First, though, I must say that any chit pull can be rendered less valuable if one player rolls all 1s and the other player rolls all sixes. But, the tables are laid out in such a way that with approximately equal dice-rolling, certain chits win against some, and lose against others. Outflank is a special case, on either offense or defense. Probe is, to a lesser degree, also a special case. Withdraw is a special case on defense. But, first we'll look at the "basic" possibilities, and expand from there.
So, that leaves assault, escalated assault, and echelon for attack possibilities. On defense, you can pick counter-attack, escalated counter-attack, cordon, or defend. I'm going to combine assault with escalated assault, and counter-attack with escalated counter-attack. Generally, the exact same chit pulls against either of those still wins. The difference is that BOTH sides have higher tables (and by the same amount: +1 on the casualty number). However, the two escalated versions do have one specific chit that ONE side receives this bonus, but not the other. I will call out this as the "ESC" (the escalated version of that chit.
So, in the most basic discussion of this, there are two attack possibilities (assault and echelon), and there are three defensive choices (counter attack, cordon, and defend).
From the attacker's perspective:
Assault loses to defend, but defeats cordon. It is neutral against counter-attack.
Echelon defeats defend, but loses to cordon (the opposite of the assault chits). It clobbers counter-attack (ESC is even worse, as the defender's table does not shift).
From the defender's perspective:
counter-attack is neutral against assault/esc., and and gets beat by echelon (slaughtered if ESC is chosen). Looks like a no-win situation, right? Well, it clobbers probe, but that's one of the non-basic choices, so we'll get to that later.
Cordon gets beaten by assault and beats echelon.
Defend wins against assault, and loses to echelon.
Other considerations:
Cordon causes the defender to gain advantage whenever the attacker is crossing water. The changes are somewhat minor, but not negligible. This is signified by the second group of attack possibilities underneath the other.
Also, leadership is not going to be fully covered in this treatise, but it really matters. So, I'll bring it up in passing as we get to the items.
There are some leader/commander factors to consider:
First, in an assault vs. defend battle, nobody uses commander tactical ratings. This can be really important in some battles. Picture Napoleon attacking Turkey, each with good-sized armies. If France chooses assault and Turkey chooses defend, Nappy's combat advantage is nullified. But, cavalry superiority is still calculated, and it is quite possible for Turkey to out-cav France. Yuck!
The other thing is that some nations or commanders gain a bonus to certain battles.
For any of the four assault vs. counter attack battles (including ESC versions of each), Turkey adds one to whatever its final morale became. All of a sudden, they may look tough to an opponent!
An Austrian commander on either side of an echelon vs cordon battle adds +1 to the die rolls (unless he already has a +1).
A Russian leader with a defending force that chooses "defend" causes his side's morale to be +1.0, provided that the attacker chose assault (or probe; see below).
Confusing? Not really. Just remember assault beats defend and echelon beats cordon. Assault vs. counter attack is neutral (both sides get bashed equally). And, counter attack loses to echelon.
Now, when I say that one chit beats another, I don't mean absolutely. I mean on average, with equal forces (including leadership), it will do better.
In order to understand HOW much better, we must evaluate the combat resolution table. This is a 5 by 5 matrix of combat results. A combat result is a morale loss number and a percentage loss number. The morale number is subtracted from the current amount of "final morale" your force has remaining. If you drop to zero or less, your side breaks. The percent loss is the percent of YOUR force that you inflict on the enemy.
This table is not random, though. As you shift to the right (bigger numbers), your percentages go up. Similarly, as you go down the table (morale number getting higher), the amount of morale damage goes up. In each case, the other number (percent vs. morale loss) also goes up as you shift right or down, but not by as much. Consider the 3-1 table vs. the 1-3 table. The 3-1 table shows 15% troop damage dealt, and 2.6 morale loss. The 1-5 table shows only a 10% troop damage loss, but 3.6 morale damage.
There are some idiosynchrasies in this, but it's a good nutshell description, I hope. Bigger is better, and higher rolls are better.
End case chit pulls:
Now, what about those pesky "end-case" chit pulls? We have outflank (attacking or defending), probe (attacking only), and withdraw (defending only). Outflank is tricky, so I'll do that last.
Withdraw:
Withdraw is an easy one to consider. Basically, you might pull this when you are badly outnumbered, or when the strategic situation says you should. You roll a die, and your forces' strategic ratings (use the commander's rating if one is present, corps ratings for each corps if not) are consulted. If you roll lower, you escape. If not, you fight it out (getting trashed in the process, usually).
Two exceptions exist, however, First, if the attacker chose probe, you are gone. No need to roll. Second, if the attacker chose outflank, you get a second chance to escape: If your oppenent's outflanking force fails to arrive, you leave, suffering only the damage from the first round of combat. There are terrain modifiers that apply to outflanks (see the tables). Finally, there's a possible bonus: If your opponent chose echelon (or outflank), then you get a +1 to your strategic rating(s) when trying to withdraw.
Probe:
The idea behind probe seems to be that you check out the defenses before committing your force. So, generally, the first round's fighting is fought on a lesser table than the following rounds. The exception to this is against counter-attack, where the defender starts blasting you even on the first round (although, you do NOT get to return the favor). This is why some players will choose counter attack frequently, even though it reliably defeats no other chit pull: To keep probe from being killing him.
Probe also has a disadvantage against withdraw: If they pick it, they successfully get away.
Finally, even on the "good" probe tables, it's not that great. Probe vs. defend is considered neutral by most players, and against cordon its advantage almost disappears if crossing water.
So, why would anybody pick probe? Well, we've left out one major chit pull up to this point: Outflank. A probing force presumably figures out where the outflankers are coming from, and thus gets monstrously high tables against outflank (although, not on the first round). Furthermore, probe is the only chit pull that beats outflank EVEN IF the defender succeeds on his outflank roll.
So, probe isn't automatically ruled out of most people's selection possibilities. But, there's even one more point to consider: What is the key thing that separates France and Great Britain in land combats? Higher morale! So, both of those powers can afford to pick probe, because they know they will still be present (barring very bad die rolls from the opponent). In my experience, GB should pick probe quite a bit of the time, just to make sure she sticks it out to the end. Most battles end before the end of the combat day, because the morale loss tables tend to end them. But, GB or France can stick it out, even though their opponent rolls well.
What this means is that high-morale forces can choose probe without fearing the first round's normally dismal results. I've seen GB defeat even France and Napoleon, WITHOUT a leader of their own. France took outflank and GB probe, and GB rolled hot in the final two rounds. Imagine how it would have gone with Wellington present? Probe is not so easily dismissed by France and GB.
But, for other powers, it's somewhat easier to decide against probe. They're not always sure they will still be present when their best tables arrive, so the probe choice is a lesser priority.
Finally, the "Napoleon" chit pull: Outflank:
On either offense or defense, outflank can be selected. To be useful, the force should have at least two corps present.
Outflank is special in that it generally wins only if the outflanking force arrives. On most tables, it gets creamed if the strategic roll gets missed (worse if missed twice). This is why I call it the "Napoleon chit pull": Napoleon is almost guaranteed to make his roll.
There are a couple of exceptions to the "always wins if the roll is made" rule. First, probe beats a defensive outflank badly even if he makes the roll. It's a disaster if he misses it, especially twice. Second, an offensive outflank is defeated by cordon, again, rather badly. Worse, the attacker doesn't even get to roll, so all three rounds are on disadvantageous tables.
But, all other choices are either a win for the outflanker, or a tie (outflank vs. outflank), provided the outflanking force arrives.
There are a number of subtleties to this that I didn't cover here (especially commander ratings). But, the basic game of "glorified rock-scissors-paper" is outlined here, and understanding these principles will improve your performance.
Good luck on those chit pulls! And, I wish you BETTER luck on your die rolls!!! (except against me, of course
).