Posts made by Charles de Gaulle

Turn 4

The Germans smashed through the Baltic States and now have a threatening mobile force there. Combined with the Finns and Germans in the north and the possibility of an attack by sea, Leningrad cannot hold out.  Dan sent many German units to Western Ukraine and made a large air assault on the Soviet industrial complex further south. His intentions on the Eastern Front are still uncertain. The Western Front has been noticeably quiet with a lone German sub sitting in Sea Zone 125 to negate the Soviet’s lend lease NO. There is still a large German air and naval presence here.

Hungary attacked Belarus with close odds but actually fought well with 3 units surviving. A few infantry were also sent south to help the messy group of Axis units in Ukraine.

Finland sits at a standstill, waiting for the Germans to take Leningrad.

The Soviet Union looks hard pressed, but Victoria decided to make a stand in the Ukraine. Further north, she was forced to evacuate Novgorod to avoid losing more troops. With most Axis forces in Western Ukraine, the Italians left behind in Bessarabia were an easy target for the Soviets. Victoria took almost no losses there. In sharp contrast, a counterattack on the Hungarians in Belarus failed miserably. The dice gave the Russkies no hits. This is a big deal because now German mobile divisions can be diverted into the Russian heartland or threaten Archangel. However, the Soviets do have considerable air and AA sort support to keep Moscow defended.

The Americans completed their South American adventure and now control Chile and have 4 IPCs extra.  Brazil and the United States will soon join the Allies and ensure Africa doesn’t fall to Italy and France will be liberated.  The Axis need to move faster if they’re going to win. Twilight is anxious to get the Americans involved.

Canada launched its own operation in Morocco, landing 4 fresh units to march east and retake North Africa. Combined with other Commonwealth forces that now form the majority of the Allies in Egypt, they may be able to squeeze the Italians in Libya to death. In a suicide attack, Twilight used his South African tactical bomber and destroyer to attack the Italian fleet to soften them up for me.

With the United Kingdom, I attempted to put an end to the Italian navy outside Libya, but the battle only ended in mutual annihilation, with the Italian transports surviving. Those German air units on Malta gave me a very rough time. With the Middle East secure, I sent some units to the USSR (we have a lend lease rule that allows them to be converted next turn) and built a factory in Persia. India will crank out more forces, including a cruiser that is now badly needed in the Mediterranean. To divert some German forces, the British made a minor landing in undefended Holland.

Kyle tried to take advantage of the situation in the Mediterranean with Italy by attacking the remaining Commonwealth destroyer by Gibraltar and French submarine outside Greece. The Italians achieved total naval supremacy, but an attack on Alexandria ended in retreat.  There are simply too many combined Allies in Egypt for the Italians to fight alone, especially now that they have to rely on their own air force in Malta to protect their convoys. There are still quite a few small Italian ships everywhere though.

Romania had to respond to the Soviet attack on Bessarabia. Holding this territory is their only NO. But like the Italians before them, they took heavy casualties fighting here. Kyle made a real game-changer further east with the Romanians, taking Bryansk deep in Russia. Since the Hungarians were able to hold Belarus, Dan could now move all his German armor right onto Moscow’s doorstep while simultaneously threatening Ukraine.  A crisis might unfold in the Soviet Union. Victoria’s only comfort is knowing the messy conglomeration of Axis forces cannot attack in unison. She might be able to hit them hard from behind and build a massive stack in Moscow. Twilight said he’s not used to seeing such an uneven front line in Axis and Allies without disaster unfolding for someone.

Most of my French units are dead, but I’m sending a transport and fighter around Africa to help the small desert force fighting in Libya. I have an infantry in Madagascar to bring up too. Home feels very far away.

Turn 3

To kill the Canadian bomber in Scotland, Dan launched a small amphibious assault there against very little resistance. This took most of the German fleet away from being able to attack the USSR, but 2 transports and some smaller ships are still near Denmark and landed 4 new units in Norway. This included 2 fast divisions to reinforce the artic army in Finland. An attack on Karelia was very costly for the Germans. The much broader assault on the USSR’s western border surprised me. Instead of putting most of his force in the north or south, Dan sent almost all of his mobile units to Eastern Poland and only took the Baltic States with a small army. Bessarabia is not empty. The pile of units in the Indian Ocean is the large international force there, including some Germans. Both Romania and Finland have received German air support to protect against potential bombings they wouldn’t have the IPCs to be able to repair.

Finland took Vyborg easily and reinforced the artic army in Karelia.

Hungary has assumed a support role and is acting as a deterrent to Soviet counterattacks.

Victoria attacked the Baltic States (the weakest link in the Axis advances) with the Soviets. To prevent an Italian or Romanian can-opener, she was forced to leave some troops in Belarus. Leningrad is holding on by a razor’s edge, but half the German fleet being outside Scotland might make it last another round or two. A cruiser in the Baltic Sea prevents an attack on Leningrad from the west, but an attack through the White Sea in the north is still possible. Ukraine has been consolidated to hold another round. Even though the Germans have a large force in the center that could theoretically march on Moscow, one disadvantage to Germany having to rely on minor powers is the necessity of split attacks. The Soviets can defend in mass, but the Axis cannot attack together. The USSR also took Northwestern Persia, which might seem silly, but we have a house rule that allows Allied lend-lease units to be converted to Soviet ones once they’re on Soviet controlled territory.

The Americans continued their South American adventure and took Peru without loss. Venezuela was much more bloody though. Chile seems to be in danger now. In the long run, Twilight hopes for these IPCs to make the losses worthwhile.

Twilight didn’t trust leaving his Canadian troops on my British transport and decided to leave them in Iceland for now. He was annoyed with the loss of his bomber and built a new one. Commonwealth forces are now playing a big role defending Egypt. Italy faces harsh odds in North Africa.

With the British, I completely overran Persia and prepared to start sending forces north to help Russia. Italy’s navy almost forced me to evacuate the Mediterranean, but a bright idea struck me—an air base in Egypt to let us scramble planes there. Once again, an Italian attack would have really close odds, so I felt bold enough to make a stand. With Commonwealth and French units in Egypt, I decided to move the British army up to Alexandria. Not much happened in the UK. I liberated Scotland from the small German attack and built a destroyer.

Romania moved forward on the Eastern Front and has a decent sized army in Western Ukraine. It won’t survive without German reinforcements though. Romania is quickly becoming comparatively rich for a minor power.

Kyle responded to my stubborn Royal Navy near Cairo by building more ships and used his Italian army in Libya to attack Alexandria. The battle ended in mutual annihilation with only the Italian Air force surviving. In Eastern Europe, Italian units killed the Partisan in Yugoslavia and reinforced the Romanians fighting in Ukraine. With the cover of a large Italian navy and German air force on Malta, Kyle can send 4 ground units to Africa every turn. One of us has to attack soon.

I lost 2 French ships in the Mediterranean, but I’m satisfied that they did their job distracting enemy forces. The long fight in north-west Africa is over. I attacked with 2 French infantry and a fighter versus the 2 Italian fast units; all 4 land units died and my French fighter is in Gibraltar now. The French are on the front lines in Egypt, and I managed to convince Twilight to let me bring Canadian troops to Morocco with a French transport. They’ll probably sink, but it’s at least a distraction using forces that can’t do anything else at the moment.

We’re all very curious what Dan will try next on the Eastern Front, although I’m pretty sure Kyle is demanding that he send units south to help the Romanians.

@SuperbattleshipYamato In other variants we have allowed neutral superpowers to invade minor neutrals, and although I wouldn’t suggest it for a basic neutral expansion, it won’t hurt much. Venezuela is pretty much the only nation the U.S. could attack without violating its naval restrictions.

I would go ahead and allow it. Makes things more interesting.

Turn 2

Dan launched a combined amphibious assault and overland attack on my French units in Normandy with the Kriegsmarine. His navy now sits in the English channel. Germany also made an enormous Battle of Britain and caused massive damage (21 total to all three facilities). It came at the cost of a tactical and strategic bomber, but Germany still has 13 planes. Armored units have been sent eastward to Germany and Yugoslavia, making it obvious what will happen next turn to the Soviets. Romania isn’t empty. That stack of German, Italian, Hungarian, and Romanians you see in the Indian Ocean is the large international force there.

Hungary removed its forces from Yugoslavia in preparation for an attack on the USSR.

Finland faces way more Soviet forces on its border than it can handle alone, but Dan sent a significant German arctic army to assist them.

Despite Germany having 3 transports in the Baltic Sea, its navy is in no position to attack the Soviets. Victoria might be able to hold Leningrad for a little while, but that massive stack in Poland could easily march north. I asked her why she left 12 infantry on border territories. With Germany relying so much on minor powers now, she said she hopes to attract some small battles and counterattack weak parts of the front. It does look like the Axis are going to attack all along the front and not pile too much into single territories. We’ll see how that goes next round.

The United States has invaded Colombia in preparation for taking over Venezuela. Oil jokes were made. Even though we are letting the Americans invade neutrals, Twilight cannot activate Brazil with American units since the USA isn’t considered to be an Allied power yet. Moving into Brazil would actually require fighting those Brazilian forces.

Canada has finally set sail. The two German subs in the Atlantic went after my British destroyer between Greenland and Iceland. This move enabled Twilight to send a Canadian bomber and destroyer after them. We are now using the Arctic Ocean to ferry Canadian troops with some aid of the Royal Navy.
Commonwealth forces in East Africa crushed Somalia. They haven’t lost anything here yet and now have a decent army to send north to fight in Egypt. Their destroyer and tactical bomber are already there helping me immensely.

The massive damage to London would have concerned me if Germany had built more than 4 transports and not made it obvious that the USSR was their priority. For the British, I still played it safe though and made a huge stack of infantry in the UK. The Mediterranean was way more exciting. I decided to combine all my naval units outside Egypt and challenge the Italians. Kyle could have tried attacking this, but it was extremely close odds and likely would have been gone to whoever rolled more luckily. I took out Iraq without much difficulty and set myself up to invade Persia next round. Egypt looks safe, but…

Italy did something I should have seen coming. Kyle took over Malta to invalidate my empire NO, but since there’s an air base there in this variant, he can rely on German planes coming to cover his fleet. He only has 7 units in Libya though, and it’s going to take way more than that to make up for all the Allies that can converge on Egypt. Italy sent an army to the Eastern Front and built some more small ships.

One thing I didn’t mention earlier was the fact Dan did not take Southern France as Germany. While I understand he might have wanted to save Italy some money, there was an Italian submarine in SZ93 that could have reached my British fleet outside Egypt had the naval base there been Axis. It would have swayed my decision to make a stand with the Royal Navy.

Bulgaria replaced Italy as the occupier of Greece. Bulgaria can also “donate” units to other Axis powers since they aren’t really able to fight all that much (can’t declare war on the USSR). They are best used to keep Yugoslavia in check and Greece defended.

Romania actually began the war in the east with a full-scale attack on Bessarabia. Unlike Hungary and Finland, Romania moves after the Soviet Union in the turn order and can declare war before Germany does and set up can-openers. We will have to see how much the Axis reinforce the Romanians here, otherwise Victoria is going to send the Russkies to crush them.

Italy took Southern France, and much to my disappointment, also Algeria. While I realized I would likely fail here, Kyle only sent his 4 land units in Tunisia and 1 bomber from Italy against my 4 in Algeria and still only lost 2 units. I had hoped to distract more air power or take down most of his army.

I felt obligated to make another stand in Morocco and sent my fighter from the UK to assist. If he wants to get the North Africa NO, he’ll have to send more than just his remaining 2 fast units and a bomber next time. With the French navy, I scattered it quite a bit. One destroyer went north to sink a German sub by Wales. My 2 submarines are in the Mediterranean in convoy zones. I’ll either distract Italian destroyers or get some IPCs off Kyle. I also have a cruiser guarding Gibraltar and Morocco from a possible attack by sea. A French transport went to Canada to help further with getting men across the Atlantic.

These first two turns were tremendously fun, and the Eastern Front looks ready to explode.

Turn 1

Germany takes Normamdy and Paris, but does lose a lot of infantry and a plane.  Dan (playing as Germany, Hungary, and Finland) managed to sink all of the British navy and even have 5 sea units floating in the Atlantic.  Even after British and Candian counterattacks, 2 German subs are still alive. He built an aircraft carrier and added a battleship and a cruiser from the Baltic Sea.  In the east, a massive German stack is in Poland, and Hungary and Finland have received German garrisons.

Since Germany didn’t attack Yugoslavia, Hungary tried to and actually had very good luck, picking up an extra 2 IPCs.

Finland is not an Axis power and operates under special rules. For instance, Finish control of Leningrad does not count as a victory city for the Axis.

Victoria (playing as the Soviet Union and Yugoslavia) left a surprising number of Russian troops on the border and threatened Finland. If Germany goes for Sea Lion, it might be over for them. The Soviets are allowed to attack neutral territories like Turkey in this variant.  Persia is a neutral nation now as well.

The U.S. can also attack neutrals, but must keep its sea units adjacent to original American territories.  Twilight (playing as the United States and the Commonwealth) sent a couple men to Central America, eyeing the IPCs available in the south.  Since this variant gives the Axis a lot more enemies to fight, the U.S. is not allowed to declare war until the collect income phase of turn 5.

The Commonwealth (an independent entity representing Canada, South Africa, and ANZAC) lost a Candian destroyer and transport and can’t safely send any help across the Atlantic until we sink those subs. I, Charles de Gaulle, (representing the United Kingdom, France, and Greece) did send a cruiser and transport to Canada to help their new destroyer Twilight built.
In Africa, the Commonwealth sent men to East Africa and sank an Italian submarine.  Those poor Italians there are really surrounded now.

As the United Kingdom, I want to tempt Dan to try Sea Lion. I got bad luck sinking a German destroyer and cruiser by Scotland and lost 2 planes.  I also decided to be cautious in the Mediterranean and only sank 1 of the 3 Italian fleets. Italy is quite strong in this variant, but does have to deal with the French in the west and the Greeks in the east. I sent my battleship to Ethiopia and destroyed the Italians there. I left my carrier by Gibraltar for flexibility and will wait to see what Germany does. I have the French and Greek fleets to distract Italy for now and can regroup next round.

Greece begins the game neutral and can’t do anything until turn 3 unless it’s attacked.

Bulgaria has a “micro” industrial complex.  These can build 2 infantry or 1 of any other unit (except bombers and capital ships).

Yugoslavia deployed a partisan.  This annoying unit spawns every turn and must be destroyed by the Axis in order to maintain free passage through the territory and the 2 IPCs.

Kyle (playing as Italy, Bulgaria, and Romania) took advantage of my conservative British attacks and sent his smaller ships and planes after the French and Greek navies. The Italians easily destroyed the partisan infantry in Yugoslavia, and Greece was absolutely crushed by an attack by land and sea. However, Kyle left Southern France alone.  I believe it was a big mistake. Interestingly, he’s sent his army in Libya to attack Tunisia and left the Egyptian front as a standstill like I did. The two Italian units left in Somalia are doomed.

For France, I was very excited to fight hard. Kyle not attacking Southern France let me destroy Dan’s German survivors in Normandy. I sent up help from West Africa to Morocco and made a stand in Algeria against the Italians. I have a small fleet by Gibraltar now. My fighter escaped to London to help out there, and other scattered units are going to help in Egypt.

Please note that some units are from other games since we have so many countries. Neutral nations are independent of each other and get their own armies. Some things might look a little confusing, like Soviet units being used to represent Chile or Japanese ones being used to represent Sweden and Spain. But they’re all independent nations.  If you see a 1914 artillery upside down, that’s what I’m using as a AA gun for some minor powers.  I like mods, but I have also invested very little into them, as you can see.

Greetings
This month we are testing an unnecessarily complicated A&A Europe 1940 spinoff. I’ll save you the headache of explaining any further and instead show you what it looks like. You’ll have to excuse the fact I have the boards split. Life has been crazy.

@Imperious-Leader Definitely fair points. Most skilled players will stack ungodly amounts of units on 1 territory even under normal prices. It’s just the smart thing to do in many places on the board. And I know many people are tired of playing the same game for 12 hours.

But I’ve always been playing with a younger audience that prefers to throw their units into combat instead of stacking. We also have typically used other house rules that introduce minor powers and invadable neutrals. So there are more casualties and split armies in need of money.

Since we don’t have as much time as we used to, we’re typically playing only one half of 1940. We’ve also introduced “quarter” versions of 1940 only using half of a theater’s game board. “Asia 1940” has been my favorite. It’s a very interesting twist focusing on only one section (albeit a new setup and rules are required), and it typically allows us to finish in only a couple hours.

We’ve also tried “Middle Earth 1940” (Eastern Front/Africa/Middle East) and even “Atlantic 1940” focusing on the Western Front and a hypothetical Operation Sea Lion. “Atlantic” still has a ton of flaws and balance problems, but it’s been really neat seeing USA and Canada attempt to take back Western Europe and Africa from a raging Nazi empire.

@barnee I a taking a look at that 1940 expansion. Really interesting and advanced stuff in there! Definitely something I’ll read deeper later.

Also something I wanted to add about Chinese units:
They only defend on a 1. That’s why they’re cheaper now. Plus, we have a rule that China must keep at least 1 land unit in every territory it owns. We let China replace its fighter when possible. (The logic behind it being cheaper is the lack of ability to attack sea zones or operate in air battles.)

@SuperbattleshipYamato Haha, yes I’m alive. It’s harder to make as much time for A&A as I used to, but I play with my buddies whenever possible.

I haven’t checked this web in years it seems, but I did respond to your question about the neutrals.

Don’t tell my girlfriend about Marianne. She’s a jealous one.

@SuperbattleshipYamato They get activated independently of each other, unless a country has multiple territories (Spain has Western Sahara; Portugal has Angola, Mozambique, and Guinea; and Mongolia has 6 constituent territories.)

So if you attack a nation, you only need to fight its territories and ships. If you failed or opted not to take or destroy all of them, the remaining must be placed into the hands of an opposing power (similar to how neutrals in 1914 worked).

So if you attack Portugal as the U.S., the Axis will mobilize Portuguese colonial troops and receive income and control over all Portuguese territories and ships. You can pick Italy or Germany or Japan or even Romania if you’re playing with minor powers. But you must represent that nation with only one power: you can’t split them up.

But if you attack Saudia Arabia or any other neutral with only one territory, nothing else gets affected. They’re independent now, and typically have a decent military.

For A&A 1940 and other variants we’ve been playing over the year, something interesting my group has tried is reducing the IPC costs of purchasable units to add more combat and variety to the games. It’s roughly based on taking 2/3 the price of the regular costs.

IPCs
1 Chinese infantry
2 infantry, Chinese artillery
3 artillery, mechanized infantry, AA gun
4 tank, submarine, micro industrial complex
5 transport
6 destroyer, Chinese fighter
7 fighter
8 tactical bomber, cruiser
9 strategic bomber, minor industrial complex
10 air base, naval base
12 aircraft carrier
15 battleship
20 major industrial complex

You’ll notice a couple odd things like why China gets cheaper units and the existence of micro (build 1) factories because we tend to combine a bunch of house rules. There are also many minor changes we use for the units themselves and setups, NOs, and other game elements to keep standards like G40 from getting totally destroyed by this sudden influx of units (since everything is cheaper). But it’s been a really fun, simple change.

Have you ever tried any major IPC adjustment with success?

@aardvarkpepper Now that you and Marc have talked through so many different aspects that I wasn’t even considering, I must admit, doing the tournament this way wasn’t necessary, and it’s far from being fool-proof. It’ll work, but as you guys pointed out, it doesn’t account for some variables or human choice.

But, my motivation (aside from having fun with everybody that’ll play) is definitely to research how biased the game might be. I’m concerned that there might be significant advantages or disadvantages to certain colors, and if there are, I hope to spot them and make adjustments. I’m thinking that the setup is already pretty well balanced, but I want to put everything to the test, because we’re not sure yet.

I really haven’t given much thought to any of the legal or marketing aspects of actually selling a game, so I’m glad you brought that up as well for me to seriously think about. And make no mistake, I appreciate every argument you’ve given. The mathematical relationships you discussed are part of what made solving this so easy. Your advice is always welcome and helpful.

If I ever think about hosting another tournament or convincing someone to accept the wacky house rules and games we come up with, I’ll be sure to read this thread again. But right now it looks like I’m ready to organize a tournament! So until we meet again, take care gentleman.

@cwo-marc I think I’ve been unintentionally making confusion by mumbling several things together —
playtesting the game itself
hosting a tournament
and figuring out the mathematical relationship I wanted

For the tournament, players would not get to determine their color or position in the turn order because I’m going to base it off of the chart I showed earlier. However, after playtesting, the final game should be just like Axis and Allies and most other games, in which players pick or agree on who plays what. So the game isn’t going to decide that for the players. I’m just arbitrarily choosing to do so to try to make a tournament for playtesting. My goal is to eventually have a game where all colors and places in the turn order are equally appealing.

Anyway, I don’t want to take any more of your time, but before you leave, I want to thank you for all the helpful questions and information you’ve shared! I knew I’d get some excellent advice from this forum.

@cwo-marc For the turn order, I would like to go back to the Axis and Allies analogy. In A&A depending on your place in the turn order, the nation that you’re playing changes. And that’s a big deal. Not because you’re going first, third, or last, but because of drastic differences between nations. With our game, it’s a similar scenario. Red is the last player that moves. But the fact that red goes last isn’t so much the issue. It’s the fact that being red gives the player a certain predetermined setup that no other color has. And if necessary, we could change that setup. Turn order, in and of itself, doesn’t play much role. Rather it’s who you’re playing with and what color you are. But indirectly, turn order does determine your color AND who moves before and after you, so it actually does play a big role in this setting.

Think of it like this. In Pacific 1940 the are five people. Let’s say I’m third in the turn order, so I’m China. If every game we play, China gets totally destroyed, even when Japan loses. We might want to consider giving China some more forces to help counter that. Now Axis and Allies is WAY more complicated and team-based, so that would indeed be a very simplistic way of doing this. But I hope that gives a better idea why turn order is important, because it isn’t just about when you get to play; it also determines what nation/color/or whatever that you get.

Now, to put another idea in A&A terms, let’s talk about “Bob” again. Let’s say that he was playing as China. And he complains that another guy, “Joe,” the UK player, never sent him any help through Burma, because maybe Joe is an adventurous guy trying to fight Japan in Java. So if Bob keeps getting Joe on his team, he might feel like he’s at a disadvantage, and more importantly, it might skew my data to make it look Bob is always losing and obscure the real problems, such as maybe China is too weak.

These are imperfect correlations, but I think it might explain a little better what I’m trying to say.

Success!

I hope I’m not crying wolf (I will double check later), but I believe I found a solve!

Thanks so much for your help gentlemen! Your ideas gave me an idea for a fun way to do this:

A more generic table can be created by making the top row “player 1 through player 21” and substituting likewise wherever the roundel or chip repeats. Each column represents a game, with position in the column determining turn order.

@cwo-marc You hit the nail right on the head. Fairness is definitely a quality that is largely based on opinion and perspective. Luckily, I don’t have anyone actually complaining to me that the game is unfair—I think most of the players are much more focused on tricking and influencing each other enough to claim a win—which is exactly what I’d expect (and maybe even encourage) in a free-for-all with 3, 4, or 5 people.

The main complaints I’ve gotten are more like, “Bob kept screwing me up because he moves right before I do.” That’s where the idea of only having to play against every opponent once came to mind, in an attempt to lessen some of the luck of the draw that’s involved.

As you may have noticed, I’ve been almost maintaining a bit of secrecy about what this game is, and that’s because it’s actually something unique we came up with. This is just me being hopeful and daydreaming, but I think the game may have market value, even if only in a digital format. There have been flaws, and we’ve been tweaking the setup try to fix that. I think the setup is at a decent standard now, but hosting these tournaments will give me a good idea of whether or not it needs more work.

I must say, I’m amazed at the depth of thought you and aardvark have explained in relation to what actually goes on in the minds of players in large competitions. I have been focusing so much on the math and given little thought to the amount of psychology involved in tactics and motivations. It’s something I’ll definitely try to consider more in any future tournaments where outside factors and real-life pressure can play a heavy role.

@aardvarkpepper Dang. To be frank, your story is a lot more philosophical in nature than I actually feel is necessary to worry about. But that’s because I should have explained something:

—This whole tournament idea is actually for a playtest. Aside from having a fun, quick-moving tournament, I’m trying to gather statistics from a large pool of players to see if there is any bias involved. The “bias” I’m talking about relates to my earlier vague reference that “turn order is important.”

In each five player game, there are five “colors,” each with their own situation on the board. My hope is that any innate advantages or disadvantages of being one color vs another color are outweighed by the much larger influence of the players themselves. After the tournament is over, my idea is to scramble the players and start over, as many times as possible to weed out any issues with the game’s balance. If there is any position in the turn order which is noticeably doing worse or better, it should eventually become evident.

The reason I’ve been putting “fair” in quotes is largely due to how ambiguous being “fair” is, given so many variables and human choices, strategies, and real-life motives. However, my objective is to make a balanced game rather than an objectively “fair” tourney. In order to gather at least somewhat accurate data, I am trying to lesson individual player influence to help make the bracket “fair,” at least on paper.

This whole “21 participant, 5-player” model that I’m so stubbornly adhering to was created by asking myself, “What’s the smallest number of games a participant could play and still get a chance at being each color (position in the turn order) and also facing every other participant?” Well, the answer is that each participant would have to play at least 5 games obviously, and since there would have to be 4 opponents in each of those games, there would be 20 opponents total plus the first guy (= 21).

So 21 is the smallest magic number for 5 player games. And it offers the unique distinction of only requiring opponents to see each other once (which, in my opinion, helps to lesson individual player influence over the data I desire). The next magic number for 5 player games is 42. Likewise, 7 is the first magic number for 3 player games, and 14, 21, etc. are the next ones.

The only reason to use larger “magic numbers” is to compensate for what @CWO-Marc has noted: even with all these stipulations, there are still many inconsistencies, as a 3 or 4 or 5 player game has groups of players than could potentially be switched around and manipulated to change results. But…as we’ve all come to conclude, it is also easy to just swap one player with another to get another valid matchup. So if I scramble the players after each tourney, I’ll get closer and closer to an accurate answer.

My hope is that the game is already “fair enough” to the point that skill level, luck, and matchups play a much larger role than the color (or rather, the place in the turn order) that each participant plays. As I’m sure some of you are probably thinking, there are easier ways to playtest with acceptable accuracy than to go to all this trouble building something around a “magic” number that was created through preset rules. But being the curious, stubborn person that I am, I want to solve it this way; it’s fascinating; it’s unique; and although it’s imperfect, it will work for me if it’s indeed possible.

The 3 player variant that you did some awesome number crunching with @aardvarkpepper is a very good frame with which to build an intense 7 player tournament with perhaps 21, or even 105 games if desired. The 4 player variant, which I’ve found several solutions for, was so enjoyable in playtesting, that we’ve already reused it several times. I must take the time to examine more in detail, aardvark, the way you solved the 3P version, as it might work better than everything I’ve tried so far.

@cwo-marc Now then, to address this beautiful system you’ve written, this is indeed the correct way to go about making the bracket. I would have never been able to explain it so informatively as you just did, but yes, this is what I’ve tried to do to create the 5-player, 21-participant version.

As you found, there are actually several ways to solve the 3-player, 7-participant version. I can attest that there are also at least 3 ways to solve the 4-player, 13 participant version as well.

I’ve tried methods very similar to what you just wrote out, and it does work. But as redrum pointed out, it becomes increasingly hard for a simple human like me to work out, because the possibilities explode greatly at 5 players and above to the point of madness.

I’ll continue diligently working on at least finding ways that DON’T work for the 5-player, 21-participant bracket. So far, by process of elimination, just like the beautiful model you wrote out here, I’ve tried many,many matchups, but they all have thus far failed. Your supposition that there probably IS at least one “solve” does give me hope, as I believe all these failures I’ve faced are purely a result of the enormous possibilities 21 players give.

Again, I’d like to thank you Marc and everyone else for giving me these ideas to consider, as I now have many good tools for working on this further.

…I just hope many crazy comrades don’t ever think of a 6-player version of our game, because I’ll probably end up losing my wits trying to solve it.

@cwo-marc I believe you’ve already solved your questions, but just to be sure, I’ll briefly answer them for clarity to everyone.

1. The answer is yes. Player A is only allowed to see Player B once. “Once” refers to certain individuals rather than combinations of individuals.
2. A different opponent is defined by who is playing. Player B is still Player B regardless of his position in the turn order.
3. Yes. Turn order is similar to Axis & Allies in which it defines a person’s place and affiliation on the board.
4. For this answer, I’d first like to say that it does NOT affect anything else. So don’t consider these numbers in calculations. However, to answer the question, there are typically 11 rounds (it can change because players can get skipped if they have no valid moves). There are almost always 54 moves (turns) total (unless the last move is an invalid one for everybody). By nature of the game, the fifth player typically only gets 10 moves while everyone else gets 11. (11*4 + 10 = 54)
5. This concept was created for overall fun (in a relatively small group of 21 people, it’s fun to get to “fight” against everybody) but more importantly, to ensure overall fairness. Since it’s a 5 player game rather than a 1vs1, luck plays a huge factor, as there is much that goes on out of your control while the 4 other players take their turns. Also, this isn’t just about winners and losers. Players will strive to “win second place” or do their best regardless, because after the 21 games are played, each participant receives points for where they placed in each game (4 points for a win, 3 for 2nd, 2 for 3rd, 1 for 4th, and 0 for fifth).