Risk Management And You: The Multi-Peak Model

[aardvarkpepper]

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.

[Dead Rabbits]

I can sort of understand the reasoning in a general sense that Allies would really like to reduce Germanys air power because of the cascade effects that has on Germanys ability to trade territory efficiently with fewer aircraft and that losing any aircraft makes it less likely that Germany will attempt an airstrike on Naval escorts after the first airstrip because they have fewer to trade with the 2nd time they might have the opportunity to do so.

The more Germany does this vs Allied fleets the more it helps Russia in terms of tempo. There is the 1st round where Germany did not have any air support for their trades of territory because they used it vs Navy, and Germany does want to use all its air when it does attack navy to try to reduce the hit backs.

Then the 2nd Round Germany has fewer aircraft to help them trade territory efficiently because of the aircraft they lost.

In a KGF scenario it is difficult for them to buy more air because they are already being outnumbered on the ground. In a defensive position Germany typically wants to maximize its ground buys every round to keep its numbers up because they are losing many to trades.

However this situation was not a general one. Germany had subs available and those subs are somewhat useless if not used for attacks when the opportunity presents itself. It is signaling that it WILL do an airstrike because of the subs. At least one attempt until the subs are gone. If Germany had aircraft only then they might not attempt the naval attack at all.

So presenting fair odds when you already know that Germany is likely to do it seems a bit brazen to me. That seems like a time to add escorts and see if Germany will take worse odds on a naval attack than 50%

[Dead Rabbits]

The reason I think this is a good time to add one destroyer is because Germany will know that their window of opportunity to attack with the sub fodder will be closing quickly. So they may choose to attack at even less favorable odds instead of allowing Allies with that extra destroyer to split off and take out those subs the next turn, or if destroyer already in range why not do that now and have the replacement destroyer take its place?

Germanys options with those subs are very limited if US fleet is in sea zone 8.

Either way you are likely reducing Germanys odds to successfully airstrike the fleet.

I am guessing the counterpoint to this is that the Allied player WANTs Germany to attack their fleet to kill aircraft and if they build an additional escorts maybe Germany won’t do that.

To me this would be fine if they don’t. Its still likely wasted IPC for the sub buy that does not end up doing anything then.

The extra escort puts Allies ahead in the number count (which is close if they have 50% odds) should Germany decide to answer with additional air buy or the extra destroyer after dealing with the German subs can split off to help support another fleet in another sea zone.

Based on the Allied players comment they were already conceding some tempo by not bringing transports forward.

Then final comments of concern about not being able to land in Finland after losing their fleet.

Ships are expensive and take time to rebuild securely and so landings are now further being delayed at a pivotal point of the game. Pressure is off Germany in the meantime. They have a window now to focus ground forces east again.

Allied player says they had follow up, however based on what I see they only have follow up to sea zone 13 not sea zone 3 which their transports are in position to move to but now cannot do so safely.

To me this is following a decision tree too rigidly. The 50% attack offer rather than adjusting that pattern to the board state.