So, based on a discussion on variance, I've proposed this as a gedanken experiment of wargaming. Don't worry if my numbers don't add up (I didn't bother to construct a system to give these averages and variances, we'll just assume they exist) ...

Assume that you have a risk/A&A style game with generic units. A power gets roughly 5 units a turn, and there's a battle between 11 units and 5 units. How often do you think the game should let the smaller side win, to make things interesting? Any how many losses should the bigger side take? Does it matter if its 10 vs 21 units? Lots of issues. Let's start with a poll.



This came up based on an idea of Larry Levy's in a comment on my blog ( http://gaming.powerblogs.com/posts/1218415424.shtml)

Historically (and assuming the smaller force is the defender) 2-1 odds do not give an attacker victory 90% of the time.

The answer depends very heavily on the era you are simulating.

Also, bear in mind that the axiom is an attacker needs 3-1 odds to dislodge a defender from a position, so I would actually put the chance of success at less than 50%.

Perhaps I should have made it 3-1 (or 4-1), although I was basing my numbers off of a risk-like system rather than the real world (I do state that it is a risk/A&A type game, rather than the real world). I didn't want to say "If the attacker has enough troops to historical justify winning routinely..." but preferred real numbers.

But you asked how often we thought the game should let the smaller force win.

2:1 attacks in a 'modern game' should result, most of the time, in the attacker getting harmed pretty bad, even if they dislodge the defender.

I though this was what dice were for; variance.

More information is needed from you to get a meaningful answer to your poll. What constitutes winning? Is inflicting more losses but not taking/keeping the territory winning? Does winning mean eliminating the other side? Does winning mean taking/keeping the territory but not eliminating the opposition? Is combat resolved in one game turn or can it continue for several turns?

If I infer that A&A/Risk style means battles are fought until one side or the other is eliminated and there is no such thing co-occupany or contested areas at the end of a turn - then I'd say 11:5 odds should result in victory more than 90% of the time. If it doesn't your game will probably have serious balance issues. It would require a huge force to attack with any certainty of winning a battle. huge stacks will accumilate as neither side is willing to attack unless they have overwhelming numbers. Basically trench warfare. A&A 2nd edition suffered from this problem a bit because infantry attack 1 defend 2 and were the best unit in terms of value. That is why they added artillery in Revised edition.

The problem in general with games that force you to roll dice until one side is eliminated is that they heavily favor the attacker if he has numerical superiority. That model does not translate to any real life situation. With 2:1 odds the attacker would usually obliterate the defender, but in real life, that is a fairly risky attack.

Here is my humble opinion for what it's worth...

There are many factors that would change the balance of power. They make for a far richer experience than looking at odds alone.

Here are the basic ones off the top of my head:

Readiness
Morale
Equipment
Location
Training
Experience
Environment
Communication

If both sides were equal in every respect, then I would say that a superior number of forces will always win out over the long run. If you want the smaller side to win, I feel you would have to allow these other factors as modifiers.

As far as I see it, dice should only contribute to the chaotic nature of war because we are dealing with fallible human beings in a complex environment after all.

EDIT: "a superior number of forces"

In re that '3-1 odds axiom' referred to above, that was some 1960s think tank analysis of the odds required to be very certain of being able to dislodge, to use the same term as above, a defender from a defensible position. It was somewhat misused over time, in particular by Avalon Hill on their 'standard' CRT which usually gave a defender some chance of eliminating the attacker against 2-1 odds (though it probably did not matter that much, since designers simply adjusted the attack and defense factors of their units to provide the historical parallel outcomes their game needed).

There were many possible outcomes at less than 3-1 odds (and of course, defenders have held out at greater than 3-1 odds, just very rarely according to the computations which produced this rule of thumb), only rarely was a defender victory which routed the attacker the outcome. Lesser outcomes would include the defender badly mauled but the attacker mauled enough to be unable to finish pushing the defenders back, the attacker calling off the attack before deciding the issue, the attacker beat back but the defender unable to risk leaving the defensive positions, or, of course, a victory for the attacker with the position taken (with, again, many possible outcomes for the defender in this instance).

In any event, a wargame is not 'interesting' because of how often, or not, a smaller force can defeat a larger. A wargame is 'interesting' because of how well it gives players the feel of what the contemporary commanders faced, how it allows the players to make decisions which follow or diverge from the historical decisions, how many different options for strategies to try and win (or not lose) the battle players have, and so on. Then smooth mechanics and clear rules should go a long way to getting people interested enough to try the game, particulary if the topic is of interest to them.