Well in heads up I won't play second place but I'll take the challenge. Just a little far from Ohio right now :(

Haha, this can get even more complex and you can think of it in term of EV (expected value). For this analysis, let's use a bet of 12 (pot of 84) just because you get nice whole numbers for two, three, and four-way draws), but it can be used for any bet size, of course. If you have a guaranteed two-way draw, you get 42 . If you three-way draw, you get 28 , and if you draw four-way, you get 21 . If you solo, you get all 84, of course.

Then it becomes a simple formula (assuming you are decent at estimating the chances of the various outcomes) to determine the EV of your stab and whether you "should" stab to maximize your value, or take the easy draw.

EV = 84a + 42b + 28c + 21 where A is your chance of the solo, B is your chance of a two-way draw, C is your chance of a three-way draw, and D is your chance of a four-way draw. My examples will only include two and three-way draws, for simplicity.

For example, if you have a decision to make whether or not to take your "guaranteed" two-way draw and finish off the third party or stab your ally and go for the solo, pretend you estimate you have a 60% chance of succeeding, 20% chance of a two-way draw, 10% chance of a three-way draw, and 10% chance of either being eliminated or leaving someone else to get the victory. You would have:

EV = .6(84) + .2(42) + .1(28) = 61.6

Because 61.6 is above your guaranteed gain of 42 for the sure two-way, you should clearly stab in this situation.


Using this analysis, the requirements of going for the solo may be lower than you expect. Assume you think you only have a 40% shot at the solo, and if you fail, you will most likely give another player the win, or be eliminated, 30% of the time, but have a chance to be included in a two or three-way draw at 15% each.

Gain = .4(84) + .15(42) + .15(28) = 44.1

In this case, trying for the stab is still the optimal decision, albeit only slightly. It just shows that even if your stab is more likely to fail than succeed, it can be the correct decision to try for it.

If you play poker, you can certainly understand this concept in terms of pot odds. When you are drawing for a flush, more times than not you are not going to hit, but it is a good decision to go for it if the odds are right.

I didn't expect this to get so technical but I think it can be an eye-opener to people who have never thought of it in these terms before.

It's an interesting analysis. I base my strategy always on similar analyses to the one you present.

Funny enough, I actually have never actually used that analysis during a game. I've certainly thought about it in terms of how big of a chance I have to succeed and what might happen if it fails, but I have never actually done the math.

However, this conversation got me thinking about it. The difficulty, of course, is accurately estimating the percentages of each outcome, which isn't always easy to do.

I think this game lasted 22 years because France kept making poor tactical orders, despite him being one of the strongest at one point. Italy played well on being reliable.
It seems France, England, and Germany couldn't negotiate things out.

Italy EOG:

Game Start:
This game was several firsts. It was my first Anonymous game, my first WTA (though I technically began a second one on the same day), and my first game as Italy. Anonymous was somewhat troublesome, as I am a firm believer in “know thine enemy” and analyze the past games of my opponents when given the chance (or, in face to face games, simply utilize what I already know about my opponents as people). It was already clear to me that different players had different reputations on the site, and this was the first game where that knowledge was unavailable to me.

WTA, to me, simply means that the rewards for soloing are higher, but so are the penalties for failing to stop a solo. There’s no “safety net” so to speak. A draw, of course, has the same outcome as a PPSC draw. There is simply a greater temptation to solo, due to the higher rewards.

1901-1902:
As this was my first time as Italy, I wanted to keep as many options open as possible. I swiftly made DMZs with France, but my attempts to reach out to England and Russia were ignored. In fact, neither said a word to me all game. It seemed that I would have to find my friends amongst my neighbors.

Things began to develop in a rather unexpected manner when Germany’s first message to me basically told me not to attack Austria, or that I could expect retaliation from him. Communication with Austria revealed that Germany had issued a similar threat to him, and thus the Central Triple was born.

This left Turkey. Our communications were friendly enough, and Austria wanted to ally with him against Russia. I was a little hesitant about this, and even more hesitant about attacking France, particularly since Germany seemed to have little interest in attacking him himself. Ultimately, I chose to be non-committal, which annoyed Turkey and Germany but built up a bit of trust with Austria and France.

1902 came along, and suddenly I was at a complete loss for what to do. Germany wanted me to attack Turkey, Austria wanted me to attack France, France had just build F Mar but insisted it was heading north, and I had no idea which of them to trust.

Ultimately, I decided to attack France, but before I could actually commit myself in that direction, Turkey stabbed Austria. Russia joined in the attack as well. Well, now I knew who I _could_ trust. I knew Austria would be insane to attack me at this point, and both Germany and France were getting set to attack England.

I ignored France and Turkey’s suggestions that I accept that Austria was doomed and join in on the partition, offered my full assistance to Austria, and convoyed an army into Greece. The alternative was to side with Turkey, whom I didn’t trust in the slightest, and by extension Russia, who remained the strong and silent type.

((More))

1903-1904:
My choice in Austria as an ally was swiftly validated, and we began exchanging long and detailed messages planning our strategy against the Juggernaut. We both know that only superior coordination would enable us to survive, and that even then we would probably need some German help. Germany finally moved against Russia in 1903, but his aid was painfully slow.

I sacrificed Greece to get Austria Serbia, but managed to get it back the following year. Turkey and Russia ended up being relatively uncoordinated, and realizing this Turkey approached us with proposals for peace. Our first “agreement” saw attempted stabs all around, and both Austria and I resolved at that point that Turkey had to go. We did manage to convince Turkey to stab Russia in 1904, but as planned we continued to attack him anyway.

It was at this point that Austria and I first began to devise grander schemes. We also concluded that our alliance was going to be a long-term one, both because we worked and communicated so well together and also because we had little trust in any of the other players. Germany, especially, let us down by pulling away from Russia and engaging in minor skirmishes with France. Austria and I agreed that Germany had offered us little but manipulation all game, and that he would not be included in any final draw if either of us had a say in the matter.

1905-1906:
As much as we would have liked to, we couldn’t afford to stab Germany just yet. Turkey and Russia were continuing to put up quite a fight. France and Germany did enter full scale war, though, and I had promised Germany that I would come to his aid, so I sent some token forces westward. This helped to tip the scales a bit, as France really was growing dangerously strong. I wanted Germany defeated, but at the hands of Austria, not France.

1907-1908:
Turkey was _finally_ eliminated, and I moved more strongly against France. Germany grew increasingly paranoid about Austria and I, so the two of us engaged in some fake skirmishes and center exchanges to appease him a little. While I thought that I had managed to earn his trust, he never really trusted Austria.

1909-1910:
Germany refused to finish off Russia, which annoyed Austria and I to no end. Both of us gave it our all trying to convince him to do otherwise, but he wouldn’t budge. After debating whether we should genuinely go for a three-way with him, we decided to have Austria attack Germany while I continued helping him finish off France.

1911-1912:
Our plan came to a grinding halt when Germany began actively aiding France against me. It became clear at this point that, despite my best efforts, Germany never really did trust me. Now we were left with five nations and, more or less, a stalemate line. Austria and I were at a loss for what to do, and even began contemplating having one of us solo the other just to deny the other three the draw.

1913+:
And then France started NMRing. This provided the opening we needed, and France was systematically pushed back. Eventually, I advanced far enough to attack Germany as well, which finally gave Austria something to do. The opposing trio was eliminated in a fairly predictable fashion from that point forward.

The main question for me, then, was what to do about Austria. Austria was among the most competent and reliable allies I had ever had, and despite periods of cooperation with France and Germany I was never able to reach anywhere near that level of trust and respect.

Ultimately, I decided not to stab Austria, though I probably could have pulled it off. I did this for several reasons. Firstly, to honor a very close alliance that had clawed its way out of what had seemed to be a rather dire situation. Secondly, because I genuinely believed that such a strong ally should be rewarded in some fashion. I probably would have been _more_ likely to stab him in a PPSC game, because then I would know that he still would receive a significant fraction of the pot as consolation. Finally, I wanted to establish a reputation of my own as a loyal and reliable ally, even in the long term.

Of course, I am no fool, or at least I like to think that I am not. While I never intended to solo, I made very sure to minimize the opportunities that Austria had to do so himself. Especially as the game came to a close, I maintained garrisons throughout my territory on the off chance that Austria had a truly silver tongue. While my defenses were not perfect, I was rather pleased with the level of defense I was able to establish with minimal threat or provocation to my ally.

And that’s the game.