What order do you roll your battles in?

     There is a right way and a wrong way to determine the battle rolling order. I think the answer boils down to information management.

     Axis and allies is a game that uses dice. Before rolling the dice, you can know the probability distribution of the various outcomes, and you can know how you might react to each result, but you don't know which outcome will occur. The trick is to "have the courage to change the things you can, the serenity to accept the things you can't change, and the wisdom to know the difference." You cannot change how the dice will fall. That is something you must accept. You can control how you react to the dice.

     But in what specific ways do you control how you react to the dice? In non-amphibious battles you control when and where to retreat. In naval battles you may control when & where to retreat your submarines. You control which units to take as losses. And you can control the order in which you roll battles. When attacking a submarine that has an option to retreat (HAW) or faces a hard OOL decision (BAL), you control how much information the defender has when the battle is rolled. [You also control battle selection and the allocation of units to battles. You can't change this once the dice have started rolling, so I leave it out of this discussion.]

      Given these variables that you _can_ control, how do you exploit it to your advantage? I offer the following principles as guidelines:
#1 Before rolling your battles, figure out if there are any decisions in one battle that could depend on the outcome of another battle.
#2 Minimize the amount of information that your opponent has when he has to make a decision.
#3 Maximize the amount of information available to you when you have to make hard dice decisions.

     But what do these principles really mean, and how do you apply them?

     I divide my battles into three main categories: 1st, there are the battles in which I have NO decisions to make. Strategic bombing raids, and typical amphibious battles are an example of this. 2nd, there are the battles in which the defender has a very significant decision to make. This could be R1-BAL, J1-HAWSZ, or any battle where the defender has a bomber that he isn't sure whether to save. 3rd, there are the battles in which I have significant decisions to make. Examples include: any battle where I might consider using a nonstandard OOL to take the territory; battles where retreat is possible (and there is a nonzero chance that the battle could go poorly); air-only attacks, etc.

     I often roll the battles in the 2nd class first, forcing my opponent to make his decisions without knowing about any exceptional outcomes in other battles. Then all battles in the 1st class, in no particular order. No decisions are possible, so order doesn't matter for these. (OK, if I have 1 ftr and 1 bmb in an amphibious attack then I might roll it last: technically its in the 3rd class, even though it is amphibious.) Then I roll the remaining battles one at a time, rolling the battle with the fewest unresolved dependencies first, and repeating this evaluation after each battle is completed. However, most class 2 battles also involve significant (hard) decisions for the attacker. If I judge the value of the information from other battles to be worth more to me than to my opponent, then I'll roll a class 2 battle last.

Now for some examples...

It is R1. the bid was 2 INF MAN, 3 INF LIB, 1 ARM ALG, $1 for GER.
Russia attacks:
1. WSP: SUB vs SUB
2. UKR: 8I:3A vs 3I:2A:1F
3. BAL: 1T:2F vs 1S:1T

In what order should Russia roll these battles?

Well, first:
What could go right / what could go wrong?
What decisions do I expect I might have to make, or my opponent might make?
What are the dependencies?

Analysis:
     In WSP, the defender almost always withdraws its sub if it survives the first round, so this is almost a decisionless battle. I count it in the 1st or 2nd class. If he sticks around, the battle is 60/40. If Ger retreats in round 1, it is 33/22/44.

     In UKR, the defender has no hard decisions to make. The attack is 98% to succeed, and expects to win with between 1 and 5 inf, 3 arm. But if I include 10% results, I could take with at least 6 INF:3 ARM (15.9%) or I could take with no INF or worse (8.7%). Since Germany has 3-5i:4a in range to retaliate, there is a significant distinction within that range. There are some circumstances in which retreat might be useful, so this is a class 3 battle.

     In BAL, the defender has a significant choice to make: OOL of sub,trn gives him a 10% chance to kill a ftr. But OOL of trn,sub increases his odds of killing the TRN by more than 5%. If the defender has not provided an OOL or special instructions, then this is a class 2 battle. Since the attacker runs a significant (9.9%+) risk of losing a fighter against the sub,trn OOL, this battle could be either a "2nd class - first" or "2nd class - last".

So the two candidate roll orders at this point are:
BAL, WSP, UKR and WSP, UKR, BAL.

     How do we decide this? It comes down to strategic priorities, and what the potential results could leave me with. I normally don't like to risk Russian fighters in R1, but if the battle in UKR goes really well I might be willing to risk giving one up. My objectives in R1 against this empty-Europe bid (with this attack plan) are (evidently) to kill one ftr, and to sink enough German boats to either save some British shipping or put more German fighters at risk. What interactions are there between the battle in UKR and BAL? If Russia loses a ftr in BAL, then I don't want to take UKR with less than 4i:3a (but a lot of the risk / luck in the UKR battle often occurs in rounds 2 and/or 3). However, if UKR went sour, it is always possible to retreat from BAL after round 1 without losing a ftr. Therefore information from the UKR battle can be used more effectively in the BAL than information from the BAL battle can be used in UKR.

     Based on that interaction, the WSP/UKR/BAL order is starting to look superior. If we go back and look at the BAL battle now, to put things in perspective, the defenders choice is really not that hard: there is no decision to make if the attackers get 0 or 2 hits. If the defender hits first and kills the TRN, then most defenders would use SUB,TRN OOL from then on. The choice is only tricky if the attackers get 1 hit before the defender dice are seen. In that case, many defenders would lose the trn first, hoping to kill the attacker's TRN. But some would still lose the sub first hoping to get a TRN kill with the defensive dice, and then have the TRN to defend in subsequent rounds. And the degree to which this decision depends on the outcome of UKR is very slight at best.

     So WSP, UKR, then BAL is the best order in which to roll these three battles.

     In conclusion, attention to the order in which battles are rolled is one thing that can improve one's level of play.

     Good players create their own luck: by paying careful attention to battle rolling order you too can be in the position to exploit a lucky 2% outcome -- or recover from a 1% disaster.

Happy rolling,

-- w0nderd0g