In previous articles, Bunnies wrote about how to get the most out of your IPC, and some of the dangers in thinking only of the immediate IPC payout of an action. In this article, Bunnies writes about common mistakes players make when thinking about probability as it applies to Axis and Allies Spring 1942.

## PROBABILITY

### DICE SIMULATORS

Dice simulator programs for Axis and Allies are valuable aids, but are no substitute for an understanding of probability. A dice simulator gives the single most likely result, but it is actually very unlikely that the single most likely result will occur. Understanding why this is is an essential part of understanding how to play well.

Consider a cat climbing a tree. At each branching of the tree, the cat takes a random branch so long as it can continue upwards. Suppose you want to know where the cat will end up. A “cat climbing simulator” that works on the same principle as a dice simulator would say that on average the cat climbs to every point on the tree. But actually, the moment the cat takes the first branching, the simulator results will be almost completely useless. At that moment, the cat has eliminated every possibility on alternative branches, but the simulator results do not account for that. If you want to know roughly where the cat will end up, you will need to use the simulator again every time the cat takes a branching, eliminating all branches the cat didn’t take from the simulator each time.

### RE-EVALUATING COMBAT EACH ROUND

Combats should be re-evaluated after every round of fire. 6 tanks attacking 6 infantry have a 80% chance of success to begin with. But after the first round of fire, if at least one casualty was inflicted by either side, the chance of success changes. The combat will no longer be 6 tanks attacking 6 infantry. If the attacker got one less hit than expected, and the defender one more than expected, the attacker’s odds drop to 37%. Even if the attacker and defender both got the expected number of hits, the chance of success still changes. In this case, it increases to 94%.

### MULTIPLE BATTLES

If a player is involved in multiple battles, there’s good odds at least one will fail. A player entering three battles, each with a 80% chance of success, may think there’s an 80% chance that all the battles will succeed. But really, the odds of all the battles succeeding is 80%^3, or about 51%. That means there’s a 49% chance that at least one or more will fail.

### NECESSARY VERSUS UNNECESSARY RISK

A player has a 80% chance to capture an opponent’s capital. Is the attack a necessary risk? Not if the player is in a strong position. If that 80% chance can be increased to 85% next turn, then 90% the turn after that, a premature attack is unnecessary. On the other hand, if the player is in a weak position and losing ground, the attack may be a necessary risk, even if it’s a 60% chance, or even a 10% chance.

A player has a 70% chance of successfully attacking a territory worth 2 IPCs. Is the attack a necessary risk? Not if the player drains his or her reserves allowing an opponent to push into a stronger position. On the other hand, if a player’s reserves are not drained too much, the risk is absolutely necessary; a player must take risks in small battles to maintain a competitive income.

In both cases, a player can determine what risk is justified by looking at the board. In the first case, a player need only look at the building forces around one’s own and the opponent’s capital. In the second case, a player will have to correctly assess the balance of power between friendly and opposing forces for control of any number of territories.

Any particular attack or defense is determined as necessary or unnecessary risk depending on the board position rather than the probability of success or failure of that individual attack or defense.

But assessing board position requires a player assess the probabilities of the possible different results of actions of the player and the opponent.

## IN OUR NEXT EXCITING EPISODE

Bunnies defines then describes tactics, as applicable to Axis and Allies Spring 1942.