The Raw Luck theorum. (How to make luck, like you make Units)

• In reference to current discussions about Stupa-stacks.  I thought it pertinent to have a discussion for everyone’s sake, about how to -make luck- for yourself, when you don’t have the pieces to win a major conflict anyways.

http://www.axisandallies.org/forums/index.php?topic=27742.0

Reality as I see it in Axis and allies, is that in each battle, there are odds (Obviously),  but the smaller the battle gets, the more likely said odds, are to have devestating effect for either side.  IE The greater the chance either parties have to suffer disaster.

We will call this disaster-factor Z.  Disaster factor being those moments, when AA guns shoot down 10 of your 11 planes, or that transport in the good old days popped 3 of your bombers in a row etc.  Even an infantry holding off against 1 inf 1 art 1 arm would do.

It is my theorum, that in situations where you are numerically outnumbered by your enemy, that you can break the numbers advantage slightly, by equally spreading out Z the disaster factor.

Simplified Hypothesis: When numerically outnumbered, a series of small battles, will yield better results, and a better-chance for luck, than a single large battle.

Example 1**********************************************************************************

Take a simple though ridiculous example.

100 fighters, fly in and attack 80 cruisers.

100 fighters, averages 50 hits,  80 cruisers averages 40 hits…  and through each continuing round, it can be expected that the ratio of fighters increases to the detriment of the cruisers.  After 2 rounds of combat, at perfect average, 45 fighters will fly home

This risk of losing this battle is MUCH llower for the fighters, as say, even if the fighters roll sub par and score only 40 hits, whilst the cruisers still score the 40 hit average,  the fighters will still retain their advantage going into the next round, compounding thier deadliness…

The fighters use their numerical advantage, to reduce their Z factor. And the cruisers, when calculations are done, have virtually NO CHANCE to survive.

But lets spread it out and see what happens…

––Example 2--------------------------------------------------------------------------------------------------------------------------

100 fighters, spread out over 80 seazones, to destroy 80 cruisers.

That`s 20 (A)battles of 2 fighters vs 1 cruiser  (These cruisers suddenly have a 5-6% chance of surviving)

and 60 (B)battles of 1 fgt vs 1 cruiser  (These cruisers suddenly have a 33% chance of surviving)

Results after the first round of battles are as follows.

(A) battles, results in an average of  28 fighters surviving and 1 cruiser surviving
(1 cruiser win 5%, 1 draw 5%, 8 single fighter wins, 10 double fighter wins)

(B) battles result in an average of 20 fighters vs 20 cruisers suriving and 20 draws.

Final Result.
48 fighters remaining, vs 21 cruisers remaining.
With subsequent battles remaining yet to be resolved.

====Concluding example===========================================================

First NOTE, that there are units Surviving the first TURN round, that now are ready for a subsequent TURN round, tying up more enemy resources.

Lets finish the last round of battles.

6 battles of 3 fgt vs 1 cruiser  = 15 fighters fly home (who suffered higher risk) 0 cruisers left

15 battles of 2 fgt vs 1 cruiser = 21 fighters fly home. 1 cruiser lives.
8 double fighter wins 1 draw, 1 cruiser lives, 5 single fighter wins
(this one was uglier to calculate simply, so in being broad I slide in a cruiser-lives and a draw, in exchange for an extra 2 fgt win.)

Hypothesis Proven:  Here you now have seen, what previously took a single turn to accomplish, yielding a 45 fighter result,  turn into what takes 3 complete turns to accomplish, suffering a higher risk yield, result in most likely a 35.5 fighter result.

Thus I conclude.

When Numerically outnumbered on a large scale (more than 5 to 10%) NOT ONLY do your units perform better as seperate forces,  but the Z -or- Risk factor for your opponent, is no longer insulated against, and your enemy suffers from it.

It also requires more units of your enemy to be tied up in accomplishing smaller goals, over a greater time, all to achieve a result that’s more favourable to you.  I could write a book on the ecomonic impact of that, but suffice to say, the fighters aren’t able to yield as high an IPC kill result per turn, when you force them to fight over several TURNS, as oppossed to several combat rounds.

Obviously there are many exceptions to this, depending on terrain, time constraints, and other conditions, (Like if you’re going to lose the game if you lose a said territory), but…

It’s an important concept to understand, that you can make your own luck/variance in Axis and Allies, by controlling, when, where, how, and how long, you fight.

• I haven’t had time to study the above in detail (busy day today), but I was wondering if it relates to Lanchester’s Laws?  (http://en.wikipedia.org/wiki/Lanchester’s_laws)

• ugh wtf… this was wayy too wordy to prove a simple point. yes 100 attackers has a harder time attacking 80 units in ONE turn if it is spread out… however if the 100 attackers attacked each cruiser 1 at a time over 80 turns… you would lose 40 fighters on avg.

First, simply put there are areas that you must defend. Â Like Moscow, spreading out too much guarentees that Moscow falls and Moscow falling is a disaster.

Second, your too simplistic example of 80 cruisers and 80 areas. Its far too simplistic, you do not have 80 areas to spread out to. You have far too few areas to defend in and many areas simply do not matter enough. So your enemy may well ignore some units simply because the existance these units in these areas does not threaten his plans.

Third if your forces are split you risk defeat in detail. That is an overwhelming amount of enemy forces crushing a small portion of your forces thus greatly reducing your enemies casualties. For instance if your 80 cruisers were split into 8 areas (a much more realistic figure). Then you would almost certainly see 50 fighters in each of 2 of those areas. at 50 to 10 your cruisers die in 1 round and the fighters only suffer 1 round of strike back. The result is the next turn you have only 60 cruisers to their 90 fighters and your powers of defense have been made weaker.

The reason you do not see counter attacks coming out of Moscow for instance. If you are surounded by a mosnter stack and 5 infantry, then attacking out with say 2 infantry and a fighter in each area will weaken your defense by 10 infantry and weaken the attack by only 5 infantry. When there is a monster stack next to Moscow you have to be aware that each turn may bring on a decisive battle. Now if you can hold Moscow then launching those counter attacks makes sense, but if the issue is in doubt trading 10 of your infantry for 5 of his may turn the battle in his favor.

It is an accepted military maxim: He who defends everything, defends nothing.

CWO Marc, I dont think this is related to the fuzzy wuzzy falacy at all.

First, simply put there are areas that you must defend. Like Moscow, spreading out too much guarentees that Moscow falls and Moscow falling is a disaster.

I believe you missed Gargantua’s point entirely.

The argument is that spreading out is the best option AFTER you’ve reach the point where you have a ZERO percent chance of surviving an imminent attack.

In doomed situations, defenders can sometimes inflict more casualties on the attacker by spreading out than they can by remaining massed together.

He’s using exaggerated numbers to illustrate the principle, that does not make the principle flawed.

• Third if your forces are split you risk defeat in detail. That is an overwhelming amount of enemy forces crushing a small portion of your forces thus greatly reducing your enemies casualties. For instance if your 80 cruisers were split into 8 areas (a much more realistic figure). Then you would almost certainly see 50 fighters in each of 2 of those areas. at 50 to 10 your cruisers die in 1 round and the fighters only suffer 1 round of strike back. The result is the next turn you have only 60 cruisers to their 90 fighters and your powers of defense have been made weaker.

If those 60 cruisers can then move out of range of the 90 fighters, attack somewhere with favorable odds, or regroup with friendly units, then defeat in detail could be better than guaranteed total annihilation.

• Edfactor,

When Numerically outnumbered on a large scale (more than 5 to 10%)

Wheatbeer’s got it, just as I posted it.

When you’ve already realized that a battle is lost,  then fighting it out stack to stack is one of the WORST things you can do.  That’s the point I’m proving.  With the caveat:

Obviously there are many exceptions to this, depending on terrain, time constraints, and other conditions, (Like if you’re going to lose the game if you lose a said territory), but…

You’ll also note I mentioned the 100 fgt vs 80 cruiser is a ridiculous example.  But it serves to highlight the -edge- I’m trying to point out.

Third if your forces are split you risk defeat in detail. That is an overwhelming amount of enemy forces crushing a small portion of your forces thus greatly reducing your enemies casualties. For instance if your 80 cruisers were split into 8 areas (a much more realistic figure). Then you would almost certainly see 50 fighters in each of 2 of those areas. at 50 to 10 your cruisers die in 1 round and the fighters only suffer 1 round of strike back. The result is the next turn you have only 60 cruisers to their 90 fighters and your powers of defense have been made weaker.

You will note FROM YOUR OWN EXAMPLE,  that several turns will be required to defeat the said force, hence enlogating the engagement, and improving your chances.

Thank you for proving my theorum.

• Here’s some small scale math to consider using http://www.dskelly.com/misc/aa/aasim.html for averages

Scenario:
10 enemy fighter attacking
5 cruiser defending

Possibility A: 1 battle, holding your ground when doomed
Cruisers mass in one SZ, fighters win with average enemy IPC loss of 28.2 IPC (essentially 0% chance of any cruisers surviving)
average enemy NET gain 31.8 IPC

Possibility B: 5 battles
Cruisers spread out over five SZ [enemy responds by attacking all five SZ with 2 fighters each]
fighters win with average enemy IPC loss of 33 IPC
average enemy NET gain 27 IPC
(that does not factor in the 5% chance per battle that a cruiser lives, because I am not good enough at math to do so)

Possibility C: 3 battles
Cruisers spread out over five SZ [enemy selects three SZ to attack with groups of 3 and 4 fighters each]
fighters win with average enemy IPC loss of 17 IPC
average enemy NET gain 19 IPC
2 cruisers guaranteed to be alive

• Good work WB.

And what’s not mentioned here, is the technical fact, that -said- cruisers now have the oppurtunity to attack/bombard on their turns as well. Â Increasing their life span, and thus increasing their IPC economic output, done by killing uints.

This concept is what needs to be conveyed to people who think that running to form a defensive super-stack, that’s never going to amount to the capabilities of the invaders stack, in a lesser-advantaged theory, Â then micro counter-attacks for border-trade states, all along the route of the conflict (Where and when it makes sense to do so).

Perhaps I’ll review a few games… as the next theory I have, works in conjunction with this…

The raw amount of battles Germany has to fight on Russian territory, is directly related to Germany’s chance to win over Moscow

In other words, the more you make the Germans fight, and the more often, the less likely they are to capture the capital.

Obviously there will be some uncontrollable factors, and this is with common sense maintained (IE not putting units uselessly in harms way)…

• The other thing to consider is the Germans not playing along.  They could just drive to Leningrad, then down to Bry, park and then start building up sitting in Bry and clearing up the areas behind them at their leisure.

The piece meal battle only will work if the Germans engage.  If they drive straight to Moscow, I think the USSR player would have some problems.

• Now that im thinking about it, this is the outcome i have experienced many times over. exellent observation and strategy if out numbered.

• Fair enough Karl,

But I never see that happen, the germans always try to take as many reasonable places as possible. Â And I’d WAY rather let them have the north, than the south, if they wanted to play with a strict focus (which in my opinion is to German detriment)

And if the Germans aren’t going to defend romania with anything, then the possibility of limited offensive operations from southern urkaine is possible.

• Fair enough Karl,

But I never see that happen, the germans always try to take as many reasonable places as possible. � And I’d WAY rather let them have the north, than the south, if they wanted to play with a strict focus (which in my opinion is to German detriment)

And if the Germans aren’t going to defend romania with anything, then the possibility of limited offensive operations from southern urkaine is possible.

you have seen it happen as you have commented on my tournament game. did not take ussr territories unless it was in a direct path to moscow.

• ^

I do that for the first 5 rounds. Stack up on bryansk then worry about taking stuff, even more so if I am doing the japan bomb russia thing.

• Gargantua,

Excellent article.  I don’t know why Jensen doesn’t have you writing some articles under the “Strategy” section of the website.  (Even the house rules section which is very outdated)

I agree with the smaller battles theory but have a couple questions/thoughts:

1. In these smaller battles you are advocating for there isn’t anything mentioned regarding the use of attacking pieces along with the russian infantry.  A small stack of only russian infantry inflicts limited damage (rolling at 1) and may not yield as effective a “whittling process” on the German infantry stacks as hoped for.  Bringing in Russian fighters helps and they can then return to safety, but I am thinking about the use of armor in these battles and either losing them or exposing them to counter-attack.  Killing German infantry at a loss of armor (maybe artillery?) seems too high a risk?  The Russian player would have to be quite crafty at both engaging the Germans approaching AND not lose more expensive pieces.

2. I have felt that the Russians should be moving with a force to take Norway which swings the economic battle away from Germany since it also negates a NO.  Allocating units for this certainly thins out Russian ability, or at least limits it, to engage in too many smaller conflicts on the approach to Moscow.  In games I am playing, the Russian capture of Norway/Finland (etc.) strips Germany of the ability to outbuild Russia on the Russian battlefront - or at least makes those “superstacks” more even.  Although, you may view the attacking of Norway as the very thing you are talking about?

• attacking force to norway… there is about what 7 inf up there? so you would need to bring about 11 inf at the least (Germany has luffewaffe)… assuming he has no transports… you may get some cash flow.

meh I do not worry of these things, usually germany has naval like 3 transports. Those units have to move up each round to make it in time for the G6 attack. Hard to stall it without getting units trapped up there.

• hmm… I’d say the north is actually more important that the south for German invasion.  I usually put a miIC in Rom, so I can defend and attack from there.  The advantage to the invasion into north Rus is that you get Len for the 5+ NO, protect the Nor/Den NO, and block the Rus NO in Arch without worrying about naval dominance.

The south has more cash I know, but if you can park in Bry, then you cut off the Ukraine and can take it at your leisure, not to mention take Vol.

I don’t know.  I guess a multi province defense by the USSR with real amounts of units could work depending.  But I would fear the German player would see it, attack only very select groupings and move right on past to bry.

Using math, tanks have a huge defensive advantage against infantry of the same IPC value, making any army tank heavy ironically have better defense.

Usually as the USSR I tend to reinforce 1 or 2 strong points, usually Len and Mur so that the Ger player has to attack me at relatively strong defense points, drawing his infantry off.

I will say a lot depends on the particulars, but just pulling back to Moscow is inviting disaster

• My theorum is really just a -general- concept.  To be used on any front, not just the German/Russian conflict.

In particular, I like to use it as the chinese against the Japanese, as living to fight another day, seems to be what works best there on average.

Having a response to allweneedislove’s -Iron Blitz- strategy, would require more specific information. But I think his strategy is quite beatable, even if he doesn’t. :P

Any strategy of attacking norway, would entirely depend on axis builds.  If there’s going to be a significant fleet built into the baltic, I’d advise against sending Russians there personally.  But if the germans go ground G1, committing some units up there to meet the british half way, would certainly be a good way to slow the german defensive down. (to a degree).

Again, those are specifics.  This was just an FYI for general gameplay information.

• I agree.

Most important in when playing Axis and Allies is to be very offencive with the allies and attack whenever possible. Considdering that Allies begin with more units and far better production Axis real advantage lies in best strategic placement of units and ability to focus all their units on one enemy at the time.

Axis units are in some ways more valuable than allied units, and much harder to replace. So generaly you want to trade allied units with Axis units whenever possible. China and Anzac units is to be considderd as the least valuable, best used vs Japan even in a 1 to 2 ratio (dont build inf with Anzac, build fleet and trannies and let US protect you)

In Europe trade british air for luftwaffe is good as well if he is going barbossa. US can make a big bomber stack and use it to defend India,Moscow and Sidney. They can also attack Japanesse fleet or kill expoced Axis ground units by attacking with overwhelming force.

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