Re: Statistical odds of AA guns + standard deviations associated low/high sample

[calvinhobbesliker]

@Imperious:

If the AA gun does not kill a plane on a G2 sealion and if you also block with cruiser in SZ 104 and you will all the battles, the UK player can only get 11 Infantry and 4 planes defense. ( builds 9 men, has 2 at start, plus 3 fighters 1 tactical)

The odds of this battle if the above all occur to win for Germany is over 50%.

If AA gun hits, it goes down to about 42%

And what is chance that AA will hit a plane?

[Imperious Leader]

1 IN 6 EACH TIME.

It is a common misconception that rolling the same die over and over again will produce a new result based on the experience of past rolls. Each new roll is reset at 1 out of 6, of about 16%

with low luck you will lose a plane, but the game is not Low Luck.

[calvinhobbesliker]

@Imperious:

1 IN 6 EACH TIME.

It is a common misconception that rolling the same die over and over again will produce a new result based on the experience of past rolls. Each new roll is reset at 1 out of 6, of about 16%

with low luck you will lose a plane, but the game is not Low Luck.

Okay, how many planes are you attacking with?

[Latro]

The odds of losing an aircraft depends on the number of attackers. If there are 6 attacking aircraft, the odds would be:

1 - odds of losing no planes

which is

1 - (odds AA miss * odds AA miss * odds AA miss * odds AA miss * odds AA miss * odds AA miss)

which is

1 - (0.83 * 0.83 * 0.83 * 0.83 * 0.83 * 0.83) = 0.67

So the odds of losing one or more aircraft with 6 attackers is about 67% … this becomes higher with more attackers of course.

8-)

[Latro]

@WILD:

Latro, my first thought was to have UK buy air units UK1 too (have done it). You can also have UK build a sub w/two tacs UK1 (28 ipc’s). Germany can’t kill the sub, and it will increase your odds in the sz 112 sea battle if Germany stays. I think Germany may just drop in another carrier G2 though, so could still stay in SZ112, but would buy fewer tpt’s. Then you have to decided to roll the dice in the sea battle, or do inf buy UK2 and let him storm the beaches G3 w/fewer ground units.

Good post none the less  :-D

My favourite counter would actually be pretending there isn’t going to be any Sealion. Go ahead with the attack on the Italian fleet, build more forces in Africa and more naval units in Canada, evacuate the airforce from the UK and let Germany have it on G3.

• UK will have effectively blocked Italy from the game

• UK can provide good naval protection for large US amphibious fleets

• Germany is out of position

I don’t think a succesful Sealion that takes so much time and effort will lead to an Axis victory.

8-)

[Imperious Leader]

So the odds of losing one or more aircraft with 6 attackers is about 67% … this becomes higher with more attackers of course.

But past results don’t translate their experience to future ones. If what you say is true then Vegas would go broke.

Each new roll is entirely clear and reset. Betting systems for Craps or Roulette don’t work in this manner, and yes i have tried them.

I do think that eventually you will roll a 1, but its the same odds each time no matter how many times you roll, which is 16.6% each roll.

Besides the CA block in SZ 104 protects the German fleet from UK1 attacks. All they can do is kill the CA and if they do they lose a second time.

If they go for Italy and Germany kills all transports and the ships next to UK, a Sealion can be possible as long as no units land from Labrador.

If UK buys anything else but 9 land units, they will lose UK as long as Germany has all her planes and that BB left.

This is the only way to stop UK from killing the Italian fleet, which is to win these battles.

[calvinhobbesliker]

@Imperious:

So the odds of losing one or more aircraft with 6 attackers is about 67% … this becomes higher with more attackers of course.

But past results don’t translate their experience to future ones. If what you say is true then Vegas would go broke.

Each new roll is entirely clear and reset. Betting systems for Craps or Roulette don’t work in this manner, and yes i have tried them.

I do think that eventually you will roll a 1, but its the same odds each time no matter how many times you roll, which is 16.6% each roll.

Besides the CA block in SZ 104 protects the German fleet from UK1 attacks. All they can do is kill the CA and if they do they lose a second time.

If they go for Italy and Germany kills all transports and the ships next to UK, a Sealion can be possible as long as no units land from Labrador.

If UK buys anything else but 9 land units, they will lose UK as long as Germany has all her planes and that BB left.

This is the only way to stop UK from killing the Italian fleet, which is to win these battles.

What? This is simple probability. If you roll 6 dice, the chance that you’ll get at least one 1 is 1-(5/6)^6

[Latro]

@Imperious:

So the odds of losing one or more aircraft with 6 attackers is about 67% … this becomes higher with more attackers of course.

But past results don’t translate their experience to future ones. If what you say is true then Vegas would go broke.

You’re right, but that doesn’t apply to this situation. The odds of the first aircraft surviving AA is exactly the same as the odds of the sixth aircraft surviving. If you look at the combined odds however, things change. It’s the same thing with flipping a coin. The odds of getting heads as a result will be exactly 50% every time … but the odds of getting heads six times in a row are a lot lower.

8-)

[Imperious Leader]

What? This is simple probability. If you roll 6 dice, the chance that you’ll get at least one 1 is 1-(5/6)^6

The dice don’t account for probability. They just roll the same way randomly. The actual odds for each roll are always 16.6%
They don’t change.

If you are in Vegas and always play the same number you will lose. The number will not come up based on the fact that it already rolled X number of times. If might or it might not. The odds are still 1/32 or 1/33 is Roulette.

If you play the same number in 10 games the odds don’t go up. All you do is give your self more chances to get that 1/32 chance but its always the same chance.

[JamesAleman]

Each die toss may be 16.6 percent, but what if you are given 100 dice of which you only need 1 to result in a 1 and that 1 showing up then has an affect in game terms?

Regardless of that debate. Any strategy that requires a series of outcomes to follow a likely probability is suspect since any one of the series can cause the system to collapse. Its my experience that not focusing your efforts results in exposing yourself to more costly battles.

My conservative rule of thumb for sea battles is to include enough force to obtain enough hits to end the battle in 1 combat round. This “sledge hammer” effect results in fewer actual combat rounds and thus fewer units being destroyed. Obviously you can’t “guarantee” an outcome, but if the objective is critical to a long term plans success, then the extra force is prudent. The more you try to do in 1 turn increases the total cost for that turn as each additional battle draws on your force inventory, which increases the number of combat rounds for all battles, thereby increasing your actual losses for the turn.

Regardless of odds, each time my opponent tosses a die, I might lose a unit, so it is in my best interest to make him toss fewer dice. For naval battles I would rather end it in 1 combat round, then give his best pieces extra dice throws.

Back to sea lion, of the 3 games I played against 4 different actual people. There were battles in each of the 3 games in which the UK player did not miss in at least one naval fight. This typically resulted in 1 Battleship surviving with a hit on it, and the axis losing 2-3 air units. 2 of those games the axis players tried to clear the whole navy at once. In one of those games I chose to let one Battleship fleet live and I focused on the Destroyers so that my subs could finish off the UK on G2. I lost 1 air unit (again cause the UK player failed to miss and I failed to hit so it went two rounds and I lost 3 units-1 was air.) I would have lost that battle but for my sledge hammer overkill which still saw my objective complete. During 1 of those games, we even rerolled the France battle three times since we didn’t want to scrap the game. The first two times, France hit 8/12 units when 5-6 hits are more likely.

There are typically 4 or 5 sea battles and the UK player is bound to miss at least once on at least 3 of those fights, but don’t be surprised if 1 of those 4 or 5 battles sees a UK player fail to miss during the first 2 combat rounds. (i.e. you will lose 2-3 units). Italy does it(fails to miss) so often in my games in sz 95, that I now throw the carrier in as a hit taker. I know the odds are against that, but a good battle plan brings you long term success regardless of dice. While you can’t reduce “bad” luck, you can mitigate its ability to disrupt your plans.

A good rule of thumb when hitting Italy: send enough force to get 2 hits a round, expect 1 hit a round and assume Italy does not miss; then you will win on round 3 and only have to lose 4 pieces to 5 hits. My strike force would then be: 1 CV, 1 Tac, 1 FTR, 1 Cruiser, 1 DD and I will win with 1 Cruiser. Anything less and you better have a back up plan for an Italy with 2 transports. With that rule of thumb you are likely to complete your objective even with flawless defensive luck and mediocre luck on offense. No objective can ever be completed if you face flawless defensive luck and disastrous offensive luck.

With regards to sea lion breaking the game, it doesn’t. Here is why:
Basically Germany has 3 choices:
USSR first, UK first, or USA first, (I play tested a convoy raiding approach but failed as Germany had no DD. The U.S. hid its fleet behind Panama on turn 3 and made 10 subs that drove off my fleet.)

With USSR first you can win without taking UK or USA.
With UK first you can only win by also taking 2/3 of USSR and Egypt or all of USSR.
With USA first you can only win by also taking 2/3 of USSR and Egypt or all of USSR.

Therefor: Taking UK or USA does not break the game as you don’t win without Russia.

[WILD BILL]

JamesAleman, you have some valid points. Just because the allies lose England in a Sea Lion doesn’t spell an axis win (it will set them back though). The question is does the income that German now has, and the loss of about 30 ipc’s that the allies will suffer (for about two rounds) be enough to offset. Will Germany be able to recover (buy enough ground units) for the battle w/“Beast From The East”. I think at some point in the near future all those tpt’s will be at the bottom of the sea by the hands of the US, or possibly a very powerful Russian air force w/a few subs (or double hit w/both).  10 tpts (70 ipc’s) is a lot for Germany to protect. Will it be forced to spend even more $ at sea. The allies can even choose not to res-erect UK for the time being if Italy is having a field day in Africa. The US can easily retake the French and UK tt to grow its own income. Germany will be spread pretty thin and won’t be able to hold all its fronts, but will it be long enough to capture the VC it needs (we don’t play w/VC’s, we like total domination, or someone says uncle). Any way the game is far from over if the allies plan for it to happen.

PS there is no redoes in war. If you didn’t get Paris deal with it!!!  :evil:

[questioneer]

Pardon me, this may be out of topic since this thread deals with “Europe only BREAK”.

everything here deals more from a “GLOBAL” perspective:

The problem is that some people fail to realize that this “Sealion” thing is a major issue. Larry created the game for France to fall in the 1st or 2nd round at the latest, I don’t believe he expected a high percentage for Sealion and UK to fall by Round 3.

Looking at the anaylsis so far, Sealion is almost a sealed deal- it is a viable threat to the Allies who have to not only hopelessly try to defend it but recover from it. Rules state that the US can’t even touch the coastal waters of Europe (including UK) and Africa til at war- end of round 3. USSR can do NOTHING until AFTER G4- giving Germany just enough time to build and place land units to defend the Eastern Front after UK takeover- by then make 80+ cash.

If noticing Sealion will happen in rounds 1-3. US will have to spend more money in the Atlantic than it wants to prepare for the liberation of UK. Japan will be very happy about that. If Japan sees those units plop onto the EUS then it can gambit for Hawaii giving the US anxiety on which way to spend the cash- or just continue to pound on China, India and ANZAC with no US support.

Meanwhile Italy controls the Med because UK had to use its Med fleet to defend against a Sealion attack on G2 so it can be delayed til G3. Italy making 20+ a turn sounds nice.

Whether the Allies can recover or not- this is a problem for the game because the UK player will soon be sitting next to the French player feeling cold and alone- whoever plays the UK and France will be sent out to get lunch an hour after the game begins because they will have no money to spend and barely nothing to do.

[Imperious Leader]

Sealion cant happen in G1 or G3

If they try G3 UK can pump in at least 20 infantry total

2+9+9 and 4 planes.

Germany cant take it with 24+ units. Germany cant build that many AP’s and Land units that can overcome it.

They do have a chance only in G2 if UK can get only 11 Infantry and 3-4 planes.

The worse threat is USA taking Norway and building a Major factory. IF that happens i still cant find a solution to fight as Germany

[Croesus]

How could you possibly say that?
IF there is a successful Sealion AND Germany does a Bang-up job in russia by G3 (EXTREMELY UNLIKELY) AND Italy Wins all of Africa:
US Income: 65
USSR Income:19 (if this game is magical for germany
Allied Income:81
Italian Income: 28+5 (On a whim)
Reich Income: 57+10
Axis Income:100
Now, this kinda sucks for the allies but in a mathmatically probable game Its approximately an even fight

[pusfilledwart]

It is a common misconception that rolling the same die over and over again will produce a new result based on the experience of past rolls. Each new roll is reset at 1 out of 6, of about 16%

the Gamblers Fallacy.

[WILD BILL]

The one Europe only game that we played the Axis sacked Moscow (G8). There was quite a few Russians left (in the north) after Moscow fell (but not enough to liberate it). Italy was also very successful in Africa early on, and ran out of Italian markers. In about the 9th round the US had already recouped most of Africa, and had Italy shaking in its boot. The surviving Russians made it so Germany had to stay put on Moscow, in fear of the Russians liberating Moscow them selves, or UK/US forces coming from the other way. In a nutshell the axis had a lot of tt, but were spread pretty thin. The US couldn’t be contained. In the 11th round we called the game. At that point it looked as if the axis were done. The US also invaded the strict neutrals in the 9th round I think (with the surviving Russians help taking Turkey). The US income was around 95 ipc’s w/Africa & the rest of the strict neutrals, and the axis income was plummeting. It was just a matter of time.

[Lydian]

@Imperious:

What? This is simple probability. If you roll 6 dice, the chance that you’ll get at least one 1 is 1-(5/6)^6

The dice don’t account for probability. They just roll the same way randomly. The actual odds for each roll are always 16.6%
They don’t change.

Yes, the chance is 1/6 for one die to get a 1, but for six dice it is 67% to get one 1 or more.
And dice do account for probability, throwing near infinite numbers of them would show so. If you throw only a few, the chances of getting an unprobable event are bigger, which can lead A&Aplayers to believe it’s not so.

@Imperious:

If you are in Vegas and always play the same number you will lose. The number will not come up based on the fact that it already rolled X number of times. If might or it might not. The odds are still 1/32 or 1/33 is Roulette.

Well, playing the same number all the time is as good a strategy as playing different ones each time… you’ll lose anyway unless you’re lucky.

@Imperious:

If you play the same number in 10 games the odds don’t go up. All you do is give your self more chances to get that 1/32 chance but its always the same chance.

Of course my odds go up. The odds for each die-roll stay the same, but my chances of winning at least once increase tremendously. Or are you advocating that if I play a number 100 times, I will only win once every 32nd time I play 100 games?

Now, I haven’t read an final answer on the question yet if Sealion breaks the game, meaning, that if it succeds the game is over.
But even if I took this for granted, so far no sealion strategy that is broken has been presented.
Jim’s is best with 42% success all in all. You have a realistiv chance of winning the game, but you still loose more often then not. Good thing is though, that if the battles in G1 turn out bad, you’re not looked into that strategy.
For a strategy being called broken, I’d say it should be at least above 50%, better 60%, though.
IL’s strategy has far worse odds, so it’s not viable. (His G1 battles are bellow 37% combined success, and his Sealion attack alone below 50% (I’ve taken his % numbers for granted and haven’t checked them)

So all in all, I’d say as long as the odds don’t go up, it’s not broken.
Would you, if you’re as good as your opponent, chose a strategy that lets you loose more often than you win? (Although if the game indeed were over after a successful Sealion, then it might be option Nr.1 if you face a much better opponent. Then 42% might be the best chance you have)
And in addition makes for a short and boring game….
In short, as is, I would not chose a Sealion strategy, unless the odds are the best any axis strategy will net me.
And I’d be interested whether the Axis really win the game in the end, if the invest heavily to take England, even if they succed.

[Imperious Leader]

The odds for each die-roll stay the same, but my chances of winning at least once increase tremendously. Or are you advocating that if I play a number 100 times, I will only win once every 32nd time I play 100 games?

NO i am saying no matter how many times you roll its still 16.6% chance. Each event is a one time thing and no past results have any bearing on future ones.

Well, playing the same number all the time is as good a strategy as playing different ones each time…

Playing more than one number increases the odds. Thats the only way. To play more events at the same time.  In poker you can easily determine the odds of getting a hand because you know the number of cards in a deck and you know the cards you got and these don’t ‘remember’ what you got last time. Only in the sence that the deck was not shuffled after each hand, can you infer differences of odds based on future draws. The dice are always a new roll from start.

If anything else were true than all Vegas games are busted because people would just play the SAME NUMBER. Since thats one of the worse ideas in any table game and we can also assume it has no bearing in this game. These are dice the ultimate gamble and why its hard to win at craps

You only increase the number of attempts by rolling more dice, not the %.

Also, my attacks are nothing as you stated 37% > The worst one is a coin flip and thats just a freebee at Labrador. Why don’t you post thew results of each of Jim’s attacks and compare.

Thats ridiculous. I used more than one simulator and posted the one that seemed more official. You didn’t look at my moves or plug them in a simulator. Most of them are 85% + combat results.

The ‘cumulative’ result of the aggregate of these results cant drop by 50%

here it is again: G1 moves

Attack SZ 106 with 1 sub ( UK has 1 DD) 2 vs. 2. 40.6% to 39.5% ( you can also bring sub to SZ 109 and get better odds, but take the bomber to SZ 111)

Attack SZ 109 1 Bomber vs. 1 DD ,4 vs. 2. 55.4% to 14% ( both die at 30.6%), alternatively: 1 SS and 1 fighter vs 1 DD  ( 92.3% vs. 3.8%)

Attack SZ 110 2 subs, 1 tactical, 1 fighter, 1 bomber vs. 1 BB, 1 DD ( should win) 99.5%

Attack SZ 111 2 subs, 1 tactical, 1 Fighter, vs. 1 BB, 1 CA ( should win) 85.7%

Attack SZ 112 1 BB, 1 tactical, 1 Fighter vs 2 CA ( should win hit on BB) 89%

Key Move: CA blocks UK Gibraltar fleet in SZ 104!

Notes:
The cruiser block in SZ  makes my BB and CV with 2 fighters protected against 3-4 of his fighters attacking on UK1  I win 80% versus his 20%

[Latro]

@Imperious:

NO i am saying no matter how many times you roll its still 16.6% chance. Each event is a one time thing and no past results have any bearing on future ones.

So according to you the odds of losing an aircraft to AA are the same if you send 1 aircraft into it or 100?

:roll:

(Sorry man, that’s just not how probability math works.)

[Lydian]

@Imperious:

Well, playing the same number all the time is as good a strategy as playing different ones each time…

Playing more than one number increases the odds. Thats the only way. To play more events at the same time.  In poker you can easily determine the odds of getting a hand because you know the number of cards in a deck and you know the cards you got and these don’t ‘remember’ what you got last time. Only in the sence that the deck was not shuffled after each hand, can you infer differences of odds based on future draws. The dice are always a new roll from start.

If anything else were true than all Vegas games are busted because people would just play the SAME NUMBER. Since thats one of the worse ideas in any table game and we can also assume it has no bearing in this game. These are dice the ultimate gamble and why its hard to win at craps

Well, if you play more and different numbers, you also invest more, thus the net gain isn’t any higher than if you played just one number with less investment. (1$ at a 1/32 chance has the same net gain as 5$ on five numbers with a 5/32 chance)
Unless you are lucky of course. And that’s the concept of Vegas. You’ll loose if you play infinite times, most will loose if they play a couple of times, and only a few get lucky and hit that 1/32 more than only once in 32 attemps (which is possible, since the events are independent, you could roll 3 times and win 3 times, just really unlikely 0,00003%, but given the number of games played, it’ll happen now and then)

@Imperious:

You only increase the number of attempts by rolling more dice, not the %.

Well yes, the probability of success for each die doens’t go up, but with the number of attemps I increase the % that I’ll, at least once, get the desired result.
More units in A&A will usually get more hits won’t they? The probability of 4 arm making at least one hit is far greater than that of one wouldn’t you agree? to be precise 93,75% compared to 50%.
This all is true in the case of independent events, such as throwing dice.

@Imperious:

Also, my attacks are nothing as you stated 37% > The worst one is a coin flip and thats just a freebee at Labrador. Why don’t you post thew results of each of Jim’s attacks and compare.

Thats ridiculous. I used more than one simulator and posted the one that seemed more official. You didn’t look at my moves or plug them in a simulator. Most of them are 85% + combat results.

The ‘cumulative’ result of the aggregate of these results cant drop by 50%

We’ll it is not really ridiculous, but you seem to have an hilarious understanding of the concept of probability. The cumulative result can’t be higher than the lowest % of any result involved, even if all the others are 100%, in which case the probability would be exactly that of the non-100% event.

To give you a figure, how the chances of succeding drop each time, lets only take your 80%+ battles into account:
92,3% and 99,5% in 109 and 110
~92% of succes in both cases

With the 85,6% in 111
~78,6% of succes in all three cases

with the 89% in 112
Chances of success in all four cases: ~70%

Now take these odds with the chances of surviving your SZ 106 attack (which in a game would not be possible, since I took the best cases for above SZs, meaning we’re short of one sub at this point) at 40,6%
and voila, we’re at 28,4%

With Jims moves (I haven’t checked if he’s right, but he has done the math) he comes up with a 42% probability, which is the highest rate of success of any Sealion so far posted. Allbeit still not high enough for me to use it (unless, I’d be playing a far better opponent, granted Germany wins the game after a successful Sealion, which hasn’t been thought out enough yet, though) and far from having to be called broken.

@Imperious:

here it is again: G1 moves

Attack SZ 106 with 1 sub ( UK has 1 DD) 2 vs. 2. 40.6% to 39.5% ( you can also bring sub to SZ 109 and get better odds, but take the bomber to SZ 111)

Attack SZ 109 1 Bomber vs. 1 DD ,4 vs. 2. 55.4% to 14% ( both die at 30.6%), alternatively: 1 SS and 1 fighter vs 1 DD  ( 92.3% vs. 3.8%)

Attack SZ 110 2 subs, 1 tactical, 1 fighter, 1 bomber vs. 1 BB, 1 DD ( should win) 99.5%

Attack SZ 111 2 subs, 1 tactical, 1 Fighter, vs. 1 BB, 1 CA ( should win) 85.7%

Attack SZ 112 1 BB, 1 tactical, 1 Fighter vs 2 CA ( should win hit on BB) 89%

Key Move: CA blocks UK Gibraltar fleet in SZ 104!

Notes:
The cruiser block in SZ  makes my BB and CV with 2 fighters protected against 3-4 of his fighters attacking on UK1  I win 80% versus his 20%

Ok, I have taken these numbers (haven’t used any of the alternative move suggestions), the combined probability is 26,4%. (Note, I took the 40,6% in SZ 106, since you need to win and survive, or the UK will bring more units to England, thus your G2 Sealion drops even more below 40%)
So, as is, your moves don’t come close to a reasonable chance of winning.

Question IL:
What in your opinion is the probability of
An AA hitting one plane?
An AA hitting six attacking planes?