Many Diplomacy games end in a 3-way draw. Often such games end that way because the surviving players do not feel that their position is strong enough for a solo attempt. A 3-way draw is seldom satisfying to the ambitious Diplomat, however, because it includes 42% of the players who began the game! Between a solo that may be out of reach and a 3-way that is not ambitious, there is another possibility: a 2-way draw. The 2-way draw can be a noble result in Diplomacy, owing to the requirement that draws must include all survivors. The need to split Europe evenly between the victors leaves no room for error, especially given the tendency among the losing players to prefer giving up a solo over being eliminated. There is no accounting for taste! The consequence of these difficulties is that a 2-way draw can be harder to engineer than a solo win, and this gives the owner of a 2-way draw sufficient satisfaction to compensate for having to share the victory. In a subsequent article, we will discuss the diplomatic aspects of the 2-way draw. In this article, we focus our comments on the strategic aspects of 2-way draws.
Let us assume that all players in a Diplomacy game are playing to achieve the best result they can get for their country. It is important to note that we are not considering "care-bear" alliances, but only alliances between two ambitious players who want to win. How does one build a 2-way draw between two players who would take a win if they could and who do not trust their ally to stand by an unenforceable agreement? The answer is based on the concept of the stable 2-way draw position, by which we mean a position in which each player has control of an unbreakable line that encompasses 17 centers. Once a player has his side of a stable 2-way draw position, he is guaranteed a place in the final result of the game. He can hold the position for the draw, or he can try to get one more center for the win.
There are but five stable 2-way draw positions as far as we have determined, plus a few minor variations. In order to make the positions more memorable, we have given them appropriate names based on the geography of the lines, sometimes with historical references. Beginning with lines that divide north from south and rotating counterclockwise, we have these lines:
1) the Juggernaut line, separating a northern power(G,R) and a southern power (A,I,T), named after thefamed Russo-Turkish alliance
2) the Saragossa line, separating a northern power (E,G) and a southern power (I,T), named after the treaty of 1529 that established for two centuries the division of colonial lands between Portugal and Spain
3) the Versailles line, separating a western power(E,F,G) and an eastern power (A,I,R,T), named after the treaty that ended World War I and detached from Germany the provinces of Prussia and Silesia
4) the Berlin Wall, separating a western power (E,F) and an eastern power (A,R,T), named after the post-World War II split of East and West Germany
5) the Stockholm line, separating France and Russia, named after the massacre of 1520, after which the Swedes revolted and gained independence from Denmark
The first four of these form a natural progression of centers. In each, the southern or eastern power controls Austria, Italy, Turkey, and the Balkans, along with 4 other centers as noted in the table:
| center(s) | Juggernaut line | Saragossa line | Versailles line | Berlin Wall |
| Portugal | southern | |||
| Marseilles and Spain | southern | southern | ||
| Tunis | southern | southern | eastern | |
| Sevastopol | southern | eastern | eastern | |
| Moscow and Warsaw | eastern | eastern | ||
| Berlin | eastern |
The Stockholm line, as compared to the Berlin Wall, includes Sweden, St. Petersburg and Munich as eastern centers in exchange for Italy. The Saragossa line also works with Portugal traded for Marseilles, but the given version seems easier to manage.
We now present the details of the unit positions, along with some discussion. Only the front-line units of the minimal positions are given, along with the number of backups needed for each unit. Unit types are included only when there is a possibility of error. A maximal list of DMZ spaces is also given. The idea here is that each player agrees to observe the DMZ's, but nevertheless anticipates a DMZ violation by the ally. The DMZ spaces provide needed security. Each player needs to be prepared to form the stalemate line after the first DMZ violation, but does not need to fully occupy the position otherwise.
The Juggernaut line
south (14 units): Arm, Bla, Rum (1), Bud, Vie, Trl (1), Mar (1), Spa, Por, Wes, F Tun
north (14 units): Sev (1), Ukr, Gal (1), Boh (1), Mun, Bur, Par, Bre, Eng, Iri, Nat
DMZ: MAO, Gas, Naf
This line works best for RT and GI, and it can be used for AR and IR as well. When the final centers are in the west, the southern power must be careful to secure Spain with significant backups before thenorthern power has a chance to capture Portugal.
The Saragossa line
south (14 units): Sev (1), Rum (1), Bud, Vie, Trl (1), Mar (1), Spa (1), Wes, Naf
north (13 units): Mos (1), War (1), Sil (1), Mun (1), Bur, Par, Bre, Mid, F Por
DMZ: Ukr, Gal, Boh, Gas
This line is ideal for EI and is also good for GI and GT. The line is easy to achieve, particularly when the final centers are in the east. The DMZ's in Ukr, Gal, and Boh give both sides a good chance to secure theirfinal centers.
The Versailles line
east (16 units): Mos (1), War (1), Gal, Boh (1), Trl (1), Ven (1), F Rom, Tyn (1), Tun(1)
west (15 unit): Stp, Bot, Bal (1), Ber (1), Mun (2), Mar (1), Spa (1), Mid (1)
DMZ: Lvn, Pru, Sil, Pie, Tus, Lyo, Wes, Naf
If the eastern power lacks northern fleets, the western power need not occupy the Baltic Sea and can get by with only 13 units. The number of units can also be reduced by reducing the number of DMZ spaces. For example, the eastern position needs fewer fleets if Tuscany is occupied by an eastern army.
The Versailles line is by far the most important 2-way draw line, being practical for fully 11 of the 21 possible 2-way alliance pairs. It is ideal for AE, AF, AG, ET, GI, GT, and can also work for EI, ER, FI, FT, GR. The extensive set of DMZ's make the Versailles line the most stable of the two-way draw positions. The western power must be most careful about Stp and Mun, while the eastern power needs to be most concerned about Mos, War, and Tun. Russia may have a difficult time securing Tunis, as this requires fleets in Rome, Tyn, and Nap, as well as Ion. France may have difficulty securing St. Petersburg, while Italy may have trouble with Moscow.
The Berlin Wall
east (15 units): Mos, Lvn (1), Pru, Ber, Sil, Boh, Trl, Ven (2), Rom, Nap, Ion (1)
west (15 units): Stp (1), Bot, Bal (1), Kie, Mun (2), Mar, Spa, Wes (1), Tun (1)
DMZ: Pie, Tus, Lyo, Tyn
This line is primarily available for ER, although it could be used for AF or FR as well. If the eastern power has no northern fleets, then the western power needs fewer units. As given, the unit in Spain supports Marseilles; however, it could support Western Mediterranean instead, in which case Marseilles would need an extra support and Western Mediterranean would not.
Possibilities for treachery are great with the Berlin Wall, with the advantage generally belonging to the eastern power. The western power must be careful to secure Tunis and St Petersburg, as well as Munich, while the eastern power need only be concerned about Berlin.
The Stockholm line
east (17 units): Stp (1), Fin, Swe (1), Bal (1), Ber, Mun (1), Trl, A Tri, Adr, F Alb, Gre, Aeg, Eas
west (17 units): Nrg, Nwy (1), Ska, Den (1), Kie (1), Ruh, Bur, A Pie, Ven (1), A Rom, Nap, Tyn, Tun
DMZ: Bar, Ion, Apu
This is an extremely difficult position, at best possible for FR, and perhaps only theoretical. We would appreciate any information indicating that it has ever actually been achieved. Russia needs 3 fleets in the north and 4 in the south. Even then, the Russian position is not quite a stalemate line. The Adriatic Sea is not adequately defended if the unit in Venice is a fleet. (We assume that the unit in Trieste is an army, since it is needed to support Trl.) However, it would be extremely unlikely that the western power would manage to get a fleet through a DMZ to Venice, given that the western position requires a full 17 units tosecure.
Stable positions that ought to be
The five stable 2-way draw positions listed above appear to exhaust the possibilities except for some minor variations, such as trading Portugal for Marseilles in the Saragossa line. There is an apparent gap in the list that must be surprising to those who have not studied the stalemate lines in detail: there is no stable 2-way draw position suitable for an EF or FG alliance. In principle, we might begin with the Juggernaut line and attempt to trade Brest and Paris for a pair of southern centers. No such line is possible. In fact, no combination of Vienna, Budapest, and Rumania can be held from the north against a determined attack from the south. Implications of this observation will be discussed later when specific alliances are considered.
Approaching a 2-way draw
The stable 2-way draw position is the theoretical basis for a 2-way draw. In practice, it is generally neither necessary nor even desirable to occupy very much of the position. It is necessary only to be prepared to occupy it in the event of treachery. The player who is attempting a 2-way draw needs to be able to evaluate the risk of loss as the position develops. It is necessary to insist on restrictions on the ally's movements and to agree to reasonable restrictions. This is more properly the topic of our second article on the diplomatic aspects of 2-way draws. One strategic point is worth noting here. The stability of a position can be increased by having certain spaces occupied by units suited only to defense. In the Versailles position, for example, armies in Spain and Tunis fill in the stalemate positions but are not the offensive threats that fleets would pose.
Turning a 2-way draw attempt into a solo
Of course the ambitious Diplomat may well see a 2-way draw as an outcome only half as good as a solo. It is quite reasonable to think of a 2-way draw alliance as primarily a means to a solo, with the 2-way draw as a backup. Two conditions allow a 2-way draw to be converted to a win. One is when the ally fails to insist on reasonable restrictions and the other is when you are lucky enough to get help from a minor power. In the absence of either of these conditions, the player who tries to convert a 2-way draw attempt into a solo is far more likely to be stuck with a large draw. In particular, we maintain that a solo cannot be stolen from a 2-way draw without 3rd party help, given proper strategy and diplomacy by the 2-way draw ally.
There are 7 countries, each of which can have 6 alliance partners. The 42 permutations of these countries include 21 redundant pairs; thus, there are 21 possible 2-way alliances. We consider these in groups. In our view, there are 9 alliance pairs for which a stable 2-way draw is not difficult, 3 pairs that can easily turn into solo wins for one of the players, 3 pairs for which extensive center swaps are needed to achieve a stable 2-way draw, and 6 pairs for which a stable 2-way draw is clearly impossible.
Smooth sailing: RT, GI, EI, AE, AG, ET, GT, AF, GR
These 9 alliance pairs have stable 2-way draw positions that do not favor either side and do not require extensive center swaps. The Juggernaut line is ideal for the RT alliance. Both the Juggernaut and Saragossa lines work well for GI and EI, with the Juggernaut probably the better choice for GI and the Saragossa for EI. The remaining pairs in this group are well suited for the Versailles line, with the Berlin Wall also possible for AF. Of course the GR alliance can achieve the Berlin Wall only if Russia allows the Germans to take St. Petersburg. These alliance pairs can even yield 2-way draws in no-press Diplomacy. The 2000 Vermont Group no-press tournament included 4 2-way draws out of just over 80 games, and these were achieved by AE, AG, GT, and AF pairs.
Unbalanced opportunities: ER, FI, FT
The ER alliance is a particularly interesting case study. Of the four stable 2-way draw positions, only the Berlin Wall and the Versailles line are reasonable for ER. The Berlin Wall is a difficult position for England to achieve. The trouble is that Russia can often get to Munich before England can. This gives Russia a tremendous advantage, should he decide to use it. He can then appear to be playing for a 2-way draw with England (unless England appreciates the necessity of controlling Munich), when in reality he is trying to win the race to Italy for the solo. (Von Moltke's ghost writer, Mr. Ledder, owes his top-10 JDPR rating in significant part to two solo wins earned in exactly this manner. Now that this information is being released to the public, he will probably have to stop playing Russia!) The Versailles line is equally difficult for Russia, as he must manage to penetrate the Mediterranean enough to control Tunis.
The FI and FT alliances are unbalanced to a lesser degree. Both alliances can easily achieve the Versailles line. However, it can be difficult for France to secure St Petersburg in either case and it may be difficult for Turkey to secure Tunis or for Italy to secure Moscow and Warsaw. The demonstration game OVER1201 provided an example of these risks. The game ended as an FI draw, but the final approach to the draw was marked by two Italian stabs followed by a position in which France chose to bypass a stabopportunity.
Careful negotiation needed: AR, IR, FR
The AR alliance can achieve the Juggernaut position, but only with careful negotiation. Normally, this alliance will lead to Austrian control of Munich and Russian control of Rumania and Ankara and possibly also Bulgaria or Constantinople. In order to achieve a stable 2-way draw, they must work out an agreement to give all of Turkey and the Balkans to Austria while the Russian takes all of Germany. Most likely, the allies will need to have Russia take some of the southern centers at first, with Austria taking them over after Russia begins to move across Germany and Scandinavia. Given the necessary center split, the Russian will have better solo opportunities than the Austrian. A Russian solo strategy would be to try to hold Rumania or Ankara long enough to take the entire northern position.
Similarly, the IR alliance can be steered into the Juggernaut with extensive center swaps. Russia has significant winning chances if he can talk Italy into a center split that allows him to keep Rumania, for thenthe remainder of the northern line gives him 18.
The FR alliance is even more difficult to steer into a 2-way draw. The Berlin Wall is a possibility, but the position seems to favor France because of the difficulty Russia will have in capturing Italy. The Stockholm line is a more natural split for the FR alliance, but it is extremely difficult to achieve, owing to the small number of DMZ's and the need for 17 units to secure the stalemate positions.
No reasonable 2-way draw positions: AI, AT, IT, EG, EF, FG
There is nothing even approaching a stable way for these 6 alliances to divide the world. Two-way draws can be achieved with these pairs only if both players are absolutely committed to the draw. These 2-way draws are reserved for "carebear" types.
What is interesting about this list is that it is fairly obvious that AT and IT alliances cannot lead to a stable 2-way draw run. The other four pairs are not obvious. We spent several hours trying to find a position for an AI draw before reluctantly concluding that no such position exists. We tried for several days for EG, EF, and FG. All four of these alliance pairs are common in the early game and can persist into the middle game, in part because both parties can grow indefinitely without boxing in the other. They cannot, however, lead to a 2-way draw among players out to win. Inevitably, these alliances end with a stab, a race to a solo, or a care-bear draw.
Compare the list of the 6 unstable alliance pairs with the list of 9 particularly stable pairs. There is a very clear pattern. Stability is generally possible only for pairs that do not have home centers very close to each other. In particular, the 6 unstable pairs include 3 pairs of western powers and 3 pairs of eastern powers. The only stable 2-way draw pairings involving powers from the same half of the board are the RT, AR, and IR alliances. Of these, only RT can be achieved without extensive center swaps.
Obviously, the criteria for a good end-game alliance are completely different from the criteria for a good opening-game alliance. In the opening, one wants an ally with whom quick collaboration against a common enemy is possible. In the ending, one wants an ally whose center of power is on the opposite side of the board. It should now be quite clear why the RT Juggernaut alliance deserves its reputation as the most feared alliance on the board. It is the only alliance of the 21 that is ideal in the opening and remains ideal for the whole game. Personally, we believe that the AR and IR alliances are as good or better than the RT. Both have clear opening targets, but without the need for immediate trust that the RT requires. Both have a stable 2-way draw option that can be managed with careful negotiation. It is interesting that few players recognize the power of either of these alliances, although the AR alliance is promoted in an excellent article by Marc St. Rose and Marcel van Vliet The Russian/Austrian Alliance.
All of the other alliances that are considered good in the opening suffer from the defect of being unsuitable for a possible 2-way draw attempt. Some of the other alliances that are good in the end-game deserve a closer look. For example, the GI alliance can be quite effective. If France and England are at odds, the resulting struggle gives Germany and Italy opportunities to cooperate in France and in Austria. Similarly, the AG alliance offers an opportunity for early cooperation against Russia, provided Germany is not under significant pressure from the west. One other strong possibility is the GR alliance. This alliance is generally considered untenable. However, it is possible for Germany and Russia to work together in Scandinavia and Austria from the beginning. Giving the northern gains to Germany and the southern gains to Russia sets up the possibility of a 2-way draw based on the Versailles line.
The expert Diplomat needs to understand that what makes a good opening alliance is different from what makes a good ending alliance. At the beginning of the game, one should communicate with all players and seek out alliances for the future as well as the present. The authors became acquainted in the game nanook, with von Moltke as Germany (natch!) and Bismarck as Turkey. In the opening, Germany allied with France and Turkey with Austria, but they also formed a mutual alliance behind the scenes. The early alliances produced early gains, but the GT alliance produced a devastating AGT attack against Russia, followed by an easy run to a 2-way draw with the Versailles line. This article grew out of our post-game reflections on the strategic and diplomatic considerations that led to the final outcome of that game. Except for rare pairs, such as RT and GI, that can easily cooperate from opening to ending, 2-way draws generally are shared by players whose alliance had no direct bearing on the opening. The player who wants to beopen to a 2-way draw needs to have this in mind from the outset of the game.
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Glenn Ledder and Karlis Povisils (gledder@math.unl.edu) |
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