Reassessing optimal number of territories: Golden Numbers

[Coleman]

In Response To The Topic In General
I'm not sure what all people were hoping I'd have to say about this.

I agree with most of the analysis, numbers don't lie.

I also agree that random neutrals are bad and most of these numbers result in a lot of them in most player counts. Turning this disadvantage into math is difficult and I have no idea how to go about it. Instead I'd want to focus on avoiding them entirely within the numbers provided.

Something to add...

Code: Select all

Players Pages
6       2193
5       582
4       2179
3       1835
2       3667

So the numbers that give 5 players a high number of neutrals don't concern me as much because 5 players is played least often. Solving 6 and 4 is probably best.

So with 6 and 4 players in mind. I believe 42 and only 42 is truly optimally fair for 6 players.

For 4 players 44, 52, 80, 88, 104, 116, and 160 are best.

Just for completeness if we wanted to start designing maps with 3 or 5 players in mind...

For 3 Players 42, 141

For 5 Players 35, 70, 80, 160, 190

Finding the absolute ideal for 2 players merits some extra discussion as 1/3 of the numbers are going to be neutral anyway so I'm not sure a random 1 or 2 on top of that matters a lot in the long run. My opinion right now is anything between 18 and 35 isn't too bad and anything above will favor the first player.

It is important to note that no one number is optimally fair for all the player counts while avoiding starting neutrals.

If you are wondering why I ignored 7 and 8... They are not a reality yet so they are not really on my mind.

In Response To D-Day
Starting both planes neutral 3 (my ideal solution) drops the total number into your desired 70, but that is only optimal for 5 players in avoiding starting neutrals, which is the least played (but still played enough) player count. I don't have a huge problem with this myself but mibi might, as it changes the focus from avoiding neutrals for 2, 3, 4, and 6 players to a game optimally designed for 5. The xml change would be negligible.

My largest concern with it is that the majority of players used to no neutrals would suddenly be confused by the high count of them when playing the map and may send false bug reports or unjustly dislike it as nothing says "D-Day is a map optimally designed for 5 players" and there is no sane way to notify everyone who plays it of the change.

[Aspect]

I dislike the d-day maps planes too... just weighing in on that point

But anyway, one thing you are all not mentioning is the player to go second, while he may have one less army to drop, has the advantage of attacking ones instead of threes. Now I'm pretty sure the odds are better 6v1 than 7v3.

As for neutral territories, I think that they are being unduly criticized. They provide an additional element of strategy to the game. Sure it adds a bit of luck, but so does a random drop in general. It's possible to start out with all of Australia, but it doesn't happen very often. The same goes for the random neutrals. They can impact the game, but what can't? Cards, initial drops, ROLLS, they are all luck based. Random neutrals should be a minimal consideration.

[Heimdall]

I don't mind games with many neutrals, however i have noticed some cases like Battle for Australia map you'll eventually end-up with Neutral territories that are totally ignored as it's better to attack another player than waste your armies on a Neutral player. Not sure what solution can be brought forward to counter this.

Keeping neutral territories at only 1 army might be a solution as this doesn't require too many resources to conquer and this lessens the luck factor.

[Coleman]

If all the neutrals are 1 then the players landing next to them actually gain an advantage instead of a disadvantage, so the imbalance would be switched.

Unless they were counting on neutrals to block for them... Either way, an increase in randomness usually results in a decrease in strategy, so I still feel avoiding random neutrals is a priority, but these sweet spot numbers are worth knowing.

[WL_southerner]

neutrals are a good thing and a bad thing, if you ever played the world knock out risk, then you know that all matches are played with neutrals they are prefix, and you need to throw a 7 on the dice to kill one army, there are 3 armys on neutrals at start of game,could it be possible to do the same have neutrals prefix like one in each continent and maybe 2 in the larger continent
oh we going to need more pixels for maps if lack up the number of players

[yeti_c]

I'm just going to Necrobump this thread - as it is really an interesting piece of analysis that should possibly be looked at by all budding Map Makers.

C.

[mibi]

i've kind of given up on trying to fit in the right number of territorities in there. neutrals are either good or bad depending on your view point, so i'll just let the digits fall where they may.

[MrBenn]

If you are wondering why I ignored 7 and 8... They are not a reality yet so they are not really on my mind.

Perhaps someone is able to re-run the figures with these included?

[MrBenn]

Current active games:

2 players - 3123

3 players - 1290

4 players - 3797

(4p doubles - 1080)
5 players - 2307

6 players - 3579

(6p singles - 2342)
(6p doubles - 381)
(6p triples - 855)
7 players - 654

8 players - 4261

(8p singles - 3134)
(8p doubles - 482)
(8p quads - 645)

(more analysis to follow...)

[MrBenn]

35 and less (the most you can start with is 11)
42,43,44 - It's no surprise that the many maps with these "classic" numbers of territories are so popular.
52,53 - the best sizes for slightly larger than standard maps
70,71 - the best sizes for large maps
80 - 5 & 6 player games require 2 conquers
88,89 - 4 player games require 2 conquers and 7 players only 1
104 - a great number (what a saddo I am ) - only 8 player games require less than 3 conquers - but still 2 - the best size for a very large map
141,142,143 - 5 player games require only 2 conquers
160 - 4 & 7 player games require only 2 conquers
190,191 - 6 player games require 2 conquers and 7 only 1

I have done some further analysis - the following territory values are optimal for at least 2/3/4/6/8 player games - ensuring that nobody starts with a multiple of 3 on the first turn (therefore requiring a single-territory capture to knock down their opponents deployment). Figures in bold are completely optimal (for ALL games). This list varies slightly from benjikat's original list, as I've used fractionally different criteria to define "optimal" :
35 and less
42,43,44
66,67,68,69
70, 71, 80
88,89
104, 114, 115, 116
138,139
140,141,142,143,160,161
176,177,178,179
186,187,188
215
224
232,233
248,249,250,251
259
260, 283, 284
285,286,287,296,304
305

[cairnswk]

35 and less (the most you can start with is 11)
42,43,44 - It's no surprise that the many maps with these "classic" numbers of territories are so popular.
52,53 - the best sizes for slightly larger than standard maps
70,71 - the best sizes for large maps
80 - 5 & 6 player games require 2 conquers
88,89 - 4 player games require 2 conquers and 7 players only 1
104 - a great number (what a saddo I am ) - only 8 player games require less than 3 conquers - but still 2 - the best size for a very large map
141,142,143 - 5 player games require only 2 conquers
160 - 4 & 7 player games require only 2 conquers
190,191 - 6 player games require 2 conquers and 7 only 1

I have done some further analysis - the following territory values are optimal for at least 2/3/4/6/8 player games - ensuring that nobody starts with a multiple of 3 on the first turn (therefore requiring a single-territory capture to knock down their opponents deployment). Figures in bold are completely optimal (for ALL games). This list varies slightly from benjikat's original list, as I've used fractionally different criteria to define "optimal" :
35 and less
42,43,44
66,67,68,69
70, 71, 80
88,89
104, 114, 115, 116
138,139
140,141,142,143,160,161
176,177,178,179
186,187,188
215
224
232,233
248,249,250,251
259
260, 283, 284
285,286,287,296,304
305

Nice work guys.
Mr Benn. perhaps this could be included somehow in map gameplay instructions for starters so that we could all beneift from it.
I'll certainly take note, it might cut down ian's work....

[MrBenn]

Mr Benn. perhaps this could be included somehow in map gameplay instructions for starters so that we could all beneift from it.
I'll certainly take note, it might cut down ian's work....

One step ahead of you there - the analysis was done as part of a gameplay guide we're working on behind the scenes

[MrBenn]

Hmmm

Revised list here - I'd forgotten to take account of the fact that you don;t need to worry about 8 player games until you reach 96 territories - so there are more optimal numbers on the list: [bold - completely optimal; standard - optimal for 2/3/4/6/8 players]

24-35,42,43,44
52,53,57,58,59
66,67,68,69
70,71,78,79,80, 88,89
104, 114, 115, 116
138,139,140,141,142,143
160,161,176,177,178,179
186,187,188
215,224,232,233
248,249,250,251,259,260
283, 284,285,286,287
296,304,305
320,321,322,323,330,331,332
354,355,356

[Evil DIMwit]

Ah, that's much better. The previous one was looking kind of thin.

[ender516]

Mr Benn. perhaps this could be included somehow in map gameplay instructions for starters so that we could all beneift from it.
I'll certainly take note, it might cut down ian's work....

One step ahead of you there - the analysis was done as part of a gameplay guide we're working on behind the scenes

Might I suggest that your behind-the-scenes discussions that go into the guide be preserved and released for public viewing (a locked topic, perhaps) along with the guide? Undoubtedly there will be commentary on the guide and the suggestions and conclusions it contains, and it is often helpful to see the thought processes that led the authors to a certain point. This kind of information can avoid unnecessary rehashing of arguments, and can also provide a jumping off point for new ideas.

[MrBenn]

Most of the bits of the guide have been pulled together from discussion threads such as this one, or from individual posts in map development threads...

[Kabanellas]

This is a spreadsheet I made that might help you to decide the best number of regions to use when creating a map.

Insert the number of regions you want your map to have and get:

-Regions per player
-Starting neutral regions
-Number of starting troops per player

http://kabanellas.webs.com/Kabanellas_Region_Distributor.xls

Have fun and good map making!

K

[skeletonboy]

I know I've seen them somewhere but I can't seem to find them now, can anyone direct me to the thread or post them here?

[natty dread]

viewtopic.php?f=241&t=105183


24-35, 42, 43, 44, 52, 53, 57, 58, 59, 66, 67, 68, 69, 70, 71, (78), (79), 80, (88), (89), 104, 114, 115, 116, (138), (139), 140, 141, 142, 143, 160, 161, 176, 177, 178, 179, 186, 187, 188

[skeletonboy]

Thanks

[MrBenn]

[merged]

[Ace Rimmer]

This is a spreadsheet I made that might help you to decide the best number of regions to use when creating a map.

Insert the number of regions you want your map to have and get:

-Regions per player
-Starting neutral regions
-Number of starting troops per player

http://kabanellas.webs.com/Kabanellas_Region_Distributor.xls

Have fun and good map making!

K

This could totally be the wrong place to post this, but i have a question. I started a 2p game on Holy Roman Empire, and thought that we would each get 14 terits, with 14 starting neutral. However, we each got 15 with 12 starting neutral. I came here to confirm against kabanellas' spreadsheet, which also says that we should have gotten 14 each. Game 6562911. I also see the same thing in Austerlitz, Game 6562910 - we each started with 11 terits and as I'm reading it, it should have been 10 terits. I also started a Poison Rome game at the same time and it gave me 14 terits as expected. Any insights?

thanks,
Jake

[thenobodies80]

This could totally be the wrong place to post this, but i have a question. I started a 2p game on Holy Roman Empire, and thought that we would each get 14 terits, with 14 starting neutral.

Hello Jake!
"Joe" has an answer for you
Both maps have starting positions, so for example on the HRE map in a 1vs1:
1player => 1 starting positions (5 territories) and 10 "normal" territories = 15
2 player =>1 starting positions (5 territories) and 10 "normal" territories = 15
neutral = 12

(Note:Starting positions are equally splitted and there's no neutral player)
More infos on starting positions in this thread: viewtopic.php?f=466&t=68154

Nobodies - "Joe"

[Ace Rimmer]

This could totally be the wrong place to post this, but i have a question. I started a 2p game on Holy Roman Empire, and thought that we would each get 14 terits, with 14 starting neutral.

Hello Jake!
"Joe" has an answer for you
Both maps have starting positions, so for example on the HRE map in a 1vs1:
1player => 1 starting positions (5 territories) and 10 "normal" territories = 15
2 player =>1 starting positions (5 territories) and 10 "normal" territories = 15
neutral = 12

(Note:Starting positions are equally splitted and there's no neutral player)
More infos on starting positions in this thread: viewtopic.php?f=466&t=68154

Nobodies - "Joe"

OK cool, thanks "Joe" Is there any way to quickly know which maps have starting positions? I like to know how many terits you start with in a giving game setting, and didn't realize that the coded starting positions affected it like that.

Jake