are wrong.
First part

There's a special rule for boards 10a-10h: each new tile has to be connected to a castle via tiles of the same colour! This rule isn't implemented on baj.
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Frédéric MOULIS
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yzemaze wrote:
bretonducalvados wrote:
Either I don't understand what you mean, or you are wrong.
First part

There's a special rule for boards 10a-10h: each new tile has to be connected to a castle via tiles of the same colour! This rule isn't implemented on baj.


OK, thanks for your reply. I didn't know this rule. blush
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Neil Christiansen
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You can play those boards without the new rule, but not the old boards with it.
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Andrew Norgren
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Intuitively, I knew that 10e and 10h are terrible, and never play them!

BUT, that might skew the statistics. I think that the "worst" maps, might not be quite as bad as the stats, but since they are certainly weaker, better players intuitively know not to pick them when given the choice. So, those maps will lose more frequently when played, because the only people that pick them are lesser players. The same is not quite true for the reverse, because no one will actively avoid board 8 (to my knowledge).

So to make these statistics more complete, it would be good to have a filtering aspect, recording the ELO of the players playing the map as well, and also other factors such as if the player tends to go for a specific strategy no matter what, or what tiles were omitted from the game. Also, the opposition's boards matter too. Of course this might be too difficult to do.....but just some thoughts on the precision.

Moral of the story: board 8 is just as OP as the stats show, but the other maps are not nearly as underpowered as they might indicate by stats.

Why is 8 so OP? 1 Sized regions are relatively much stronger, when they are any color but animals. Animals are the only terrain that benefit immensely from having 5 and 6 sized regions (or at least, don't have a drawback). Size 3 and 4 regions are by far the worst, since the curve is a slowly growing exponential, while the decrease in points for the time period of completion decreases at a linear rate.
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J. Alex Kevern
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Atomation wrote:

Why is 8 so OP? 1 Sized regions are relatively much stronger, when they are any color but animals. Animals are the only terrain that benefit immensely from having 5 and 6 sized regions (or at least, don't have a drawback). Size 3 and 4 regions are by far the worst, since the curve is a slowly growing exponential, while the decrease in points for the time period of completion decreases at a linear rate.


Also, I would add that having 6 separate brown "building" regions is really conducive to scoring scoring points from yellow knowledge tile that score 4 points per building.
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I'm lost on these 10x boards. Where do they come from? I have the 4 expansion boards that are numbered 13x. They are different from these. Please explain the difference.
 
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caltexn wrote:
I'm lost on these 10x boards. Where do they come from? I have the 4 expansion boards that are numbered 13x. They are different from these. Please explain the difference.
http://www.boardgamegeek.com/boardgameexpansion/110926/the-c...
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Steve Duff
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Man, board 2 sucks, just played it tonight. Horrible start area way on the edge limits your early expansion, and a nearly impossible to complete size 8 city area. yuk
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Brian Coppedge
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Atomation wrote:
Size 3 and 4 regions are by far the worst, since the curve is a slowly growing exponential, while the decrease in points for the time period of completion decreases at a linear rate.

This is a really insightful observation; however, I can't resist pointing out that the triangular numbers grow quadratically.
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So does it make sense to give each board a score bonus/penalty, based on these numbers? I like the variety of playing with different boards, but for a game so mathy, it seems a shame to give players unequally good starting positions.
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Dave K
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Wow... Had no idea board 8 was so overpowered. Will keep in mind. Thank you for the analysis!
 
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grasa_total wrote:
So does it make sense to give each board a score bonus/penalty, based on these numbers? I like the variety of playing with different boards, but for a game so mathy, it seems a shame to give players unequally good starting positions.
It might be a good idea, but I would just ban board 8, never use 1 anyway and play 10s against each other only.
If you'd like to figure out an adequate score bonus/penalty you might consider waiting a few months. I still intend to update and expand the stats later this year.
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Katherine Boag
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Could use an update to the pictures post.
 
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Happymrdave wrote:
Wow... Had no idea board 8 was so overpowered. Will keep in mind. Thank you for the analysis!


Is it only overpowered if you are 1st Player?

Am I reading it correctly.

The percentages drop below all the previous boards in a 4p game.

WHY play this game 2 player?

 
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