The next topic is tips on mathematical modeling for use in solo (or any other gaming). Some of these have been mentioned or alluded to in the paragraphs above, and I'll deal with them in greater detail in a subsequent article if there is any interest in my doing so (and room in the magazine). General points, many of which are (or should be) obvious to the experienced gamer but may be worth mentioning for the beginner include:

1. Decide what you want your model to represent before you start developing it. The one you develop or choose should follow reality as much as possible. For example, a weather table should be weighted to the area and time of year you are modeling.

2. Different results are obtained by different random methods. The range of numbers are nearly the same whether you roll lD100 or 10D10, but the frequency of occurrence ofthe numbers is vastly different.

3. The level of depth that you go into should be enough to satisfy your sense of how detailed things should be, balanced against the desire for speed or simplicity (Rome vs. Carthage... Rome wins on 1-5, Carthage on a 6. It's a 4. On to the Barbarian invasions).

4. The impact of the range of variables you consider in making a model can be multiplicative rather than additive - or in other words, when a situation modeled that has 4 possible outcomes has two new variables added to it, the new range of results are going to be more on the order of 16 possible results than 6.

5. Many variables are too hard to capture mathematically and the effort to do so add little while greatly bogging down the process. A simplifying assumption may allow you to capture the feel of the process without modeling all of the details of the actual process. The ancient rules set DBA vs. WRG7 is a good example of trading detail for simplicity, but maintaining the feel for the battles.

6. Keep notes so when you use the model the next time 6 months from now, you will have some idea of how you arrived at the conclusion you did.

7. If it isn't fun, and it doesn't work, discard it. This isn't a math class, it's a game, and it's supposed to be enjoyable.

Source material

The next topic for this article is a list of some of the source material where you can go for additional information on solo gaming. Although some of these may be a little hard to find, most public libraries are in a cooperative venture where, if there is a copy in the (state, regional, district, etc.) system, they can get it for you for the price of postage from where they find it, to you. There are also a variety of out-of-print book services that may be able to help you if you are looking for a copy to keep. The sources that I'd recommend you look in to are:

1. LONE WARRIOR. It is a great source of ideas as well as points of contact for help with questions, additional detailed information, etc.

2. SOLO WARGAMING. D. Featherstone. ISBN 0-7232-6063X. Published in '73 by Frederick Warnes & Co. The original bible on the subject, and a great source of additional ideas to use.

3. MILITARY MODELING'S GUIDE TO SOLO WARGAMING. S. Asquith. ISBN 0-85242-934-7. Not as long, and not as detailed as the Featherstone book, but useful and an easier to find source.

4. COMPLETE WARGAMING. D. Featherstone. ISBN 0-7153-9262-X. A great book to have for all of the other items it has, even if non-solo. Several scenarios from a full range of time periods, and ideas usable in solo play. Generally available in libraries and can be ordered through most major bookstores.

5. SETTING UP A WARGAME CAMPAIGN. T. Bath. WRG book, available through most hobby shops, or through KEEP WARGAMES in the UK. Not too much on actual solo play, but the best compilation of campaign building ideas that I have seen. Since running a campaign in solo is often the gamer's desire, it is an invaluable reference. Also includes section on characterization.

6. PROGRAMMED GUIDE FOR WARGAMERS & SCENARIOS FOR WARGAMERS. Both by C. Grant, both WRG books. The first is by far the more useful of the two for solo play, with programmed deployment, orders, and responses for both sides. The second is just scenarios, but using the principles of the first book, you can build your own solo mechanisms for the second. Also, most of the scenarios are generic enough that they can be readily adapted for any time period you desire.

7. ADVANCED WARGAMES. D. Featherstone ISBN 0-09-087350-5. Published by Stanley Paul. Another treasure trove of ideas for all gamers, but includes a chapter on solo as well.

8. Experimental Game Group's "MATRIX Game" and "Campaign in a Day". Chris Engle's system is a very good source for ideas that work well on setting up the initial scenario. It can also be used to resolve the internal arguments that take place inside a leader's head, or at his staffmeeting for which tactics to use, or, in a solo campaign, used to resolve the events occurring "off-stage" that you either don't want to game out and/or are too hard to model. Although he no longer publishes the Matrix Game on the subscription basis, back copies may be still available.

9. CHIVALRY & SORCERY. Fantasy Games Unlimited. Despite the title, this is more a set of rules for Medieval Europe campaigning (including the economies of towns, castles, cultural notes, as well as miniatures rules for fighting mass battles, etc.) than anything else. The original, plus the follow-on source books which cover specific subgroups (one has Vikings, Picts, Gaels, and Steppe Nomads, another is on feudal Japan, another is for the mythical Saurian nations, etc.) have a great deal of information that can be used. These soft cover books can sometimes be found on the discount tables in gaming shops since the rank and file fantasy gamers have moved on to other things.

10. GUNSLINGER and FIREPOWER (two Avalon Hill boxed games). Each provides a model for solo play which governs how the opposition will function. Some ideas for hidden troops in FIREPOWER.

Logic Trees

The final item is the example of two logic trees to program the performance of your solo opposition. The flow of this tree is to enter the first question, and sequence through each line, passing on directions that do not apply until you either come to a direction that applies to your character (if yes, go to 5c) or you enter the next question. until you come to a direction that applies, carry out that action, then stop. An example is included below.

In a skirmish game, I'm playing the Riffs attacking a French Foreign Legion fort. Using a red-black card draw system (one card of the appropriate color per man) to see which side gets to choose to "move" a man next, I draw a card for FFL. I pick one of the legionnaires, and consider:

1. Am I wounded?

a. If no, go to 2.
b. If yes, avoid hand to hand combat as long as ammo supply holds out. Go to 4.

2. Is the enemy in hand to hand range?

a. If yes and you are unloaded, go to 3.
b. If yes and you are not unloaded, go to 3f.
c. If no and you are not unloaded, go to 3d.
d. If no and you are unloaded, go to 3c.

3. Am I in hand to hand contact from the previous turn?

a. If yes, fight hand to hand.
b. If no, and there is an immediate threat to me, or a fellow legionnaire who cannot respond fully (wounded, back turned, already engaged), within move distance, move to contact, then fight.
c. If no and unloaded, reload. If out of arnmo and there is no immediate hand to hand threat, scavenge if available, or if not, fight hand to hand until dead.
d. If no and there is a major unengaged threat (e.g. Riff with dynamite) within range, shoot him.
e. If no and there is an enemy leader within range, shoot him.
f. If no and there is a scaling ladder or grappling hook adjacent to my position, dislodge the ladder/hook.
g. If no, attack closest threatening Riff.
h. If no, move toward closest ladder/hook.
i. If no, move to get clear line of fire on other Riff.
j. If no, move to assist wounded legionnaire.

4. Is my weapon loaded?

a. If no, go to 3.
b. Shoot the closest personal threat.
c. Shoot the greatest threat to fort or fellow legionnaire (e.g. Riff with dynamite, about to open gate, or about to attack FFL member from rear.
d. Shoot the closest enemy leader.
e. Go to 1.

Information not in the table would be obvious from the layout of the game. So for whichever one of these legionnaires I decided to move:

NAME	WEAPON	WOUNDS?	LOADED?	ENEMY IN HTH RANGE
Capt. Arn	Pistol	yes	yes	yes
Sgt. Baker	Rifle	no	no	no
Pvt. Cook	Rifle	yes	no	no
Pvt. Dirk	Rifle	no	yes	no
Pvt. Ernst	Rifle	yes	yes	no

The flow for whichever man you chose would be as follows:

Arn: 1a (yes), 1 b (yes, go to 4), 4a(yes), 4b (shoot the closest personal threat).

Baker: 1a (no, go to 2), 2a (no), 2c (no), 2d (yes go to 3c), 3c (no, unloaded, but none to scavenge), 3d (can't), 3e (no), 3f (yes, dislodge hook, but be prepared to fight HTH as required by 3c when necessary).

Cook: 1a (yes), lb (yes, go to 4), 4a (no; go to 3), 3a (no), 3b (no), 3c (no & unloaded; reload, scavenge if necessary).

Dirk: 1a (no, go to 2), 2a (no), 2b (no), 2c (yes), go to 3d), 3d (none in sight), 3e (no), 3f (move toward scaling ladder).

Ernst: 1a (yes), 1 b (yes, go to 4), 4a((yes), 4b (shoot the closest personal threat).

More Branches

This is a fairly simplified version. If desired, you could either make probabilistic branches to the tree to obtain a different flow (e.g. step 3b: if no, and there is an immediate threat to me within move distance, move to contact, then fight (60%). If you rolled within the 60% you would move into a fight, if you failed, you would go to the next line number) or set up alternate, simplified trees (1/3 chance of any given soldier using one of the first three logic trees, the fourth to be used automatically if a preset condition exists, e.g. Iosing battle badly, less than 25% of FFL f orce left, all will charge closest foe and engage hand to hand until the last man is dead (Vive la France! ! Vive la Legion! ! ! !)).

No morale rules are included in my simple tree for the FFL since the assumption is that they know this is a fight to win, or die slowly and painfully for losing. No tree is required for my loyal band of Riffs since I'm playing them, but one could be generated if the game was to be run in "Clockmaker" mode. If my Riffs take too bad of a beating, we will retreat into the desert as Allah wills until the next battle. This decision can either be subjective on my part, (OK, how badly can I afford to get mauled in taking this fort) or by a preset number (the attack will break off if not successful in 12 turns, or at 30% casualties, or the death oftwo leaders), or by the use of a morale table.

Second Example: Countries

My second example is a simple tree for governing the conduct of countries in a six nation DBA style campaign game. The countries can have a range of political situations as follows:

1. Allied
2. Friendly, non-aligned
3. Friendly, Neutral
4. Hostile, Neutral
5. Hostile, non-aligned
6. At War

In the game, the political maneuvering is an important element, since if you end up at war with another country, your flanks will be unprotected. Similarly, an alliance with someone on the other side of your foe can either keep him from attacking, or cause him to split his forces for two different battles where you and your ally may each enjoy numerical superiority. Each nation is limited to one senior diplomat (uses a D8) and two junior diplomats (uses D6).

For each home nation, consider regarding the other five in tum. However, any changes that occur from the negotiations at the start of the turn (this turn), all of the results take effect at the same time (end of negotiation phase this turn), rather than having a domino effect on each other. That is, if Arder is allied with Borath, and is friendly neutral with Donnerstaag, at the start of the turn, the fact that Donnerstaag declares war on Borath will not move Arder to a hostile neutral situation until the end of this turn. A nation will try to improve relations 60% of the time if currently neutral, and 80% of the time if at war and lacking allied support, or if significantly disadvantaged (e.g. at war on both opposing borders - only able to carry on one of the two wars).

1. Find the current state of diplomatic relations.

2. Do I desire to improve the status of diplomatic relations? Roll % dice to test if needed.

a. If yes, go to 4.
b. Goto3.

3. Do I desire to go to war?

a. If yes, declare war.
b. If no, do nothing and diplomatic relations remain as before. Exit tree for this negotiation this turn.

4. Do I have a diplomat in place?

a. If yes, go to 5.
b. If not, send one. Exit tree for this negotiation this turn

5. Is there a counter effort from an opposing diplomat (e.g., both A and B are trying to win over D; A and B are hostile towards each other)?

a. If yes, go to 7.
b. If no, and my diplomat has been there for more than 1 turn, go to 6.
c. Increment the influence counter by 1. Exit tree for this negotiation this turn

6. Roll appropriate dice (D6 or D8) and add the current influence counter number.

a. If 2, you have disgraced your country, and are no longer welcome for negotiations. Diplomacy level worsens by 1 on a roll 2-5, by 2 on a roll of 6, and otherwise does not change. Exit tree for this negotiation this turn.
b. If 4 or less, you have disgraced yourself, and are no longer welcome for negotiations. A new diplomat can be sent in 2 turns. Exit tree for this negotiation this turn.
c. If 5-8, Diplomacy level improves by 1 on a roll of 2-5, by 2 on a roll of 6, and otherwise does not change. Exit tree for this negotiation this turn.
d. If greater than 8, countries become allies. Exit tree for this negotiation this turn.

7. Each diplomat rolls his dice, and add their current influence counter value. Compare the results.

a. If the difference is 3 or less, the diplomatic efforts this turn cancel each other, and neither side increments their influence counter. Exit tree for this negotiation this turn.
b. If the difference is 4 - 8 or less, the diplomatic efforts this turn cancel each other, but the winning side increments their influence counter. Exit tree for this negotiation this turn.
c. If the difference is 8 - 10, the diplomatic efforts of the winning dice roll this turn cancels the others effort. Go to 6 and roll for result.
d. If the difference is 10 or more, the loser is banned for D6 tums from diplomacy. Go to 6 and roll for result.

These same logic trees can be modified further, depending on your desires. Trees of the same sort can also be done on a unit basis rather than individual man basis for larger scale battles.

Conclusion

In conclusion, the idea is to have fun. I hope this article is of some help to other gamers. I would be interested in feedback on my system for characterization, suggestions on other solo methods to use, and other source material for solo gaming. I'm also interested in trying to help other solo gamers (both those starting and those who have been doing solo for some time), and discussions on other aspects of gaming. Good luck and enjoy!

Game Theory: Part 1 (in LW 116)

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