An example clearly shows that these 11 dislodgements could easily all be forced disbands! They may also all eleven be ordinary retreats, and we shall be leading up to an example where the number of possibilities for these 11 retreats is maximized.
We can say much more than that. In Spring 1901, no unit may be dislodged, since no unit borders upon two others. (In fact, only F Tri and A Ven border at all!)
In Fall 1901, there can be at most six dislodgements.
According to the rules, a unit must retreat to: "a space to which it could ordinarily move if unopposed by other units.... The unit may not retreat, however, to any space which is occupied, nor to the space its attacker came from...." At least one neighboring space is sure to be occupied. (The one which supported the attack.) Thus, the number of legal retreats is two fewer than the number of legal moves unless the support and/or the attack came from a space to which the attacked unit could not legally move. (For example, a fleet on a coastal province can be attacked from an inland province, or an army can be attacked from off-shore.)
Here is a list of the spaces from which there are the most legal moves. (Adjustments have been made for the exceptions mentioned above.)
| Unit | Neighbors | Max # Retreats |
| F NTH | yor edi nwg nor ska den hel hol bel eng lon | 9 |
| F MAO | nao iri eng bre gas spa por spa naf wes | 8 |
| F ION | tun tys nap apu adr alb gre aeg eas | 7 |
| F ENG | mao iri wal lon nth bel pic bre | 6 |
| F BAL | lvn pru ber kie den swe bot | 5 |
| A BUR | mar gas par pic bel ruh mun | 5 |
| A GAL | war ukr rum bud vie boh sil | 5 |
| A MUN | bur ruh kie ber sil boh tyr | 5 |
| F TYS | wes lyo tus rom nap ion tun | 5 |
| F NOR | ska nth nwg bar stp swe | 5 (if attacked from Fin) |
| A RUM | ser bud gal ukr sev bul | 5 (if attacked from BLA) |
| A TRI | tyr vie bud ser alb ven | 5 (if attacked from ADR) |
| A VEN | tyr tus rom pie apu tri | 5 (if attacked from ADR) |
(If we also included the possibility of disbanding,
then each unit
would have one more retreat option than listed above.)
Any other unit would have at most four possible retreats regardless of where it was attacked from. (Exactly four retreats in the case of F Aeg, F Bla, A Con, F Den, F Lyo, F Nwg, A Ser, A Sil, F Swe, A Tyr, A War, and F Wes. Also, U Kie, and F Spa/sc if attacked from certain neighbors.)
However, certain of these spaces are adjacent to each other. To wit:
Note that if both A Tri and A Ven are used, then one would only have 3 retreats, so let's just use A Tri. Now, eliminate the units Eng/Mun/Gal/TyS whose adjacencies to other units chosen for placement would have lowered the number of possible retreats for each of them to four. Replace them with some units with four possible retreats (Lyo, Con, and War) which are not adjacent to any other unit to be forced into retreat.
The resulting configuration has no adjacent units except for Norway-North Sea. These two units thus have, between them, (9-1)*(5-1)=32 possible retreats.
Replacing Norway with some other unit with 4 retreats would give 9*4 = 36 possible retreats. (Counting the possibility of disbanding, the comparison is 9*5 = 45 against 10*5 = 50.) So moving the Norway dislodgement to another location from which four retreats are possible would indeed improve the total. However, we see that all such locations (F Swe, A Tyr, A War, F Wes, U Kie, and F Spa/sc) are either occupied by an attacker and/or placement of the Norway unit there would reduce the number of available retreats for another dislodged unit (just as placing it in Norway does for North Sea).
We then observe that to achieve the largest end result, however, it is best to reduce the retreat possibilities from the unit which itself has the greatest number of possibilities. For example, consider a situation in which one unit can retreat to five uncontested spaces and a second unit can retreat to four uncontested spaces. Now add the fact that you must add a third dislodged unit, but by whose placement you must eliminate one of the retreat possibilities for one of the other two units. It becomes clear that this third unit should be placed such that the unit which can retreat to five spaces should be reduced to only four possibilities, rather than placing it such that the unit which can retreat to four spaces be reduced to only three. (In other words, if A is the number of uncontested retreats for the third unit, your choice is to go from 5x4=20 in the initial situation to either 4x4xA=16A or 5x3xA=15A.)
From this, we can conclude that placement of the eleventh dislodged unit in Norway (where it takes the ninth available retreat away from North Sea) offers more possibilities than would placing this dislodgement anywhere else on the board.
Note also that in the proposed solution the units attacking a given unit do not hinder or constrain the retreats of any other units.
Thus, the solution is optimal and leads to 8x8x7x5x5x5x5x4x4x4x4 = 71,680,000 possible retreat combinations, and 524,880,000 when you include disbands. Of course, the number of resulting positions is considerably smaller due to the shared retreat locations (that is, although the fleets in the Gulf of Lyon and the Mid-Atlantic are both eligible to retreat to the south coast of Spain, only one of them, at most, may do so).