Proposed Changes to 1v1 (2 player) games

[NewSheriffInTown]

First Player Advantage​

First player advantage in a 1v1 game has always been an issue. Marcos and I are testing out a hack to the current code that should help balance out 1v1 games.

The new rule proposes that only for the first turn of the first player in a 2 player game, they will be able to deploy their troops, but not attack or reinforce.

After that, the games plays out as normal.

SUMMARY OF THE NEW 2 PLAYER GAME PROPOSAL

Games Starts : Round 1

Player 1 - First Turn

1. Starts Turn
2. Deploys Troops
3. Ends Turn

Player 2

1. Starts Turn
2. Deploys Troops
3. Attacks
4. Reinforces
5. Ends Turn

Round 2 : Game Continues as Normal

In essence, this reverses the roles of first and second player, as attacker and defender. It allows the first player to build up their defences against the second player's attack.

Once tested to see if it works, we plan to implement this new rules and observe the outcome for a couple months.

Fortunately, our database contains every 1v1 game played on every map, so we know exactly what percentage the first player advantage has in a 1v1 game.

(The full stats have been posted before in a thread somewhere in this forum, but I can't seem to find that thread at the moment)

Nevertheless, in a couple months we will analyse the statistics and see what sort of impact this rule has in balancing out 1v1 games.

Thanks!

OTHER THREADS ON THE SAME TOPIC:

https://www.majorcommand.com/forums/threads/7917-Bidding-System-for-1st-Move-in-1v1

https://www.majorcommand.com/forums...n-Different-Maps-advantages-and-disadvantages

 

[AuraCraft]

To prove this is not a solution I have run a trial but it was dismissed by staff.
100 first turn games; I still won the majority; a % similar to the current figures, 60-66% ? The results were dismissed by staff.
The roles were not reversed. If anything, player 1 gets to decide where player 2 can't take his 1st card, which will be the only available command. Player 2 then attacks somewhere else to get a card and player 1 takes the command coz player 2 didn't deploy there (tbh I didn't tell my opponents I was running an experiment. So like in any 2player game they felt they had to take a 1st turn card and indeed my deployment steered them away from where I didn't want them to deploy. Maybe if they realised they didn't need a card they might've deployed on the same location as I had, but in that case the logic behind this idea doesn't apply; turn 2 would just be a regular turn 1 with 6 additional units on both sides.


The real problem is that player 1 has X units more than player 2 (throughout the game) where X = half the every turn bonus (terts divided by 3) so in a classic evolved game that's 3.
Why?
Turn 1, player 1: player 1 has 60+6=66 / player 2 = 60
Turn 1, player 2: player 2 has 60+6=66 / player 2 = 60+6=66.
Turn 1 average: player 1 has 66 / player 2 (60+66):2 = 63. A difference of 3 which is the only explanation for the first turn advantage. you'll find out in 2 months

edit
ps
originial topic suggesting this solution

 

[NewSheriffInTown]

Interesting..... So what do you suggest?

 

[AuraCraft]

ty
I suggest that in a 2p classic evolved game, the player who has the first turn starts with 3 instead of 6 units, then the game continues as usual. (so p2 gets 6 in turn 1, then p1 gets 6 in turn 2, so does p2 etc)
so the player whose turn it is has the advantage, not the player who went first. that means on average, the advantages even out.

or on a smaller map, when the (terts / 3) = 4, then p1 starts with 2 units instead of 4.
on a larger map, when terts/3 = 8. then p1 starts with 4.

 

[NewSheriffInTown]

ty
I suggest that in a 2p classic evolved game, the player who has the first turn starts with 3 instead of 6 units, then the game continues as usual. (so p2 gets 6 in turn 1, then p1 gets 6 in turn 2, so does p2 etc)
or on a smaller map, when the (terts / 3) = 4, then p1 starts with 2 units instead of 4.

In that scenario, would player 1 still attack and reinforce?

 

[AuraCraft]

In that scenario, would player 1 still attack and reinforce?

yes.

since my measure already evens the odds, there's no reason to add further restrictions

 

[NewSheriffInTown]

FYI, Here are the results of all games, all settings, including real-time which I will try exclude later:

2nd Player % wins

42.1 ~ Duck & Cover
40.6 ~ NUKES!
40.6 ~ 1984
40.4 ~ Mesopotamia
39.2 ~ Classic MINI
38.4 ~ The British Isles
38.3 ~ The Twelve Domains
38.0 ~ USA
37.6 ~ Classic Evolved
36.3 ~ Conflict Africa
36.2 ~ Australia
36.1 ~ North America
36.0 ~ Classic Antiquus
35.8 ~ The Forgotten Kingdom
35.8 ~ Sea Of Japan
35.7 ~ Middle East
35.7 ~ Classic Massive
35.5 ~ South America
35.5 ~ Balkan Peninsula
35.4 ~ Cold War Europe
35.2 ~ Far East Asia
34.9 ~ Philippines
34.8 ~ Mars
34.7 ~ Rivals of Rome
33.2 ~ Barbarossa
32.4 ~ Mexican American War
30.1 ~ Europe Massive

 

[NewSheriffInTown]

yes.

since my measure already evens the odds, there's no reason to add such restrictions

I have a feeling that a game with unlimited reinforcements would still give player 1 and advantage even with 1/2 the troops.

 

[riskyone]

In that scenario, would player 1 still attack and reinforce?

I have talked with AuraCraft about this. I believe this is a better solution then the first player deploy and end turn. It was a few months back, maybe longer. He added some great info in a forum thread on the subject. Some at first will think it's unusual because we haven't been playing that way, but I'm all for evening out the first player advantage and this is the best idea I have heard yet. BTW, I'm in a game that went to a side game of -1, are there unofficial rules to -1. Right now I'm in a game where I wasn't able to get under my prior troop count. What is the suggested resolution.

 

[riskyone]

FYI, Here are the results of all games, all settings, including real-time which I will try exclude later:

2nd Player % wins

42.1 ~ Duck & Cover
40.6 ~ NUKES!
40.6 ~ 1984
40.4 ~ Mesopotamia
39.2 ~ Classic MINI
38.4 ~ The British Isles
38.3 ~ The Twelve Domains
38.0 ~ USA
37.6 ~ Classic Evolved
36.3 ~ Conflict Africa
36.2 ~ Australia
36.1 ~ North America
36.0 ~ Classic Antiquus
35.8 ~ The Forgotten Kingdom
35.8 ~ Sea Of Japan
35.7 ~ Middle East
35.7 ~ Classic Massive
35.5 ~ South America
35.5 ~ Balkan Peninsula
35.4 ~ Cold War Europe
35.2 ~ Far East Asia
34.9 ~ Philippines
34.8 ~ Mars
34.7 ~ Rivals of Rome
33.2 ~ Barbarossa
32.4 ~ Mexican American War
30.1 ~ Europe Massive

Far East Asia is a lot lower on the list then I expected. I also thought Classic Massive and Balkans would be right above Europe massive.

 

[AuraCraft]

I have a feeling that a game with unlimited reinforcements would still give player 1 and advantage even with 1/2 the troops.

That's true; Unlimited reinforcements are very much in favor of whoever gets to reinforce first. but almost all 2 player games are not unlimited reinforcements or even 3 reinforcements.

 

[AuraCraft]

FYI, Here are the results of all games, all settings, including real-time which I will try exclude later:

2nd Player % wins

42.1 ~ Duck & Cover
40.6 ~ NUKES!
40.6 ~ 1984
40.4 ~ Mesopotamia
39.2 ~ Classic MINI
38.4 ~ The British Isles
38.3 ~ The Twelve Domains
38.0 ~ USA
37.6 ~ Classic Evolved
36.3 ~ Conflict Africa
36.2 ~ Australia
36.1 ~ North America
36.0 ~ Classic Antiquus
35.8 ~ The Forgotten Kingdom
35.8 ~ Sea Of Japan
35.7 ~ Middle East
35.7 ~ Classic Massive
35.5 ~ South America
35.5 ~ Balkan Peninsula
35.4 ~ Cold War Europe
35.2 ~ Far East Asia
34.9 ~ Philippines
34.8 ~ Mars
34.7 ~ Rivals of Rome
33.2 ~ Barbarossa
32.4 ~ Mexican American War
30.1 ~ Europe Massive

Far East Asia is a lot lower on the list then I expected. I also thought Classic Massive and Balkans would be right above Europe massive.

Indeed; to some extent, this ranks the maps from few to many terts. mini maps on top, massive on the bottom. (which proves my point)

 

[NewSheriffInTown]

Indeed; to some extent, this ranks the maps from few to many terts. mini maps on top, massive on the bottom. (which proves my point)

To get a better indication of what is happening, I'm trying to filter out real-time games and unlimited reinforcement games. Stay tuned....

 

[haWD96lz]

To prove this is not a solution I have run a trial but it was dismissed by staff.
100 first turn games; I still won the majority; a % similar to the current figures, 60-66% ? The results were dismissed by staff.
The roles were not reversed. If anything, player 1 gets to decide where player 2 can't take his 1st card, which will be the only available command. Player 2 then attacks somewhere else to get a card and player 1 takes the command coz player 2 didn't deploy there (tbh I didn't tell my opponents I was running an experiment. So like in any 2player game they felt they had to take a 1st turn card and indeed my deployment steered them away from where I didn't want them to deploy. Maybe if they realised they didn't need a card they might've deployed on the same location as I had, but in that case the logic behind this idea doesn't apply; turn 2 would just be a regular turn 1 with 6 additional units on both sides.


The real problem is that player 1 has X units more than player 2 (throughout the game) where X = half the every turn bonus (terts divided by 3) so in a classic evolved game that's 3.
Why?
Turn 1, player 1: player 1 has 60+6=66 / player 2 = 60
Turn 1, player 2: player 2 has 60+6=66 / player 2 = 60+6=66.
Turn 1 average: player 1 has 66 / player 2 (60+66):2 = 63. A difference of 3 which is the only explanation for the first turn advantage. you'll find out in 2 months

I disagree with this analysis. While its likely to be right for some maps it will be wrong on others. Lets assume on a map you start with each player with 21 territories. If the first only deploys then the second player deploys and attacks they likely take at least one territory. Now the first player will only get 6 troops. Maybe he is able to get the second player down to 6 as well, but maybe not. If not the second player is now +1 on this turn and can grow that.

Really there are two things at play. One is first turn advantage that Arua partially captures. This probably makes the game 60-40 since the small maps where each person starts with 8 territories and spends most of the game with a 3 deploy have a 60% win rate for the first player. Whether this advantage is because you go first so you can define where the battle or have on average more troops and cash sets earlier (setting matter here probably) is not clear. Likely both contribute, but its not clear how to separate the effects.

The second issue with 2 player, which is ignored as it is now is on the second turn the first player usually gets more troops. The first turn is even so on average you get about the number of troops by rule. But then on the second turn whoever goes first likely gets an average reply, but then the second player loses troops. This is an effect that impacts them significantly and grows, but is only seen on larger maps and matters more the larger the map gets though terrain and rules matter too. On average this effect is about 5%.

The question is does Sherriff's change make things more even or Aura's. I think they address different problems. Sheriff is solving the first mover advantage and to a lesser extent possibly the extra troops. The second player will not cash sets on average first (set rules matter), could get a territory advantage early on, but have fewer on average troops. Arua's addresses the troop lead part, but not the first mover advantage though it probably makes it a bit smaller, by halving the troop lead on turn 2. So still going first will have an advantage.

I think personally, any changes will even things out, but they have different changes. Neither is obviously better though Im' happy to be convinced otherwise. That said I don't trust 100 roll trials as its too small to show the true probability. There could be up to a 10% chance this was just bad luck and we don't know enough about the sample (maps played) or even the exact rate of wins, which is a big enough rank to be almost 1 sigma.

So I say try one, but would vote for a simple solution.

 

[AuraCraft]

@Hawdz; 1st player does attack in his first turn in my solution for the 1st player advantage. I already clarified that to Sheriff when he asked in this thread

You're free to disagree but it's not clear why. You reply doesn't disprove the basic formula* (or even go into it)
Also your "5%" decrease seems like a random assumption. (If I had to guestimate I would say 15% reduction so perhaps somewhere between 48 vs 52 to 50/50 but it's just that, a guess.)

What map starts with 21 terts for each player in a 2 player game? I think most maps avoid the problem you describe by starting with 11/14/17/20/23 terts; {[multiples of 3] minus 1}, rather than multiples of 3. (chosen as such by the developers to avoid that problem)

*For a mini map I would suggest a 1st player 1st turn deploy of 1.5 rounded up = 2 instead of 3. The same for all odd numbers; rounded up.

Note that my solution implies that while the 1st player does get to attack first, but with only half the 1st turn's units he will often not take a tert in the 1st turn and not be the first to take a card and cash a set... especially with the mini maps since the 1st turn's deploy is just +2.

 

[haWD96lz]

If the game was balanced with each person having the same chance each would win 50% of the time. So the math is as follows. The small maps e.g. mini average about a 40% win rate for the second player. This means going first is about a 10% advantage or 20% if you want to add both sides of it.

Then a rough average of all the maps is about 5% more so average going second on a random map is about a 35% win rate. We could do a rough regression if we really wanted to between territories and and extra win chance. Map topology and rules matters too so I just was quick and dirty.

So what I'm saying is the extra troops seem to add 5% to a players win rate, while going first adds about 10%. These are probably not completely independent variables so yes your change would reduce things by a bit more probably. That said its not much more.

As for your shooting from the hip claim. North America will start with 21, south america with 18, sea of japan and USA with 16. So those are all not your one less than divided by 3. I didn't look at all the maps. Its likely a coincidence is more of them fall in the camp you describe.

Sheriff's proposal gives the second player some of the first turn advantage, but not all, but does not address the possible troop imbalance issue as strongly. As I said some of it will end up getting handled by attacking though you are right that is map dependent.

Either way neither proposal will make the game 50/50. My guess is both will make it somewhere between 55-60% for the first player though you have to try to see.

Given this thoughts I'd suggest trying both together and seeing what happens or something like that and I don't have a strong preference between them if only one is chosen. They are both relatively simple. That said the more changes made the more it will confuse people especially new people.

I mostly started posting because the analysis being down was weak and only thought about first order effects and part of the story.

Note half the extra troops might have lose a small chance at taking a teritory on small maps, but not on large maps, where the first turn deploy will still be large. In an attack 5 v 3 is about 2/3 vs. 6 v 3 which is 7/9 so its notable, but not huge.

 

[AuraCraft]

Those 5% and 10% what do you base that on, other than guestimation? I'd think it's the other way around. Indeed, 100 games is not sufficient to base definitive conclusions on, but it is enough to notice a trend and the trend I noticed when deploying 6 but skipping 1st attack was that I didnt lose much more than in games when I didnt restrict my 1st turns actions. 2nd player 1st strike only cost me a few games; getting 17 terts cost me a few games, but I won a few coz the deploy without attack steered my opponent away from the only available command.

You can't take a random % and base conclusions on how to proceed on them. I think we should just run the experiment sheriff suggests and the one I suggest.

South America and North America 18, ok... 16 doesn't count. Anyway, you based your problem on the assumption that in my solution 1st player cant attack (he can) so the problem is non existent unless a double restriction would be implemented; half the 1st turns deploy + no 1st turn attack for player 1 (but noone is suggesting this)
Moreover, to get clear results, the two shouldnt be combined in one single trial. (Im not sure if thats what you're suggesting but I wanna be clear anyway)
Id suggest first we try sheriff's solution, then we try mine (or the other way around)
if both restrictions are implemented at the same time and it doesnt get close to 50/50, it's impossible to determine which factor is to blame.

 

[NewSheriffInTown]

Okay, I now have the most accurate stats to date.

First I just want to mention that I did some other analysis (not listed here) and the results were interesting.

It may be no surprise, but Fixed Force raises the 1st player advantage to the 80's and 90's on some maps. So Fixed Force games are not included in the data below.

Also, and this is surprising to me, unlimited reinforcement did not improve the 1st player advantage, in fact, it lowered the 1st player win percentage on 17 of the 26 maps, and there was only a negligible increase in in 1st player wins in 6 of the 9 other maps. Only 3 of 26 maps were 5-10% higher due to unlimited reinforcement. Unlimited reinforcement is included below.

These stats have been filtered by the following criteria.

All data below is:

• 2 Player Games
• Casual 24 Hour
• All Reinforcements Types
• Chance Only (Not Fixed)

% of 1st player win ~ % of 2nd player win ~ map

59.3 ~ 40.7 ~ NUKES!
59.8 ~ 40.2 ~ Duck & Cover
60.0 ~ 40.0 ~ 1984
60.0 ~ 40.0 ~ Classic MINI
60.5 ~ 39.5 ~ Mesopotamia
60.6 ~ 39.4 ~ Classic Evolved
60.6 ~ 39.4 ~ The Twelve Domains
62.3 ~ 37.7 ~ USA
62.5 ~ 37.5 ~ The British Isles
63.5 ~ 36.5 ~ Australia
63.9 ~ 36.1 ~ Classic Antiquus
64.3 ~ 35.7 ~ Sea Of Japan
64.4 ~ 35.6 ~ The Forgotten Kingdom
64.4 ~ 35.6 ~ Balkan Peninsula
64.8 ~ 35.2 ~ Cold War Europe
64.9 ~ 35.1 ~ North America
64.9 ~ 35.1 ~ South America
65.0 ~ 35.0 ~ Conflict Africa
65.2 ~ 34.8 ~ Middle East
65.3 ~ 34.7 ~ Barbarossa
65.5 ~ 34.5 ~ Far East Asia
65.6 ~ 34.4 ~ Philippines
65.9 ~ 34.1 ~ Classic Massive
66.3 ~ 33.7 ~ Mars
66.5 ~ 33.5 ~ Rivals of Rome
66.9 ~ 33.1 ~ Mexican American War
70.3 ~ 29.7 ~ Europe Massive

So there is literally a 60-70 percent chance you will win as a first player in a casual, non fixed force game. Higher if you choose fixed force.

And of course, a 30-40 percent chance you will win as a second player in a 2 player game.

 

[JCUK]

Thanks for the effort of producing the stats, it will certainly help me choose maps and settings when I create future tournaments, particularly 1vs1.

 

[periwinkle]

Interesting .....perhaps we can do a quick stats collection? Let's say for 1 month...try just deploying for the first player and see if it corrects anything....if you aren't happy with the stats...then we can try auracraft 's suggestion ...maybe just pick 1 map with the most traffic..like classic evolved? Not sure if this is the best solution ...just a thought.