Having been asked about the solo mechanisms I used in various forums and in the Comments section from time-to-time, I thought it might be helpful if I wrote a blogpost to describe how the mechanism works, particularly for those who have one of the Polemos rulesets and are thinking of using them for solitaire games.
I'll use Polemos Marechal d'Empire as an example, but all the other rulesets in the Polemos series that I have played (Polemos General de Division, which is the other Napoloeonics set, Polemos WSS, Polemos ECW and Polemos SPQR) use broadly similar systems.
In a face-to-face game, at the start of each move each player (CinC) generates tempo points by throwing 1D6 and adding one for every corps, division or brigade commander directly subordinate to the CinC. The C-in-C then decides (in secret) how many of these points to bid to gain the 'tempo': the right to go first in the turn and also, in some rules, reduced costs for the actions of the CinC's units. The highest bidder gets to go first and is given a couple of additional points for winning, too. The remaining points are used to allow the CinC's units to perform actions: moving, rallying, reordering formations, that kind of thing. Some of the Corps commanders also generate their own points, so their units can always do (some) things, whereas poorer commanders need direct supervision to make things happen.
What I do in a solitaire game is reverse this process, slightly. I assume that the initial 1D6 roll is a constant, to reflect a commander's quality. The best commanders are assumed to roll '6' every time, competent commanders '5', poor commanders '4'. This system could be refined further, but I have found this spread works fine. Then I randomize the tempo bid, using the highest possible dice that can't bid equal to or more than the number of points generated. So Napoleon with an army of 5 corps would have 11 points (6 for him, 5 for the subordinate commanders) would roll a D10 for his tempo bid. Mack with an army of 3 corps would have 7 points (4 for him, 3 for the subordinate commanders) would roll D6 for his tempo bid. I find that this allocates command effort in a nuanced way and also constrains the actions of me as the solo player enough to give an interesting game.
There are other ways of using the Polemos rules to give a good solitaire play: there are some interesting rules on the Yahoo group for playing one side actively against a more enemy-controlled side.
The DBx series of rules (I play DBA and Horse, Foot & Guns) is more straightforward (but less nuanced): each side in turn rolls a D6 for its activity points and does stuff with them. I think that the constraints generated for each side by this dice roll create a perfectly adequate solo game.
Philosophically, I try and create insoluble problems for the other side as my basic way of playing solitaire games, rather than trying to 'trick' one side or another. For example, in my recent Waterloo game, as the French player I was trying to create a series of no-win situations for the Allied player: one example would be Hougoumont, where the French player is trying to commit enough troops so the Allied player feels obliged to match, or even better overmatch, to secure the position. Whichever side does this best in the solitaire games tends - but only tends - to win.