From Discord:
This is one of those game where everything seems to go wrong.
Not gonna go into details, but opponent was giving away a lot of territory and Germany was buying lots of air and 2 sub. I calculated my fleet and decided to go for a 50% survive. 32% the attacker would survive with 2 bombers. That would be ok, since I had some back up, and it would take pressure from Russia and the future fleet. Of course he took the fight and got top 7%. Now he still has 7 air and I’m way behind.
Japan is going full in India, which I can maybe hold on for another round.
What would you do?
The first thing is to understand the risk model on a fundamental level. A lot of players cite “50% win” or “32% 2 bombers” and leave it at that.
But actually, no. Very much no.
Outcomes in Axis and Allies are a multi-peak distribution. Suppose you have 50 tanks fighting 50 tanks. What do you think will be the result?
Some players will respond one or two tanks on each side. Others will imagine vagaries of dice and respond five or six, or even more.
But what actually happens is early rounds of dice results tend to be reinforcing. If attacker gets lucky and defender unlucky on just the first round, maybe next round the trend will reverse but even more so, cancelling out the earlier luck? No. To compensate for first round luck, much more luck would be needed the second round. That sort of luck can happen! But actually second round expectations should be mapped onto their own probability curve, that’s the expectation.
In other words, if you’re lucky initial rounds, that’s probably going to mean the rest of the combat will go that much more your way.
For the example of 50 tanks vs 50 tanks, either attacker or defender will usually end up with 10 tanks.
https://axis-and-allies-calculator.com/graph.php?cmd=barchart&rules=1942&battleType=land&roundCount=all&attTank=50&defTank=50
. . . which is the second pitfall.
A lot of players might look at a curve and say oh, they can bet on the “average”. But it’s not an average (a single number), It’s a distribution.
Suppose I were to say that 50 tanks fight 50 tanks and either attacker or defender has about 1-2 tanks surviving. No huge surprise there? Things evened out?
But looking at the numbers, it’s about as likely that 16-18 tanks survive for only attacker or only defender. Like, whaaat? (But really, that’s about how it works out.)
So if you thought, hey, 50%, maybe attacker loses, maybe both sides pretty much get wiped out -
Well, after the opening round of fire, if the attacker got lucky (which probably happened here), the odds of mutual wipe went down, and the odds attacker survived with a chunk of units went up. (And that’s exactly what happened).
The third pitfall is thinking an opponent won’t attack if they only have 50%.
Here, the attacker had subs as fodder. If things don’t go great, well, it’s just cheap subs.
On the other hand, if things go well, probably blow up a lot of defenseless costly transports.
So in that situation, should attacker attack or not? Well, they could take that chance.