Hi, I just played a game of a&a revised.  Each power started with one "special ability "  The US had superfortress making the bombers immune to AA fire.  The US rolled 3 dice for heavy bombers round 1.  By round 2, the US had long-range heavy bombers, and caught the Japanese fleet off guard destroing it.  On round 3, the
US reduced the German IPCs in industrial bombing by 26IPCs, at the end of round 3, the US had 8 bombers that are long range, heavy, and immune to AA fire.

So, all the US has to do is get technology which is reasonably likely to attain because you get to choose which technology to research.  It is most likely to take 4 dice for technology to get heavy bombers, so it’s relatively cheap.  Even without long-range, it is only a matter of 4 turns before the US has enough bombers to reduce Germany’s income to 0.  How can the Axis ever win?

Maybe technology should cost more? or is it only fair without it?

if you start building fleet early on with germany it will “telegraph” your move to the allies, if they realize what you are trying to pull, they can easily hold uk long enough for russia to take you out (5-6 turns)

The best bet I think is save the initial 12, or maybe save 8 and build an artillary (As you will need one more for optimal odds on uk)

Now, depending on what the allies bid, you can attempt to save all 40 on ger1.  Take all uk convoys and destroy all uk fleets, not the med one.  Make it not possible for uk to retake any convoys the next turn.  Battleship to gibraltar.  Turn 2, try to get as many subs with your battleship and destroyer in bay of biscay, two moves from denmark straight.  Still depending on what allies buy and what they are doing, you might be able to save again.

All the while get your artillary moving toward germany, so when you build 11 (or 12) transports on germany turn 3, you will have all your artillary in germany.  This includes the artillary from africa.

Now, with fighters in range, and ready to load 22 (infantry and artillary) units 5-6 fighters and bomber and bombard, you should have odds on taking uk, and if not, don’t forget wave two the next turn (you can use a few tanks here since you will be low on artillary)  This is also for retaking uk to finally hold it if the usa retakes from the first attack.

If wave2 (on turn 5) fails, you will most likely lose.  If the allies build significant defensive forces before you build your fleet, build an army instead and invade russia.

if d-day had not happened, the russians might have taken berlin 2 months later

please post images of the game, it sounds like a weird game, I have not seen axis take uk or usa because allies surrender first

If you just want to download the program:
http://www.firethroat.com/aaodds/aaodds-0.30.tar.gz

I see what you are saying, I already did this for non-low luck battles,

The program can calculate battles using random numbers or it can calculate the battle mathmatically using some sick convoluted co-recursion I came up with, feel free to read the code I added extra comments in calcodds.c

I was mainly asking for a more efficient algorithm I don’t think one exists.  This method works great for small battles, just don’t try 30 units, it will take years.

I did not do caching, but I don’t think it would matter much, either the database is massive, or the speed up won’t be noticable, am I wrong?

If there is a bug with a single transport can hitting 5 planes,  it is exactly the situation I don’t understand.  What really does happen?  What is the official rule on battles where certain units  can’t hit other certain units?

Calculating the battles manually is O(n!) operation, so it works ok for small numbers but above a certain value it is ridiculous (above 9 units), of course 5inf vs 5 inf takes longer than 5arm vs 5 inf since there are many more rounds involved.  and much deeper recursion.

maybe I will do lowluck soon,  (or maybe you can try all the source is included)  It has a basic lowluck setup for regular dice, if I knew the real rules maybe I can make it fully complient.  My way is roll one dice for each type of unit, I think it’s is simple and reduces luck a lot.  Honestly it’s kind of pointless since the calculations are within .05% after a second for the iterated approach, and it works for huge battles.

For subs I would just have two types of subs, first strike and non-first strike to solve this, that is already done.  There is not a good way to move subs between stacks between rounds.

Thanks for the feedback.

ok I fixed it, exact odds for small battles converges instantly, but as I thought it takes very long for large battles

It is exponentially slow to calculate, and my algorithm isn’t great, but the best I can do is maybe a 10x speedup with a lot of work.  With a battle with 9 units it takes 3 seconds.  It takes 30 seconds for 10 units!

It’s true that exact odds is very interesting,  but for large battles, it does not converge in a reasonable amount of time, so I should include both methods at least in the calculator, really iteratively is adequete, this is just for fun.

So, please think of a very fast way to do this calculation!!

I will add low luck support (as soon as I learn the correct rules) and hopefully it will always be reasonable for this.

btw, sorry for all the posts :(

I have it working now for exact odds to some degree :(  It will do one unit vs 1 unit.  It is close for other battles but there is a bug somewhere… give me a few days.

For 1 armor vs 1 infantry

Exact Odds mode
Attack:  50.00%     Attack takes: 50.00%
Defense: 50.00%     Annihilation: 25.00%

any programmers have an idea on a good way to write exact odds?  I have now two co-recursive functions calling eachother with for loops and ahaha it’s messy!  It then has to keep track of the situation where neither unit hits the other, and re-normalize the values at the end of a round.  I’m happy I did it with random numbers first!

@Avin:

…it would be a lot easier to produce one for lowluck!..

This is a good observation, but battles with units like subs and fighters (and destroyers) tend to mess everything up as they can’t hit certain units.

What are the official rules regarding this?  Say 3 fighters and two subs attack a battleship and 5 subs in lowluck what happens? is it the same as a normal battle?

I have now the option for low luck, but it only combines units of the same type, so for 7 infantry and 3 armor attacking 15 infantry, three dice are rolled.  Is this incorrect?

Because of this situation with units can/can’t hit other units the possible outcomes is greater than  25, also with aa guns the outcomes are greater too.  I see this as not being an easier problem to solve programming, but computationally much easier for a computer to calculate exact odds with low luck.

I would like to note also that for small battles with my calculator my computer rolls 500,000 rounds a second and converges to the nearest tenth of a percentage  a second.  Theoretically the odds will converge after an infinite amount of time, but for practical purposes they will converge always correctly, and you can see this.  If the calculator reports otherwise, then the random number generator is at fault.  Calculators that only roll 100 or 1000 battles have serious problems, that is why I have my program always rolling in the background, so if needed it could calculate a battle with thousands of units given enough time.

How should I graph retreats?  I have now a plot of all the outcomes by likelyhood, but I would like to also plot battles that result in retreating, I’m not sure what goes on what axis.  Do I need two plots?

Thanks for all the ideas

can you explain why this logic isn’t faulty?  I think 12 infantry win more than 95% against 1 inf.  I think it’s less than .01% for the side with 1 inf.

@aaFiendish:

Looks nice, though I haven’t played with all the features. It’s obviously simple to add in other units (like naval), so you should when you have the chance. One thing that I find extremely useful is a breakdown of what units are left at the end, and what the percentage of each result is. That is, if I attack with 2 inf vs. 1 inf, what is the likelihood I would have 1 inf remaining vs. 2 inf remaining? That is a simple example, but it’s more useful in larger battles.

I have naval units if you run the program with naval.un as command line, or you can make your own by cloning and editing units.

That’s why the program can plot the battle with gnuplot.  I might also add a feature to give you average ipc loss overall giving each unit an ipc value.

I was hoping that someone would write an odds calculator that mathematically computes the odds instead of running the simulations towards infinity and assuming the results are good. It would also be extremely quick to mathematically compute versus running samples. The math gets a little hairy though.

This was my initial plan, but as far as I can tell it is much slower.  Running battles to infinity converges in less than a second even on very slow computers.  If I have a battle with two units, it’s simple, a 2 dimentional problem with a grid, each unit has a dimention.  With two attacking one defending, it requires 3 dimentions.  With 40 units it’s 40 dimentions.  It’s also quite complicated when battles have multiple rounds.

For example with 1 inf vs 1 inf, it is simple, out of 36 possible outcomes, for 4 the attacker wins and takes, for 2 they both kill eachother, and for 10 the defender kills attacker.  For the rest of the outcomes it is a new round so the odds are really out of 16 instead of 46.  so 25% attack takes, 12.5% annihilation, 75% defense (this includes annihilation)  Ok great! so what about when there are 30 units, now many many cases require that I compute annother battle.  What about cases where subs can’t hit air units?  Anyway I might try this, but it seems slower. 
Any other ideas?

Thanks for the motivated work. It’s obviously still in beta, so hopefully you will keep the features coming. Btw, it also works fine in freebsd.

It’s good to know it works on freebsd, I have only tested with linux solaris windows and openbsd.  Now to try macos…