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.