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Author Topic: Luftwaffe vs Royal Navy  (Read 16178 times)
ncscswitch
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« on: January 14, 2006, 06:43:36 pm »
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OK, this has come up in several threads, so going ot post some analysis of it.

This concerns my posted opinion that Germany can take out the Allied navy in the Atlantic at least twice, and possibly reduce its transport capacity a third time.  Some folks do not want to believe that.  And since the only offer to test has been with "low luck" dice, why bother with the game, and just use the simulator.  Here are the results...

G1: 
A.  Germany attacks the UK SZ containing 2 trannies, 1 sub and 1 BB (UK and Russia ships)  They use their Baltic tranny, 1 sub, and 3 figs for this attack.
B.  Germany sends 1 sub, 1 fig and 1 bomber against the UK BB off Gibraltar
C.  Germany sends 1 fig after the tranny off eastern Canada
D.  Germany sends the tranny (loaded for Egypt) and BB against the sub off Egypt.

Results:
A.  87% of the time Germany wins this battle.  54% of the time they will have 2-3 figs left, with equal percentages of both results.  The next most common result is to win with 3 figs AND a sub.  But we'll forget the sub since it will be sunk by the RAF and go with the statistical result that Germany wins with 3 figs a plurality of the time.
B.  99.3% of the time Germany wins this fight also.  53% of the time they win it WITH the sub still alive, 42% with both aircraft still alive.  Since the sub, if it lives, will be killed by the UK bomber, we'll ignore that result and go with both the fig and bomber surviving.
C.  72% of the time the Fig kills the tranny and lives.
D.  93.6% of the time I win this fight too.  Only question is if the INF land in Egypt.  56% of the time they do.  But, regardless, the sub is dead 97.9% of the time.

Now, Germany has 1 bomber and 5 figs left (OK, we'll round down and go with 4 figs, even though you see the odds favor 5 figs left).  UK has 1 naval unit on the board, a tranny off India.

G2:
Did UK build a navy in UK1?  If so, and with maximum US assistance, the navy in UK waters in G2 is  2 TRN (one US, one UK), 1 AC, and 2 figs.  Germany hits this force with their AF of 4 figs and 1 bomber.
Result:
This is a tougher battle.  Germany only achieves total victory 60% of the time, and mutual destruction another 7% of the time.  BUT, the odds of either tranny surviving is less than 2%.

But, if US sent their tranny to Africa in US 1...
then Germany wins 83% of the time against the loaded AC and 1 tranny.
And they do so with an average of 1 FIG and 1 Bomber, with an almost equal chance of 2 figs (27% vs 26%)

Now, let's do G3, assuming UK built on UK2, and again on UK2 built a second AC AND that the US sent 1 more fig to protect it (they could not afford 2 figs with a 3 tranny buy).  Let's also add 1 UK tranny, eventhough they very well may not be able to afford one with losses in Africa and Asia, and the US tranny moved from Africa, and 3 more US trannies sailed in from the US.  Germany has 1 fig and 1 bomber left.

Even in THAT case, while I cannot win the battle as Germany, I still sink 1-2 allied trannies, leaving only 3 for use in UK3 and/or US3.


But what if UK waits until UK3 to re-build their navy and US builds an Atlantic capital ship plus trannies to send to UK?

OK, let's try this... Germany has 4 figs and 1 bomber left.  In UK2 UK builds an AC and 5 trannies.  In US1, US builds an AC and a fig for it.  In US 2 the US sends 2 figs to the UK AC, moves their new AC and 1 FIG to UK along with their original tranny.  Hell let's say that somehow the US fig survived Pearl and was able to make it to the new tranny in US2 also.  Just to maiximize the amount of forces that CAN be in UK sea zone come G3.  2 AC's, 4 figs, 6 trannies

Again, based on the odds, even with that MASSIVE amount of firepower for defense (an amount of firepower that means that while they have trannies built, neither nation built jack squat to load onto them, let alone support any other theater)...
30% chance of 3 trannies sunk
23% chance of 4 trannies sunk
22% chance of 2 trannies sunk
10% chance of 5 trannies sunk.

That has you hitting Europe in late G3 with only 3 trannies worth of stuff, assuming you coordinated perfectly and all surviving trannies are from the same nation to be able to attack together AND that there are materials to actually transport (and since it is only UK can that can have 3 trannies left all from one nation, and since UK spent ALL of their money on navy in order to get those 3 trannies to survive, there is only 2 INF and 1 ARM to transport in UK3...

Again, it will be Turn 4 before your trannies are able to be re-filled, and more trannies built.


No matter how you slice it, if Germany is willing to sac it's Air Force, UK and US can be kept out of Europe until Turn 4, except perhaps for a token landing.
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DarthMaximus
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« Reply #1 on: January 14, 2006, 07:55:47 pm »
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Not worth it for multiple attacks, IMO, unless UK messes up or US doesn't reinforce.

First, if your odds are correct:  (I've got no reason to doubt you)

A - 87
B - 99
C - 72
D - 93

The chances off winning all of these in the same game is only about 60%

(.87 * .99 * .72 * .93) = 58%

So your only really looking at the perfect scenerio b/c about 60% of the time something goes horribly wrong.

Germany (on rd 2) with 4 ftrs and bom vs. 2 trns, 1 AC, 2 ftrs is not a good idea.

You end up trading valuable ftrs for Allied trans.  This will not slow down the US and UK will not have to buy an AC on UK 2 and can just go with trans.

I will invite the remaining 2-3 G planes (if the have any left), to attack 6 tans (3 US, 3 UK) on rd 3.

Also, Russia will be a serious threat to Germany.  I think you can see from our game, with no German Airforce Russia will crush EE very early.

You can't afford to trade the valuable German planes for lowly transports.

Now if the Allies don't don't reinforce the UK AC then sure you might have a shot, but I personally think the Ftrs are too powerful for defense to throw away in rds 1,2, or 3.

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ncscswitch
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« Reply #2 on: January 14, 2006, 07:57:39 pm »
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Just another outlook on the game... a way to attempt to keep US and UK out of Europe as long as possible.

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DarthMaximus
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« Reply #3 on: January 14, 2006, 08:10:49 pm »
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I like going to W med sz with my sub, BB and trn, then if you have your BB alive or something you can try 4 ftrs, 1 bom AND 1 BB to go after the UK on UK 2.  And if you get a sub hit you may even have your sub alive.

It is just very hard to slow the Allied shipping.
I like to wait till rd 4-5, when Japan can bring over 3-4 ftrs and bom as well.  NOW if you time it right you can nail the Allies right in the middle of the crucial part of the game, when Russia is on the decline, UK income is low 20's.

If you can cost them 2-3 turns in the mid part of the game, you can really turn the tide, I think if you go early on, the benefits aren't as great as they are if you wait for Japanese back-up.
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ncscswitch
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« Reply #4 on: January 14, 2006, 08:14:21 pm »
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Had never thought of holding off for the Japan AF to transfer... always looked at it as a Germany first, then Japan in terms of an Af double hit in Europe.

Will have to try that when the opportunity presents itself...
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Avin
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« Reply #5 on: January 16, 2006, 09:06:52 am »
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ncscswitch, an honest question: do you understand how lowluck actually works?
« Last Edit: January 16, 2006, 09:24:33 am by Avin » Logged
ncscswitch
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« Reply #6 on: January 16, 2006, 03:15:47 pm »
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ncscswitch, an honest question: do you understand how lowluck actually works?

A bit off topic for this thread, but yes.  It is the statistical average roll, + or - 1

And it does not allow for things that are GOING to happen in a real game, like the 3% chance of Darth taking EE with the forces that he did.  REAL games mean REAL variables.  You play the odds and HOPE. 

Low luck is like betting on a football game, but the bet not applying if the game is a blowout.  Sorry, either bet on the game as it is played, or don;t bother.

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Avin
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« Reply #7 on: January 16, 2006, 06:52:18 pm »
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I ask because elsewhere you promised a discussion on my challenge and in this post you initially seemed to indicate that this was that post, but your statistics clearly indicate that you were not considering low luck at all, because when I plug the same battles into a simulator, I get different numbers than the ones you claim. I'll probably elaborate more on this tomorrow, but I'm going to sleep now.
« Last Edit: January 16, 2006, 07:02:43 pm by Avin » Logged
Bashir
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« Reply #8 on: January 17, 2006, 02:14:42 am »
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42% with both aircraft still alive.  Since the sub, if it lives, will be killed by the UK bomber, we'll ignore that result and go with both the fig and bomber surviving.

With LL you will have 100% chance both your aircraft will still be alive... because you have 2+3+4=9 attack points... 9/6=1 1/3 hits..
The odds of the bb hits a plane in a non LL game are still not big... The chance Germany hits nothing on the first round and the UK bb hits is 7.4%! So how in the name of god did you come on the 42% only both your aircraft survive?


The UK zs battle is off too.
You will have 2+3+3+3=11 offensive points. Def has 1+1+2+4=8 def points.
So first round you prolly have 2 hits. Def makes 1 hit on average.
Second round you will have 1 one or 2 hits... (50-50 on the second) and the def prolly has 1 hit (5/6, because you kept a trannie instead of a sub)
*If there is a third round you will have 1 hit and the def has prolly 1 too (4/6)

So howcome your odds on having 53% chance on both 2 is the same as 3 fig left?

C. Germany sends 1 fig after the tranny off eastern Canada

C. 72% of the time the Fig kills the tranny and lives.

I think the appropiate way to calculate this one is 1-p(tran hit and fig misses)-p(tran hits and fig hits)= 1-(1/6 x 1/2)-(1/6 x 1/2)= 0.83 => 83%So in my calculation you have 83% chance that yo kill the trannie and your fighter lives...

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aaFiendish
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« Reply #9 on: January 17, 2006, 07:45:18 am »
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Now, Germany has 1 bomber and 5 figs left (OK, we'll round down and go with 4 figs, even though you see the odds favor 5 figs left).  UK has 1 naval unit on the board, a tranny off India.

You guys never do your odds right  evil

On battle #1 you have as you say a 87% chance of winning the battle. So...13% of the time you lose all your fighters. In other odds, 26% of the time you lose one fighter. 12% of the time you lose two fighters. So, your odds of losing at least one fighter are 51%, in the battle alone. In your battle against the transport, 28% of the time you lose your fighter. So you are not "rounding down" by any means. The odds of you losing one fighter in round 1 is 79%, pretty high. The odds of you losing two is...(13% lose all fighters + 12% lose two fighters + 3% mutual destruct) 28% + 28% (tranny battle) / 2 = 28%. (the above paragraph is prone to errors, just like yours though).

So, 28% of the time your attack on the 2nd round will be 3 fighters and a bomber in battle #2, which ought to still let you clear the transports but eliminates a third attack. Even if you attacked the second time with 4 fighters and a bomber, despite your 59% chance of winning, your odds of a third attack are less than stellar. 41% of the time you lose all attacking, 16% of the time you are left with just a bomber. So...57% of the time you can't really can't attack a third time.

Anyhow, apart from odds, I would say that you are overlooking something critical. Every round the US transport moves to the UK seas it is dropping troops. It's great that you keep sinking the US transports and all, but if you attack a third time and manage to kill two transports I am just going to take US transports as a loss. As shuck-shuck is not established yet, it's not really a big deal. I just keep building transports and troops at home, giving me a full load into finland/norway. 6 inf + 3 transports a round is quite attainable, though it may be 5 inf + 3 transports once mainland forces are depleted. Obviously they would prefer to be doing more, but your strategy is only stopping the UK from landing. However, the loss of SOLELY UK troops is more than made up for by the lack of your luftwaffe.
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Avin
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« Reply #10 on: January 17, 2006, 07:53:29 am »
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Interesting you should bring the Eastern Europe battle up. Let's take a look at that battle, and compare the possible low luck outcomes versus the possible ADS outcomes.

The battle involves 17 inf, 3 arm, 2 ftr (RUS) vs 9 inf 7 arm (GER).

Here is the table of possible outcomes (assuming the battle is fought to completion and no one retreats), with the winner on the left, the amount of units remaining, and the probabilities for that outcome under ADS and LowLuck (LL) on the right. Let's also assume that the attacker kills off fighters before losing his last armor.

WinnerInfArmFtrADSLL
DEF670<1%0%
DEF570<1%0%
DEF470<1%0%
DEF370<1%0%
DEF270<1%0%
DEF170<1%0%
DEF070<1%0%
DEF060<1%0%
DEF050<1%0%
DEF040<1%0%
DEF030<1%0%
DEF020<1%0%
DEF010<1%0%
DEF000<1%0%
ATT010<1%0%
ATT0111%0%
ATT0122%0%
ATT0223%0%
ATT0324%0%
ATT1325%<1%
ATT2326%<1%
ATT3328%4% ***
ATT4329%19%
ATT53210%38%
ATT63210%26%
ATT73210%10%
ATT8329%2%
ATT9327%0%
ATT10325%0%
ATT11323%0%
ATT12322%0%
ATT1332<1%0%
ATT1432<1%0%
ATT1532<1%0%
ATT1632<1%0%
ATT1732<1%0%

*** - actual result of battle in your game

As we see, the actual result in your game was statistically unlikely in either ADS or LowLuck, but possible in both. DarthMaximus in either dice system should have expected a more favorable result. In both dice systems, the median result (5-6 infantry alive for the attacker) is the same, and there are a quite a range of possibilities outside that median result. However, it's curious that in ADS, it is actually more likely that DarthMaximus would have rolled worse than the exact outcome that was achieved. This is because although the odds of getting that result is more likely in ADS, the variance (or standard deviation) of results is much greater in ADS than LowLuck. This is the reason I like LowLuck: the "unlikely" scenarios of ADS are still possible in LowLuck, which makes every game different and forces players to adapt to dynamic changes in balance, but at the same time rules out the "extreme" circumstances of say, DarthMaximus actually losing that battle with your full armor regiment intact. While any individual "extreme" outcome is in ADS so insigificant to consider alone, when you consider the number of these outcomes it makes it so that you really cannot always expect to win such a decicisive battle, if you play enough. Someone recently posted the idea that any given player can expect to only win 80% of his games because of strategy and the remaining 20% would be affected by bad dice; this makes it so those proportions are more reasonably tilted towards strategy.

If I wanted to play a game where the dice can easily make a huge difference, I would play Risk, because the majority of the fun in that is the social interaction. And I play that on a somewhat regular basis. There is a good deal of "potential" strategy in that game, but the dice can make or break any valid one, and yet it is still often fun because you really don't expect to win the majority of the time, because it's pretty clear from the get-go that this isn't too much of a strategic game: it's more luck and politics than actual strategy. I've often won huge swatches of territories because I happened to be rolling well despite being the weakest player on the board at the start of my turn, and on the other end of the spectrum, I can recall at least one game where I was the strongest player on the board, and the next strongest attacked me on a whim with a moderate sized army only to win without taking any casualties, so he kept up the process until he had completely eliminated me from the game without loss to himself, destroying at least 30 infantry and taking over more than a continent, with only around 15 or so of his own infantry to start with. Statistically unlikely sure, and I walked away from that game somewhat disappointed, but more amused than anything else  because with a dice system like Risk's, you expect these oddities to happen once in a while.

Axis and Allies on the other hand, is designed to be a more strategic game. I have very rarely played a game of Axis and Allies with more than one player controlling a side. In those cases, the social interaction did indeed add to the fun, but when I play online, that simply does not translate for me across the web. Unfortunately, the way the dice is set up according to the box, it actually has the potential to be more random than Risk. Good players are aware of this and deliberately conduct battles only when they can be more certain of results - not throwing away their armies in a 50/50 crapshoot unless they are already behind and are open to the possible but unlikely event of good dice swinging a decisive battle to their favor. However, the desired guarantor is hard to pin down because of the "extreme" outcomes discussed above. In every ADS game I have observed in the last year or so (since I started playing LowLuck), and every game I remember playing before then, one player or another will inevitably get some horrible dice within the first couple turns. Now if this player was a significantly inferior player to begin with, this makes little difference. Conversely if this player is a significantly superior player to begin with as well, this player is usually able to overcome this disadvantage until the dice inevitably land in his favor again. I've seen both these outcomes happen particularly when I would play others who are new to the game - if I get bad dice, I actually kind of like it then, because it gives my opponent some support and hope, and at least stretches out the game a bit so it doesn't seem like I decimated them.  However if both players are roughly equally matched, then an early blow is often crippling: I can usually predict the outcome of the game from that point unless another extreme dice result occurs in a way that is significant to alter the balance. After reading through most of the latest threads on the Games forum here, I can say that that seems definitely to be the case - except where the player with the good luck is gracious enough to offer to his opponent the ability to "revise" the dice to a more reasonable result. In this case, why bother playing with ADS anyway, since it seems you're not willing to deal with its consequences? For instance, we have the G1 attack in your latest game on the North sea, where the outcome you got was actually not that unlikely even - it had a high chance of being the outcome even had you been playing LowLuck (I think it would have been about 20% in LowLuck, the second most likely outcome). But DarthMaximus, being extremely gracious to you since I suspect he rightly considered your overall position and strategy to be significantly inferior, offered to give you a fighter or two back for free. Well, consistent with what your gaming philosophy appears, you rejected his offer. I suspect that if you had lost all your airforce without having killed any of his units, you would still have rejected a similar offer. Well, I'm sorry, but that's playing a game that's significantly different from the game I play. If your only goal is having fun, that's great, because a person can have fun no matter what happens. You can still potentially have fun if you were imprisoned and being tortured, so of course you can still have fun by knowingly playing out a losing game. I play not purely because of the fun itself, but because I derive having fun from developing my strategy further and seeing it successful if it is superior to my opponent's, or seeing it fail if it is inferior. Currently I started playing a (LowLuck) game after seeing that you were not interested in playing, and I don't think I'm doing as well as my opponent is, but it's hard to tell even though we're in round three. There have been some statistically unlikely events that have happened, that have affected both our strategies, such as my inability to kill Germany's navy in R1 while losing the Russian navy completely, but because there has been nothing gamebreaking, it has been a match of my strategy against my opponents. A majority of the games I play end up being 10 rounds or more because unless one of us is significantly weaker, our strategies cannot count on waiting for a good dice result and then taking advantage of that; rather, there is a depth of play that is present but rare in ADS games in my opinion with the constant struggle of well matched forces.

So anyway, regarding the "simulations" you present in this thread, I say they are irrelevent to your support. My entire critique of your strategy was based on a simulated game I played based on expected results, and you remained unconvinced. I remain certain that by exchanging the German air force for the combined navies of the UK and the US, you open the possibility of direct and relatively unsupported invasion from Russia. These statistics you bring up in this thread have nothing to do with Russia's stack that is growing steadily as you expend most of your energy making pre-emptive attacks against the west. (By the way, in the original thread where you brought up this discussion, you had assumed that Germany would buy 1 fighter per turn for the first couple turns, which I don't see discussed anymore - did you give up on that?) So if you are unwilling to accept my simulation, all I can do is say that by playing an actual game where the dice don't determine the balance of the game (granted it's possible for this to happen in an ADS game, I'm just not really interested in taking the time to play one when the possibility is reasonable that it won't),  I am sure you will find that your strategy may have seemed just as good in your head as the Sea Lion Scare, only to find that it does not work in practice.
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Octopus
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« Reply #11 on: February 13, 2006, 09:17:48 pm »
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Switch,

you are asking excellent questions, but you must consider the statistical reality that the Luftwaffe cannot hold off the Royal Navy.  At some point you need to consider what that cutoff is to stop attacking. 

Clue: Which is more dangerous to Germany? The Royal Navy or absence of the Luftwaffe.
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Biofury
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« Reply #12 on: February 14, 2006, 01:08:54 am »
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I heard a quote awhile back and I might be off...

"If you see a white plane it is the British, If you see a black plane, it is the US, If you see no plane then it is the Luftwaffe"
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Octopus
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« Reply #13 on: February 14, 2006, 05:16:08 pm »
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Actually, you are right on the money.

 wink

Octo
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Guerrilla Guy
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« Reply #14 on: February 14, 2006, 05:55:42 pm »
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and if you see a ballistic, frustated man you know that it was a french plane...
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