Alone in the library of the Calhamer Club, I spent eighty minutes lost in thought, devoted to my vain attempt to resolve what I had come to think of as The Curious Case of the False Start. On the surface, it seemed a simple enough problem, set for the British Crown by the deviously clever Sultan of Suwat. To obtain an extension on an important mineral lease at the Port of Suwat, my friend Sherlock Holmes had been asked to supply the solution to the following puzzle:

We are given a Diplomacy board set up with the pieces in their starting positions, but we are told that despite this fact, the game has already begun. Further, we are told that although no neutral supply centres have been captured and all of the players' home centres are in their own possession, it is also true that no piece on the board started the game in its current position. In short, each power has managed to depart from — and then return to — its original board position, without having any of its original units sitting on the spot where it started the game.

The problem is to determine how quickly this rearrangement of pieces can take place. Not only that, but the Sultan required that the number of dislodgements be maximized, and that to ensure that the mystery was properly solved, the number of dislodgements should be brought by royal messenger to him. As if this was not enough, the Sultan's location (where he was waiting to receive this dispatch) was also left unspecified, except to say that the Sultan awaits the royal courier at the location into which the single unit that retreated in the puzzle withdrew after having been dislodged.

Before Holmes stepped away to dine with an acquaintance, leaving me in my puzzled state staring at the Diplomacy board, I had discussed the problem with my friend, exhausting all of the "trick question" possibilities. I was told that (far from being a variant game in which pieces do not begin the game in their usual location) the game is standard in every way. I also learned that the resolution to the problem did not revolve around the fact that the pieces had been accidentally or intentionally removed from the board, and simply replaced with different pieces of wood.

When Holmes returned to the game room, I was quite pleased with my efforts. "Holmes," said I, "I am happy to report to you that I have made significant progress toward solving the Sultan's puzzle."

"Indeed?" questioned Holmes. "Perhaps my continual urging to use your not inconsiderable talents for deduction have not been wasted! Let us see what you have determined."

With some measure of pride, I began. "I am fairly certain that the feat can be accomplished in a mere four movement phases. That is, a game could in fact be beginning 1903 with the positional and centre ownership situations identical to those as at the start of the game, but with the pieces in each position different from those that began the game there."

"Excellent," cried Holmes. "You are precisely correct. I admit, Watson, that I was slightly concerned for you after your initial ruminations had you sailing the Russian fleets all the way from one port to the other."

I flushed a bit at the recollection. My first thoughts had indeed concerned the lengthy trip that the two Russian fleets would need to make to dock themselves each in the other's port. With a twinkle in his eye, Holmes had left to take his sustenance while I was busily counting the length of time that would be required for a Sevastopol to St. Petersburg sail.

"Yes, Holmes," I responded. "I quickly realized that the task of rearranging the pieces could be done much quicker by cooperative action with foreign units. I reasoned that by dislodging the two fleets and rebuilding them with new fleets, the problem's central requirement (that the pieces on the board would be different from those that started the game there) would be fairly met."

"Quite so, Watson, and indeed dislodgements are the key to every facet of the solution to this fascinating puzzle."

"So I realized, Holmes, and I admit that it was with some measure of self-satisfaction that I have spent the past hour or more trying my level best to quickly return the board to its starting position — but with different pieces at each location — without taking possession of any neutral centres and while dislodging as many pieces as possible. It was while doing this that I realized with surprise that the task can be completed in a mere two game-years."

Holmes picked up from here. "Surprise, Watson? Surely it is more than obvious that it can be accomplished for any single power in two game-years."

"True, Holmes, but I admit I was astonished to find that all of the powers can do so in the same timeframe simultaneously."

"Indeed they can, Watson. In fact, as is easily seen, some powers can do it in half that time, finishing the task in only one game-year, although it is not a stipulation of the puzzle that any of the powers in fact do so."

"Yes, Holmes. France, for example, can arrange to have its fleet dislodged by an English attack into the Channel in Fall of 1901 and rebuild the lost fleet in the coming Winter adjustments phase, while having moved his Marseilles army to Paris and vice-versa."

"Correct, Watson. Like France, Austria, Russia, and Turkey can (with assistance) also accomplish the feat in a single year, by simply swapping the positions of their two armies while suffering the Falltime dislodgement of their fleet or fleets. As with France, the key, of course, is that the dislodged fleet is removed and then rebuilt, rather than retreated.

"Since the English army and the German and Italian fleets cannot possibly be dislodged and disbanded (and then rebuilt) in the first game-year, these three powers require two game-years to accomplish a rearrangement."

The great detective then concluded his lucid restatement of the task. "The ability of those four powers to accomplish the task in a single year is, of course, interesting, though not of consequence to us, as our task remains simply to accomplish it for all powers within the minimum time, which as you have found is two game-years, while maximizing the number of dislodgements."

"Yes, Holmes, and to this end, I have devoted the past hour to rather gleefully dislodging as many units as I could while recreating the game's starting position within the span of two years."

"Excellent, Watson, and to what conclusion have you come as to the number of dislodgements and the Sultan's location?"

"I am afraid, Holmes, that I remain a trifle confounded regarding those details. I have determined that a total of nine dislodgements can be made, but as to which single unit must have been retreated rather than disbanded, and the location into which the retreat must have been made, I am in a quandary. I fear that my nine dislodgements must simply be incorrect, for I am unable to determine from them where the Sultan awaits."

"Nine dislodgements is a fair attempt, Watson, and you are to be commended. You are correct, however, that a greater number is possible and until you discover those that you have thus far missed, the Sultan's location shall remain hidden to you."

"I regret, then, Holmes, that I feel I must request your assistance. I have been dislodging units willy-nilly throughout your luncheon, and despite being fairly sure in the knowledge (that you have just confirmed for me) that it must be possible — as I have begun to say — to 'squeeze' more dislodgements into the two game-years, I have been unable to better my total of nine."

"Right, then, Watson," said my friend, checking his pocket-watch. "Although my potted ferns will require their care before long, I believe that we have time for an illustration of the solution." With that, Holmes sat with me at the Diplomacy board, restored it to the starting position, and addressed me.

"Let us begin, of course, with the Spring 1901 moves. As you may have realized, the key moves of the solution will take place at the crossroads of Europe." At this point he pulled the Russian fleet on St. Petersburg's south coast to Livonia, the German fleet in Kiel into the Baltic Sea, and the Berlin army to Prussia, putting beyond doubt the short-lived fate of Russia's Northern fleet. He then pushed the Budapest army into Galicia and the Warsaw army into Silesia, where it found itself surrounded by red and black armies, when (rather to my surprise) he advanced the Munich army northeast into Berlin.

I had indeed determined that maximizing the number of dislodgements involved rushing the armies on the board toward each other. It seemed to me, and now it stood confirmed by Holmes, that the proximity of the German, Austrian, and Russian armies must be put to good use. However, while I was sure in the knowledge that the Bavarian army, being so centrally located at the start, would play a significant role, I wondered why Holmes would have chosen to concentrate the action where he did, putting the Munich army into Berlin, when he could just as well have let units congregate on Warsaw, Galicia, or, in cooperation with Vienna or Venice, on that very magnet of the board where it begins the game, Munich. I chose to stay silent at this time, and not reveal that this was where my thoughts had been attracted to for most of the evening.

"We have but two game-years to replace the Turkish fleet and Russia's southern fleet by dislodging and rebuilding them. Obviously, then, only one of the Sevastopol and Ankara fleets can be dislodged in 1901." Holmes moved the Turkish fleet to Armenia, the Sevastopol fleet into the Black Sea, the Moscow army to Sevastopol (both in preparation for a Falltime dislodgement of the Turkish fleet), and moved the Turkish armies into a position to allow them to end the first game-year in each other's original location, sending Constantinople to the vacated Ankara, and Smyrna into Constantinople. Turning his attention to the west, Holmes moved the French fleet from Brest to the English Channel, and to prepare a Falltime dislodgement of that fleet, Holmes then moved the English fleet from Edinburgh into the North Sea for cooperative action with London.

As if I should know his reasons, Holmes quickly moved the Italian units from Venice to Rome, from Rome to Tuscany, fleet Naples to Apulia, and the Austrian army from Vienna to Tyrolia and the Austrian fleet into Venice. My friend proceeded to finish with the French turn by pushing Paris to Burgundy and, to my surprise, Marseilles to Piedmont.

Taking all this in, I felt obliged to contribute something at this point. "I find your opening curious, Holmes. Most strange to me is your moving the Marseilles army to Piedmont. I had not considered such a thing and while I see that it masses a great many units together, the easy road to Paris through Gascony, to achieve the exchange of places of the two French armies, seemed far too obvious to avoid. Are you quite sure of your footing here? As you had mentioned to me, one of the powers meets the conditions a year early, and what you are proposing with Piedmont seemingly makes it impossible for France to do so....unless — I see! you intend to dislodge that army and rebuild it in Paris, with Burgundy moving to Marseilles to complete the French swap in the single year with one more dislodgement than I had divined! Brilliant!"

Holmes smiled. "Some but not all of that is indeed my intention, Watson. And yes, I believe we have found what may be the first of the dislodgements you overlooked."

Spring 1901 Movement Phase

"We have now created the game position going into Fall of 1901, Watson. Obviously, as with every standard game, no dislodgements have yet occurred. They will, however, begin to come quickly as we progress toward the solution."

"I can see that, Holmes. Here in the first Fall phase, you have managed to set up many units for destruction. The French fleet in the English Channel, the Turkish fleet in Armenia, the French army in Piedmont, the Russian army in Silesia, the Austrian fleet in Venice and the Russian fleet in Livonia are all vulnerable to attacks having the strength to dislodge."

"Well done, Watson. Indeed, each of these dislodgements does transpire. Attend while we step through the Fall turn. As you recounted, the French army in Piedmont is dislodged by an Austrian attack from Tyrolia, supported by the Italian army in Tuscany."

"Could it have been otherwise, Holmes? That is, could Italy have made the attack supported by Austria instead?"

"Perhaps so, Watson, but taking account of the geography in this part of the board, seeing as how only armies are involved here, and because Piedmont is not a supply centre, it matters not in this case. In other situations, however, the manner in which the units are dislodged is quite important to the solution. If the wrong unit is moved, the number of possible dislodgements is reduced."

Taking this as his lead, he then dislodged the French fleet by moving the English fleet from the North Sea, indicating that it was given support from the fleet in London.

"An amusing opening, Holmes. The normal move to develop the English position would be for North Sea to support London into the Channel. Why would you choose such a hideously compact form?"

"Foresight, my dear Watson. Knowing how the English army will be replaced, the choice should be obvious, no?"

I did not admit to the great detective that the question of the lone English army had stumped me before. It could not be swapped, so it either would have to be dislodged or disbanded in Winter if a home centre were taken, something that was unlikely to happen now. But on the where and how, I was completely in the dark.

Holmes appeared to take no notice of my discomfort, as he pushed the Italian fleet from Apulia into Venice, indicating that it was supported in this move by the army in Rome, and in this way dislodging the Austrian fleet. This I could understand, as it put the Italian fleet immediately in peril from an attack by the Austrian army in Piedmont and a rebuilt Austrian fleet in Trieste. Furthermore, the Italian armies would have no difficulty swapping positions, as Venice had already moved to Rome and the army in Tuscany was next to Venice.

Encouraged by this, I held out my hand to stop Holmes from picking up the next piece. "Allow me." The Turkish fleet in Armenia could either be dislodged by the Russian fleet in the Black Sea or the Russian army in Sevastopol. As in the previous case I reasoned that the fleet would need to be set up for a future dislodgement, but the army, which had started in Moscow, could end in Warsaw only if it stayed in Sevastopol this turn. Unhesitatingly I therefore attacked the Turkish fleet with the Russian fleet from the Black Sea, making the army in Sevastopol support the attack.

The remaining French army's order was obvious to me. I moved Burgundy to Marseilles, thus allowing France to fully complete (after builds were made) its replacement of pieces in this first game-year.

Before Holmes could comment I briskly tapped the army in Silesia, gesturing for a moment of thought. Either Galicia or Berlin could dislodge it. But if the attack came from Berlin, that army could just as well have held in Munich, as both spaces border Silesia. Knowing my friend's penchant for avoiding meaningless moves I concluded that Berlin was there to support, so I dislodged with the Austrian unit from Galicia instead. Observing this, Holmes seemed to relax as he took out his pipe and started to relight it.

For the Russian fleet in Livonia I had again a choice between the German fleet in the Baltic Sea and army Prussia. Applying the same logic as for Armenia I moved the fleet to Livonia supported by the army, as Prussia was only two moves away from Munich. While taking the Russian fleet off the board, I considered its options. The Prussian army could move either back through Berlin or through Silesia. Both spaces were occupied, Berlin by the second German army, Silesia by the Austrian army having just dislodged the Russian army there. Berlin would be able to support Prussia to Silesia, and again to Munich (adding one more critical dislodgement to the total!) if an army could be waiting there to be martyred for the cause. But which army could be in Munich for such victimization? Tyrolia had just moved away to Piedmont and I had moved the French army from Burgundy to Marseilles, leaving no foreign units able to end the turn in Munich to allow us to add one more dislodgement to the total.

It was then that I looked again at Silesia and at the pieces I had taken off the board, and it struck me! Barely hiding my excitement, I picked up the Russian army that I had declared to have been disbanded after losing Silesia, I placed it squarely in the centre of the board and I triumphantly proclaimed: "It appears to me, Holmes, that you have informed the government to send a courier to Munich, where the Sultan will be waiting for him in anticipation!"

Watson's Proposed Fall 1901 Movement Phase

"Not unless I wanted the mission to fail," Holmes said shaking his head. "Did I not tell you that no centre would change hands at any time?"

"But that was not a criterion of the puzzle," I protested, before continuing in good stride: "Munich will be recaptured by Germany when Prussia moves through Silesia towards Munich, dislodging armies on both upcoming turns, aided in doing so by the army in Berlin. As Prussia started in Berlin and Berlin in Munich, the end situation will have them swapped. Furthermore, the temporary capture of Munich allows the German fleet to be removed during the upcoming Adjustments, and it can be rebuilt in Kiel a year later when Munich is recaptured. Surely this much progress cannot be improved upon?"

The great detective, with a bemused expression on his face, continued his attempts to relight his pipe before commenting. "Watson, you did an excellent job lining out the path that the German army in Prussia will be taking to arrive at the Bavarian heimat. However, in your haste to get there, you missed an opportunity to increase the number of dislodgements. Consider this German fleet. Instead of removing it during Adjustments, thus making it unavailable for service in 1902, it would be more profitable if it could be dislodged, would it not?"

"Perhaps so, but it is stranded in the middle of nowhere with no enemy units in sight!"

"Ah, but those enemy units can be built, Watson. Tell me how many Russian units were dislodged."

"Well, Livonia of course, and Silesia. Ah, and no home centres lost. So Russia is entitled to two builds. He can rebuild a new fleet in St. Petersburg and an army in either Moscow or Warsaw, and all three locations border Livonia! So that's how you plan to dislodge the German fleet!"

"We have thus proven that there's no need to capture a home centre, and indeed that it even would prove to be counterproductive to do so." And with that Holmes picked up the Russian army in Munich and tossed it back in the box.

I was unsatisfied, though. "I understand your argument, Holmes, that it may be of benefit to retain the fleet, and not to suffer Germany to lose a home centre, but I do not see that doing so has gained us anything. Allowing the German fleet to be retained and dislodged comes at the price of surrendering the Munich dislodgement that my proposed set of orders had gained for us. So it would seem, as they say, to be 'a wash', for now there will be no unit in Munich to be dislodged when the army from Prussia arrives there."

"All in its own time. Since the Prussian army's march to Munich will take two seasons, any victim of a dislodgement in Munich need not be present there quite yet; such a unit still has the Spring season to use to travel into Munich, there to await its fate."

To my astonishment, Holmes then pushed the French army that I had moved to Marseilles back to whence it came – Burgundy.

I protested this. "Holmes, I had moved Burgundy to Marseilles to complete France's piece-swap within the first game-year, as you said that one power would accomplish the feat in that time. If not France, then which?"

The look of disappointment that Holmes shot at me was withering. "I believe you overlooked this simple final move," he said, as he pushed the Turkish army in Ankara south to Smyrna. "We have thus swapped the Turkish armies and are able to rebuild the dislodged fleet in its original home centre, all in the first year."

I was indeed chastised by how obvious that was, but Holmes continued, surprising me further: "Speaking of finalizing things from where you have taken us, though, Watson, that Russian fleet could better stay in the Black Sea. We shall have Russia's army dislodge the Turk from Armenia instead, and use the fleet instead to support the attack." He returned the Russian fleet that I had landed in Armenia back to the water and he put the army from Sevastopol in its place.

"Really, Holmes?" I exclaimed. "But this leaves the the army unable to move to Warsaw during 1902 to complete the swap!"

Holmes simply mysteriously pointed to the vacant Ankara, and said: "See here the lion's den." Smiling, he added: "We have now established the complete Fall 1901 season, and can move on to the Winter adjustments."

Holmes's Fall 1901 Movement Phase

"Would you care to move us along, Watson?" my friend queried.

"Well, as there are no Fall retreats, ..." I said, leaving a small pause, but to my disappointment Holmes didn't interrupt. Silently vowing to do better in my analysis of the second game-year I continued, "... the adjustments will hold no surprises. All the dislodged fleets are undoubtedly rebuilt in their starting centres."

I took up the discarded fleets and placed them back on the board, the Austrian in Trieste, the French in Brest, the Turkish in Ankara and then paused, eyeing the one Russian fleets in my hand and the two vacant Russian ports on the map. Realising that the German fleet in Livonia was there to be dislodged, I confidently and placed the Russian fleet on the south coast of St. Petersburg, and dropped the second back in the box, knowing that Russia's second build must be a new army to assist in that very dislodgement.

Casually clearing my throat, and reaching for my cup of tea (which had been cooled to near freezing), I said, "As for the armies, Holmes, if you would do the honors?"

That was a calculated move, to hand the reins to my friend. With the French army having held in Burgundy, France had two open build locations for its single army build, and Russia had three from which to choose in placing its own solitary new army! (Of course, in order to assist in the dislodgement the German fleet in Livonia, an army build in Sevastopol would be of little use, but Warsaw and Moscow were equally eligible.) I imagined there to be a chance that the placement choices I may have made in France and Russia would be of no consequence, but I was far more comfortable with Holmes making them.

Holmes complied in good humor and unhesitatingly placed an army in Paris, then paused, as if waiting for the realisation that suddenly hit me. Of course! The English army must still be dislodged, and to make this happen, Holmes was planning to convoy that army to Picardy where it would be surrounded by the full might of the French military! The new build had to be made in Paris, as a newly-built army in Marseilles, necessarily tasked with assisting in the dislodgement of the English invader, would be unable to end the upcoming year in either of Paris or Marseilles to complete the piece-replacement!

Yes, suddenly the Anglo-French fates seemed clear to me, and in a flush of excitement, imitating the way Holmes had referred to Ankara as the lion's den, I pointed to the vacant Picardy and said: "The pirate's cove!" I laughed heartily at my own joke, but Holmes only frowned. "Picardy, Holmes! Pirate's Cove. Picardy. It's a wordplay!" I cried.

"I see," Holmes commented, nodding. Then, turning his attention to Russia, he picked up the new fleet that I had placed in St Petersburg, studied it for a moment, and said, "Undoubtedly this will come to you as a surprise, Watson, but it should not. One should always take all possibilities into consideration. In this case, a fleet build is of all too-limited help." Dropping the fleet into the box, he took two new Russian armies from it and placed them in Warsaw and Moscow.

"But Holmes!" I cried in protest, "Russia will be lacking one of its two fleets!"

"Only temporarily, Watson. There's no condition that the same combination of units should exist throughout the game, and for our needs, two new Russian armies will be quite useful. To satisfy the condition of returning the board to its initial condition, since we are unable to do so here at the conclusion of 1901, we can wait to rebuild the retired Russian fleet at the end of the second year, which we are now ready to begin considering."

Winter 1901 Adjustment Phase

To begin 1902, Holmes started by moving the Austrian army from Piedmont, indicating that it had the support of the fleet in Trieste, allowing the army to dislodge the Italian fleet from Venice. Further illustrating the remark he had made during builds – that the Russian fleet I had proposed building was not mandated – he said, "Observe here, Watson, how even the Austrian fleet that you placed on the board a few moments ago could have instead been an army. In the upcoming Fall phase, while the Italian army in Tuscany mounts its attack to remove the invader in Venice (with Roman support), an army in Trieste could relocate to Vienna or Budapest, and the Austrian army dislodged from Venice would then be rebuilt as a fleet. But as this variation does not alter the result, we will let it stand as is, and allow that the Austrian chose to build his replacement fleet in 1901."

Turning his attention to the West, Holmes asked me, "You have by now discovered the reason for moving the North Sea fleet to the Channel?"

I replied eagerly. "Indeed I have, Holmes. The fleet in the Channel is needed to convoy the English army to the continent here in Spring 1902. In Fall, that same fleet must move to London to complete England's piece-swap. Meanwhile, the London fleet must move to Edinburgh during this second year, either through Yorkshire or the North Sea. If that fleet, rather than the one that began the game in Edinburgh, had taken the Channel assignment, it would not have been able to reach Edinburgh by year-end."

Pleased with my explanation, I moved the fleet from London to the North Sea, then picked up the army in Wales and dropped it in Picardy, saying: "As to the destination of the convoy, it must be here, the pirate's cove, cozily tucket between the two French units in Brest and Paris that will bring its downfall!"

"You are correct to a point, Watson. However, your so-called pirate's cove is not Picardy," said Holmes dryly, as he exchanged positions of the English army and the French fleet, "... but Brest. The reason, Watson, is elementary. If the English army were to be sent to Picardy here in Spring, France would need to dislodge it there during the Fall turn and would therefore end up with a unit located outside its home centres at the end of 1902. It is necessary to the conditions of our task that any unit dislodged in the final movement turn must be located, to begin that turn, in a home centre belonging to the attacking power. The only exception is if that power is allowed to remove units in Winter due to a loss of centres, something which is not possibly the case here, as no power has gained centres in 1901 that he can afford to surrender during 1902."

I had to admit that what my friend said made sense, and I felt rather ashamed for not keeping that simple tenet foremost in mind as we neared the solution. "I see that now, Holmes. And Ankara, unlike Picardy, fits that requirement, which is why you called it the lion's den. While the Turkish fleet, during Spring, moves out to dislodge the Russian army in Armenia (with support from Smyrna), the Russian fleet in the Black Sea can take its place in the lion's den. Turkey then simply needs to reverse its action, dislodging the Russian fleet from Ankara in the Fall (still using the same support from Smyrna), and ending the turn in its home supply centre, as required. It is as if an innocent lamb had unwittingly entered the vacant lion's den only to be devoured when the animal returns."

Holmes smiled as he manipulated the pieces on the board to execute the Russo-Turkish moves that I had described. "You're becoming poetic, Watson. Now to finish the puzzle, very little remains for us."

I felt obliged to bring up the subject of the single retreat that the Sultan required to be performed. "We have still not discovered the whereabouts of the Sultan, Holmes. Now, I have given this subject some thought since my earlier error. You might accuse me of being incorrigibly fixated upon Munich, but if the single retreat was not performed by the Russian army in Silesia last turn (as I had mistakenly proposed), I believe that it must be performed now, by the Austrian army that took its place there. Once again, I propose that the unit is dislodged from Prussia with support from Berlin, and the victim army will retreat to Munich where it can be dislodged once again by the same two armies, with the German completing his position-swap. It stands to reason that the Sultan must be in Munich after all!"

"It pains me, Watson, that you have failed to realise both the mission of the French army in Burgundy and the advantage to having foregone Russia's opportunity to rebuild its fleet after 1901, by instead building two new Russian armies. Certainly, allow Silesia to be dislodged now in the manner you described, by the Prussian army beginning its trek to Munich. But it is the French army in Burgundy, Watson, not an army being retreated from Silesia, that is slated to enter Munich and await the Fall-time dislodgement there."

Again, my ego was bruised, but what Holmes said next was curative. "However, Watson, you are correct on one point: the unit now in Silesia is indeed the one that shall perform the single necessary retreat. We have created two new Russian armies for this year for one reason: to cooperate and get for us not one but two dislodgements! Had we built a Russian fleet instead of a second army, we would not be able to accomplish this feat. But as it stands now, we can; quite simply. In Spring, the Warsaw army, with help from Moscow, dislodges the German fleet in Livonia. And in Fall, ...."

I saw it then. I exclaimed, "In Fall, Holmes, that same army simply returns to Warsaw, again with support from Moscow, and in so doing, it dislodges a unit there! That unit must of course be the Austrian that had been dislodged from Silesia in the Spring! The Austrian must retreat from Silesia to Warsaw! The Sultan is in Warsaw!"

"Quite so," was all Holmes said in response, drawing from his pipe.

Spring 1902 Movement Phase, with Retreat

I sat stunned at the unassailable logic and beauty of my friend's reasoning. Holmes looked quizzically at me, then back at the board. Suddenly, he stood up and paced to the lobby, where he had a short conversation with the desk clerk.

Clearly pleased with himself, Holmes returned to his chair and sat. Perplexed, I asked, "Will you tell me what that was all about, Holmes?"

"With pleasure. I asked the clerk to transmit a message from me to the Foreign Office. I have extended an invitation to the Sultan of Suwat to visit London, with excursions to Wales and the Channel Islands. I have hopes that this invitation will be wired in time for the courier to deliver it along with the lease extension so that we may have an answer from the Sultan soon."

"For what purpose did you issue that invitation, Holmes?" I asked, confused.

"Oh, nothing but an innocent quid pro quo, Watson," said Holmes, absently.

What do you think caused Holmes to invite the Sultan to London? Was it something he saw on the Diplomacy board? To be continued....

Indicating he considered the subject closed, the great detective continued. "Now, to return to the board, Watson, let us take a tally of the dislodgements that have occurred."

Obediently I started to count. "There were six in the first Fall season. In Spring of 1902, I count four: in Venice, Armenia, Silesia, and Livonia. As for the second Fall season, let me see...."

One after another, I executed and counted the final dislodgements:

1. Picardy returning to Brest with support from Paris, dislodging the English army;
2. Armenia returning to the lion's den of Ankara with support from Smyrna, dislodging the Russian fleet;
3. Silesia completing its slow trip from Berlin to Munich, using support of the army Berlin to dislodge the French invader;
4. Tuscany finishing its voyage from Rome to Venice, using support from Rome to dislodge one of the Austrian armies; and
5. Livonia returning to Warsaw with support from Moscow, dislodging the second Austrian army after it had retreated there.

Having done that, I announced: "Five more dislodgements in Fall 1902, Holmes, for a grand total of fifteen. That's just fabulous! That's an average of five dislodgements for each season in which dislodgements could occur!" Nearly two-thirds of the starting units have been dislodged in a mere two game-years, one of them even twice, without ever having increased the number of units on the board, as no neutral centres were taken."

Fall 1902 Movement Phase

Holmes tapped his pipe to empty it. "I will agree with you that it is quite a marvel. Did you notice that the eight units that were never disbanded are pairs of like-type units that belong to only four of powers? These four powers only had to disband and rebuild the unit of which type they held only one, while the other three powers ended up disbanding and replacing every one of their units."

"I see, Holmes. It is possible to divide the powers into two camps, those that lost all their starting units and those that simply swapped the positions of their same like-pair."

"In fact, there are many more remarkable facts about this solution. But let us first complete the Sultan's assignment for us by rebuilding the missing units."

With that, Holmes placed one French, one English, and two Austrian armies, and furthermore one German, one Italian, and two Russian fleets in their respective home centres, restoring the game completely to its starting situation.

Winter 1902 Adjustment Phase

Puffing on his pipe and admiring what the ignorant bystander would assume is nothing other than a table freshly laid for Diplomacy, Holmes said, "Notice, Watson, that the term we used – 'lion's den' – to describe a location from which a unit attacks, and then immediately returns, attacking once again, applies not only to Ankara and to your 'pirate's cove' of Brest, but also to the Sultan's retreat, Warsaw. In each case, the hungry 'lion' that returns home to feast is a unit that had been built anew in the Winter of 1901."

"There are several other curious facts worth noting about the solution as we have constructed it here, Watson. Consider that in every season after the first:

"there was one unit (the army in Constantinople) that did nothing but HOLD;

"there was one space (Venice) that consistently saw a unit dislodged;

"a different power may have issued nothing but HOLD orders, and thus could even have been in civil disorder (in Fall of 1901, this power was France, in Spring of 1902, it was Italy, and in Fall of 1902, it was Austria)."

"Furthermore, Watson, note that there were two powers – Italy and Turkey – whose units never left their own national borders."

"All fascinating trivialities, Holmes, but trivialities only. The more important question is: How can we know for sure that this is the optimal solution, and thus the only one that satisfies (and locates) the Sultan? Perhaps more dislodgements can be found in any one or more of the game-seasons? Take the first Fall season, for example. Six dislodgements is certainly a fine number, but couldn't there be seven or eight?"

"You are correct, Watson, that without going into more depth we cannot provide ourselves with the ultimate proof you describe, but we can gain confidence by exploring the various alternatives. For instance, since a single dislodgement requires at a minimum three units (the dislodged party, the dislodging party and the supporting party), when starting out with twenty-two units the maximum number of dislodgements is logically seven."

"Ah, right. And the limitations of the board setup will likely prevent us from reaching this maximum in the first year."

"On the contrary, Watson, it is quite possible to see seven dislodgements in Fall 1901, without even changing many of the orders in our solution. The problem is rather that it is impossible from each of these positions to conduct a 1902 game-year with eight or more dislodgements, at least not without taking more advantage of retreats, a course of action that was forbidden to us. Only by surrendering (in exchange for position) one of the seven possible 1901 dislodgements were we able to add one more than a seventh to those transpiring in 1902. That, as it happens, is something we were only able to do by using the position we gained to take best advantage of the single retreat allowed to us."

Can you confirm for yourself the statements that Holmes made?

Consulting his pocket-watch, Holmes rose and said, "Now I am afraid, Watson, that we simply must return post-haste to our apartments in Baker Street, where my potted ferns will be wanting my full attention."

-- Dr. John H. Watson
via Manus Hand and Mario Huys
(manus@manushand.com and marioh@diplom.org)