The Axis Dummy Turn

[Clausewitz]

Since the idea of including Italy in AAR is not really workable, I was wondering if the Axis 2-3 turn handicap could be addressed by giving the Axis a third "Dummy" turn after the USA plays.

During the turn, both Axis powers can move, attack and buy tech rolls, but cannot build new units or collect income.

[Defiance]

I don't like the idea of an 'extra' Axis turn: the 3 against 2 is what gives A&A a special gaming spirit in my point of view... This principle 3vs2 gives both Axis and Allies advantages and disadvantages in the game.

I disliked the idea of Italy as a third axis power as well. I think we should keep the game with the 5 major powers as it is, although China should be represented a bit more realistic, but still under US control in this game.

Just my 2 cents

[DocD]

I don't like the idea of an 'extra' Axis turn: the 3 against 2 is what gives A&A a special gaming spirit in my point of view... This principle 3vs2 gives both Axis and Allies advantages and disadvantages in the game.

I disliked the idea of Italy as a third axis power as well. I think we should keep the game with the 5 major powers as it is, although China should be represented a bit more realistic, but still under US control in this game.

Just my 2 cents
I agree Defiance. It's been 3 vs. 2 for eons....why change what works.

[Nuclear]

Just add Italy, and force England to spend its asian money in India, and its pacific money in Austriall. And the money that it recieves from Africa can only be used to buy units in Africa. Also restrict Canada's 4 IPCs, so that only Canada can use that money. This way, the UK's money is much more spread out, and makes taking over certain areas such as Austriall more important. Now Italy could collect money from Southern Europe which would be worth 8 IPCs instead of 6 and would also collect the money from Africa. Also if you notice this, there is a mistake on the game board. Italian East Africa should be under Axis control and that would be given to Italy. This would give Italy 11 IPCs in the game and I would put their turn after Japan's, to ensure that they could possibly do something before America does something on their first turn. Those are my Ideas. Also I forgot to mention that China's IPCs would have to be spent in China and therefore the USA's IPCs would be slightly less in the start of the game.

[SCIPIO]

Nuclear, there is no mistake on the game board regarding Italian East Africa, when A&A begins, the italian territories (Somalia+Etiophia+Eritrea) were already done! It had been occupied by UK in 1941!

[Nuclear]

Sorry about that, I just looked that fact up in a history book, and have found out that you are right.

[SCIPIO]

Sorry about that, I just looked that fact up in a history book, and have found out that you are right.

no worries, you don't have to apologize, I was only correcting you...
:)

[Blasherke]

Just add Italy, and force England to spend its asian money in India, and its pacific money in Austriall.
Have you ever played the TripleA version with Italy implemented as a 3rd Axis power? Well, i have, and it sucks. The biggest disadvantage for the Axis is that Germany is no longer present in the Med Sea. This means, a german amphibious attack against Caucasus or Ukraine is no longer possible. Playing Germany becomes really boring that way (you can only direct your tanks to the east, or, for the brave ones among us, try a sealion) and difficult, if the russian player has enough experience. And directing the Italians towards Caucasus just takes too long.

Greetz,
Blash

[Nuclear]

In the real war, the Germans did not have much access to the Med. Sea. That is one reason why the allies thought that it would be easy to invade Italy first. You can play with Italy, it just takes some time to balance everything back out.

[General Norde]

Some historical info.
Italy, even if it was the 3rd most powerful axis nation, was nothing compared to the 5 represented in A&A. It's industry and manpower were clearly outmatched by the British and German war machines as the country was not much industrialized by then. And if you look at it, some other minor countries were gathered under a single banner. Canada, Australia, NZ, South A., Persia, Iraq under UK. China and brazil under US. Siam under Japan. Finland, Bulgaria, Hungary, Vichy and Romania under Germany.

Should we play it as a 3rd power?
I believe no as this weakens germany by splitting its budget and by giving the germans a severe divided military control disadvantage. Even if the US and soviets play one after the other, I don't believe their turns need to be splitted as their theatres of activity often differ greatly with the exception of Sinkiang.

For that local IPC spending type of game, here's my advice:
If you want to play games where money is spent locally, play Europe at War of Bells of War (a game with 3 complexity levels), two rare to find yet very exciting board games or the PC game Hearts of Iron. A&A is meant to be relatively simple to keep games shorter and I believe it should remain that way.

[Nuclear]

Axis and Allies, is simple, get out of town. Axis and Allies is just like the game chess, except there is a factor of chance which is unpredictable. If one were to study the game long enough, they could win the game with any nation, at anyplace, and at anytime. Just to begin with there are tons of more opening moves then in Chess. Now if you use Logs, (the math type, sorry not from trees type), you could calculate out a rough estaminte on how the game should go for each side. Now the idea of chance with the dice comes in, and that is what makes or brakes your stratigie.

[Blasherke]

Axis and Allies is just like the game chess, except there is a factor of chance which is unpredictable. Just to begin with there are tons of more opening moves then in Chess.
Have to disagree on that one! Don't know if you play chess a lot, but I do, and there are an awful lot of opening moves. It's possible that the guys you play against always use the same moves, but I can assure you that there are many variants. And in chess, it's much more difficult to predict the countermoves, which is, for an experienced A&A player, not the case.
A&A IS an intelligent game, but even a newbie can win from an experienced player, if the dice decide so. This is not the case for chess, or you should feed your grandmaster opponent a lot of whiskey first :D .

[Nuclear]

First off, I have been down to a chess state meat. I am on the High School Chess team and am the Captain. Maybe this is why I play with my friends touch move Axis and Allies, where if you touch that piece, you must move it. If that move forces it into combat, than so be it.
In addition, if you had finished reading my post, you would have discovered and read that I did in fact state that there was a level of chance in the game. Every time you roll a die, the chances of it being what you want are still out of six. Most people do not realize that the pervious rolls have no effect what so ever over the next. A person could roll a one 50 times in a roll, and still would have a 1/6 chance of rolling a one again. That is why when I play; many people like to roll one die at a time, instead of rolling a bunch of dice. Each die still has a 1/6 chance of being a 1. I am in Calculus at school, and know how stuff works mathematically. Moreover, if a newbie can beat you, he or she is either a faster learner than you, smarter than you are in that field, or the dice simply just went that person's way.

[Caractacus]

Nuclear, why do people throw their dice separately? As you correctly said, it makes no difference when you throw the dice or what the previous reults were - for this reason, throwing dice together or separately does not affect the probabilities. Have you tried explaining to them? Perhaps they just like the thrill of watching each one roll...

[Blasherke]

First off, I have been down to a chess state meat. I am on the High School Chess team and am the Captain. Maybe this is why I play with my friends touch move Axis and Allies, where if you touch that piece, you must move it. If that move forces it into combat, than so be it.
In addition, if you had finished reading my post, you would have discovered and read that I did in fact state that there was a level of chance in the game. Every time you roll a die, the chances of it being what you want are still out of six. Most people do not realize that the pervious rolls have no effect what so ever over the next. A person could roll a one 50 times in a roll, and still would have a 1/6 chance of rolling a one again. That is why when I play; many people like to roll one die at a time, instead of rolling a bunch of dice. Each die still has a 1/6 chance of being a 1. I am in Calculus at school, and know how stuff works mathematically. Moreover, if a newbie can beat you, he or she is either a faster learner than you, smarter than you are in that field, or the dice simply just went that person's way.

You can claim to be whoever you want, since I can't controll it, I will only react to what you write concerning the game. I don't know why you reacted so defensive: I DID read your entire post. But, since you're aware of the luck-factor involved in the game, I couldn't understand why you consider A&A to be on the same level as chess. Chess has been played for more than 1000 years, and maybe will be played for at least another 1000 years. Don't know about A&A, however...
Furthermore, that math lesson was completely irrelevant and unnecessary: I think every member on the board here, knows the principle of the dice.
And your statement about the newbie was exactly my point: if the dice decide so, a newbie can win from any experienced player, which is impossible in chess.

[General Norde]

Wow, I though we were talking about a dummy turn here. And it seems that you guys all agree on the overall simplicity of A&A (compared to other much more complicated games). So lets all dance together and party all night long! :o

[Nuclear]

Nuclear, why do people throw their dice separately? As you correctly said, it makes no difference when you throw the dice or what the previous reults were - for this reason, throwing dice together or separately does not affect the probabilities. Have you tried explaining to them? Perhaps they just like the thrill of watching each one roll...

Here is the thing, if I roll all of my dice at one time I have less odds of winning. For example, lets say that I need a 1 on a die to score a hit, and I have 5 inf. If I roll all 5 on one turn, me probabilty of getting all five hits is as follows: 1/6 times 1/6 times 1/6 times 1/6 times 1/6, which is 1/7776. Well you are most likely going to say, well I only have 3 Inf, so it is not as bad, though the odds for throwing three 1s on one roll is 1/216. Though if I through one die at a time each and every time I through the die, I have a 1/6 chance of getting a hit. Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776.

[Vollick1979]

Here is the thing, if I roll all of my dice at one time I have less odds of winning. For example, lets say that I need a 1 on a die to score a hit, and I have 5 inf. If I roll all 5 on one turn, me probabilty of getting all five hits is as follows: 1/6 times 1/6 times 1/6 times 1/6 times 1/6, which is 1/7776. Well you are most likely going to say, well I only have 3 Inf, so it is not as bad, though the odds for throwing three 1s on one roll is 1/216. Though if I through one die at a time each and every time I through the die, I have a 1/6 chance of getting a hit. Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776.

First, one must ask oneself if what they are writing or saying is making any sense. You claim that rolling the dice one at a time increases the probability of winning. Does that make sense? Do the dice know they are being rolled seperately or as a group?

Secondly, the last sentence you wrote is equivalent to comparing apples to oranges. You compare the probability of getting all 5 hits (which is correct at 1/7776 or 0.000129) and the probability to get a single hit on 5 throws of the dice (which is equal to 1-(5/6)^5 or with probability 0.598)!

I hope this explains the errors you've made in your calculations.

[Blasherke]

Here is the thing, if I roll all of my dice at one time I have less odds of winning. For example, lets say that I need a 1 on a die to score a hit, and I have 5 inf. If I roll all 5 on one turn, me probabilty of getting all five hits is as follows: 1/6 times 1/6 times 1/6 times 1/6 times 1/6, which is 1/7776. Well you are most likely going to say, well I only have 3 Inf, so it is not as bad, though the odds for throwing three 1s on one roll is 1/216. Though if I through one die at a time each and every time I through the die, I have a 1/6 chance of getting a hit. Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776.
Very funny, Nuclear.

[Nuclear]

I am not trying to be funny here, I am serious. And thank you Vollick1979 for proving that you have higher odds, by rolling each die one time at a time.

[Stephen]

Nuclear,

If what you say is true for 5 dice, it should be true for 2 dice, correct?

If I throw one die first, and then the other, here are the possible outcomes.

First dice/ second dice.

1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6

----------------
Now, if I roll them together, here are the possible outcomes:

1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6

Now can you please show how the odds of getting these results are different?

[Nuclear]

No you are wrong, if I roll one die at a time and I need a 1 for a hit all of us would agree that if I rolled one die, I would have a 1/6 chance of getting a hit. This would limit the numbers like this for one roll:
1
2
3
4
5
6
Then If I roll a second die, these are the results that I can get. I have the same chances of getting a 1/6 again.
1
2
3
4
5
6
I see a possiblity of getting two hits is 2/12 which is 1/6 or about 16.6%.
Now if I roll two dice at the same time, I can only get the following results
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
Now I only see the the chances of getting two hits is 1/36 or about a 2.8%, which is much lower than the chances are when you roll one die after the other. Just try rolling doubles, now limit that double to only two 1s. Much harder to get. The reason that throwing each one seperatly is better odds is because the die has no knowledge of the pervious roll, and therefore its odds are rest to 1/6.

[Vollick1979]

I am not trying to be funny here, I am serious. And thank you Vollick1979 for proving that you have higher odds, by rolling each die one time at a time.

I didn't prove that you have higher odds by rolling each die one at a time. It must have been your warped logic that construed such meaning. By the way Nuclear, if you want the probability of getting two hits you multiply the probabilities. If you actually believe that the probability to get 2 hits is 2/12 which is 1/6 or 16.7% as you state then could you please tell me what the probability is to get 10 hits or 100 for that matter? (When you get the same 16.7% think if that makes sense.)

[Nuclear]

ok, imagine having 2 quaters, you want to get heads twice in a row. Now if you flip the coin once, you have a 50% chance of getting heads. Once you have gotten heads, you have another 50% chance of getting heads. Though if you begin fliping both quaters at once, you could get a:
heads and heads
tails and tails
tails and heads
heads and tails
that would now be 4 different combinations. The reason that doing one at a time is better, because each time I flip the coin I have a 50% chance of getting heads. The pervious flip has no effect on the next and therefore it remains 50%. Just try fliping two quaters at the same time, and see for yourself how many times you get two heads. And then try fliping just one and then flip another one after that. You will be suprised to see that if you flip one at a time, you are more likely to get heads and heads.

[DocD]

ok, imagine having 2 quaters, you want to get heads twice in a row. Now if you flip the coin once, you have a 50% chance of getting heads. Once you have gotten heads, you have another 50% chance of getting heads. Though if you begin fliping both quaters at once, you could get a:
heads and heads
tails and tails
tails and heads
heads and tails
that would now be 4 different combinations. The reason that doing one at a time is better, because each time I flip the coin I have a 50% chance of getting heads. The pervious flip has no effect on the next and therefore it remains 50%. Just try fliping two quaters at the same time, and see for yourself how many times you get two heads. And then try fliping just one and then flip another one after that. You will be suprised to see that if you flip one at a time, you are more likely to get heads and heads.
What the Hell!!!
Why does everyone want to be a DR and sound more crazy than anything!

You are comparing two different things....of course....they will be different!

[Nuclear]

Actually the whole debate is on if rolling one die per turn is better than rolling all the dice on one turn. That is the debate and I was simply using an example that was simplier to use instead of a six sided dice, to prove my point.

[Vollick1979]

ok, imagine having 2 quaters, you want to get heads twice in a row. Now if you flip the coin once, you have a 50% chance of getting heads. Once you have gotten heads, you have another 50% chance of getting heads. Though if you begin fliping both quaters at once, you could get a:
heads and heads
tails and tails
tails and heads
heads and tails
that would now be 4 different combinations. The reason that doing one at a time is better, because each time I flip the coin I have a 50% chance of getting heads. The pervious flip has no effect on the next and therefore it remains 50%. Just try fliping two quaters at the same time, and see for yourself how many times you get two heads. And then try fliping just one and then flip another one after that. You will be suprised to see that if you flip one at a time, you are more likely to get heads and heads.

Either your Calculus teachers should stick to teaching Calculus because what they are teaching you about probaility is basically complete crap! OR what you are saying about dice is just garbage.

Series the second, I mean Nuclear why don't you try flipping coins because if this is a fair sample of your math skills you're going to need lots of practice in making change cause I predicting a lifetime of working the cash register at McDonalds!

Ask your calculus teacher at school tomorrow and seriously if he tells you you're right, demand your money back!

[AllWeNeedIsLove.]

ok, imagine having 2 quaters, you want to get heads twice in a row. Now if you flip the coin once, you have a 50% chance of getting heads. Once you have gotten heads, you have another 50% chance of getting heads. Though if you begin fliping both quaters at once, you could get a:
heads and heads
tails and tails
tails and heads
heads and tails
that would now be 4 different combinations. The reason that doing one at a time is better, because each time I flip the coin I have a 50% chance of getting heads. The pervious flip has no effect on the next and therefore it remains 50%. Just try fliping two quaters at the same time, and see for yourself how many times you get two heads. And then try fliping just one and then flip another one after that. You will be suprised to see that if you flip one at a time, you are more likely to get heads and heads.

please tell us you are joking. if not, sit down and think about what you have said. if you still do not realize your mistake, you should consider yourself lucky to hold on to a job as complex as one at mcdonalds.

[Zero Pilot]

I can almost hear Vollick1979 gnashing his teeth from here over this one.

Stephen spelled it out as plainly as can be done... Nuclear, read his post again. It's pretty clear there is no difference between rolling a 1 and a 6 together, or rolling a 1 then a 6 one minute apart... which is exactly what you're trying to convince us.

This isn't a "riddle" based on some tricky wording mind you. ~ZP

[pagan]

Nuclear: you are wrong on this.

You are stating that rolling a SINGLE roll on a d6 as COMPARABLE to rolling 2d6.

1/6 on a d6 for a SINGLE hit (you are correct!)

1/6 TIMES/multiply/product 1/6 on TWO rolls of a d6 AND each rolling the SAME number = 1/36 (TRUE)

one roll on a d6 DOES NOT EQUAL two rolls on a d6

You really need to ask yourself what the chances are for you to get a 1 on d6 rolling 10 dice individually compared to rolling 10 dice all together. mathematically the chances are equal. Don't forget to Multiply! You'll have to figure out how to calculate averages over multiple rolls adn make sure that each side has the SAME NUMBER OF ROLLS.

According to your method of analysis, You will decrease your chances to get a hit the more dice you use. So If you get to roll 10 dice individually, you will have more hits than another person rolling 100 dice all together. Because according to you the chances to roll a specific number are decreased as the number of dice increase.

[SCIPIO]

I am not trying to be funny here, I am serious. And thank you Vollick1979 for proving that you have higher odds, by rolling each die one time at a time.

AHAHAHAHAHAHAH sorry Nuclear, I must laugh here! Vollick did say you are wrong! And you are! Because rolling the dice all together or one at times IS THE SAME!!! Maybe suspence it's the difference! :)

[Blasherke]

Nuclear: you are wrong on this.

You are stating that rolling a SINGLE roll on a d6 as COMPARABLE to rolling 2d6.

1/6 on a d6 for a SINGLE hit (you are correct!)

1/6 TIMES/multiply/product 1/6 on TWO rolls of a d6 AND each rolling the SAME number = 1/36 (TRUE)

one roll on a d6 DOES NOT EQUAL two rolls on a d6

You really need to ask yourself what the chances are for you to get a 1 on d6 rolling 10 dice individually compared to rolling 10 dice all together. mathematically the chances are equal. Don't forget to Multiply! You'll have to figure out how to calculate averages over multiple rolls adn make sure that each side has the SAME NUMBER OF ROLLS.

According to your method of analysis, You will decrease your chances to get a hit the more dice you use. So If you get to roll 10 dice individually, you will have more hits than another person rolling 100 dice all together. Because according to you the chances to roll a specific number are decreased as the number of dice increase.
Like he said.

[Doctor Strategy]

Nuclear,

They are the same. If you roll three six sided dice seperately for getting a one, here are the results. First die, 1/6, second die 1/6, and third die 1/6. Chance of all three getting a hit 1/6 x 1/6 x 1/6 or 1/216. Eventhough the individual die has a 1 in 6 chance of getting a one to get three hits the odds are still 1/216.

Rolling three dice at once for the chance of getting hits. Each die has a 1 in 6 chance to get a one result. And to get three hits is 1/216 also.

You made a mistake in comparing the seperate results with the total results.
You forgot that when rolling three dice seperately before you rolled the third die you had already rolled two dice no matter what the results were.

In summary, each die has a 1 in 6 chance of getting a one result whether rolled seperately or together.

[Nuclear]

My Calculas teacher has conformed me correct. Because when you roll them one at a time, you know what you just got, and therefore can determine the chances of getting what you want in the next roll. Your chances are slightly higher due to you knowing what you got on the first die.

[Defiance]

Nuclear, can't you just stop with this crusade? This is so plain simple... you are wrong and your teacher's answers is even totally ridiculous. Read it yourself and find out your mistake: "determine the chance of getting what you want"

[Nuclear]

You are wrong, my school has won over 3 math state Championships. You want to know what the school is. It is GBN or Glenbrook North High School. It is rated as one of the top schools in the state of IL and in the nation. Now if you call me stupid or my teachers stupid, I would just like to know how stupid and wrong you are.

[Caractacus]

Actually, you're both right, in a sense.

Nuclear is explaining something that doesn't really affect the chances but IS true in that many people believe that the previous rolls affect later ones because of probability. That is, many people think "well, I've thrown five dice in a row without getting a '1', so I MUST get one now, surely...". This is a very seductive way of thinking - and it's wrong. This is the element that Nuclear is, wittingly or otherwise, explaining.

However, the 'throwing the dice at once or separately' issue is a bit of a red herring: your knowledge of whether you hit or not the first time will not affect the dice. Similarly, the dice are unaware of what the other dice have rolled/are rolling. Therefore, the probability is the same.

The difficulty is that when you compare the chances of getting, say, two 'heads' on a coin flip either simultaneously or consecutively you MUST compare the chances of getting the two heads BEFORE flipping your two coins; if you compare after flipping one (in the sequential version) you will likely fool yourself into thinking that you are now MORE likely to throw a 'head'.

If you are still sure, Nuclear, offer the following bet to your teacher and keep playing until you bleed him dry if he says 'yes' (which he won't):

"I'll throw two coins together and if I get two 'heads', you pay me one dollar.

Then you throw the coins one at a time, if you get two 'heads', I'll pay you 99 cents."

Of course, this involves a lot of crappy small change, so I suggest you keep a paper record until he's got bored or too poor and then cash in.

Mind you, I don't know about the spinning properties of the coin you'll use - if you're unlucky, some will throw heads more than others - so use the same coin, right?

My piece.

[Vollick1979]

LEARN ABOUT CONDITIONAL PROBABILITY!!! Given you have already rolled a 1, then the probability that on a second roll is indeed 1/6. BUT the probability of rolling that initial 1 is still 1/6.

Let,

A=the event that a 1 is rolled on the first dice.
B=the event that a 1 is rolled on the second dice.

The Probability of B given A has occurred is written as P(B|A).
The formula for P(B|A)=P(A and B occur)/P(A)

So for this example, P(A)=1/6, P(B)=1/6, the probability that both happen is from the nice table that Stephen and I posted is 1/36.
P(B|A)=(1/36)/(1/6)= 1/6.

So the probability of the second dice coming up a 1 given that the first dice came up 1 is 1/6. This is a long way from saying the probability that both dice come up 1 is 1/6.

Well if, as you say, you're school is one of the tops in the state of Illinois then I'm concerned about Illinois' future. Nah, it's probably just one dumb kid, making a fool out of himself.

Nuclear if you could please ask your "Calculas" teacher to visit the site and "conform" you are correct, I'd really appreciate that! :D

[DocD]

WoW, this is unbelievable....I'm seeing statistics being argued left and right.....never saw this much action in my statistics class!! :D

[pagan]

What you see is statistics being argued Right & Wrong.

Let it go Vollick! You know you are wrong! LET IT GOOOOoooooo......

It all about whether a person is truly incorrect in his thinking, able to be shown his error, and correct himself accordingly for the better. (as in my case)

As in your case, you should go to a more 'Denoting-Method' : where if A (nuclear) differs from B (you), then the difference between A+B subsists. SO _ ~(A differs from B), then A=B.

You should 'C' the futility...... (lol - I assume no one finds this as funny as I do...:( )

[AllWeNeedIsLove.]

Here is the thing, if I roll all of my dice at one time I have less odds of winning.... Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776.

timing of dice means nothing.

ok you have had time to think about it and you still think this is correct. if this is what your fancy boy school is teaching you, you should ask for your money back.

[tactical]

This thread is so strange to see on the AH boards, I remember a time when people would argue about buying a AC on G1, heh. Anyways, to this new person who claims to be from a school that wins many awards, yes, congrats.

I have read the arguements from both sides(well, one side versus everyone else). And I am going to have to side with everyone else.

Nuclear, you are probably very good at math(basic definition for all schools), but your reasoning and grasping of the concept you are trying to explain is backwards. I could sit here and try to explain the faulting of your logic but you will probably not "listen" or "see" what I am trying to say since it appears you have not understood what some other posters are trying to tell you.

So here is my challenge to you. I want you to print out all the pages on this thread. Take them to your teacher, have him read the thread, then come back to this post, and comment on it. I am not ridiculing you, only trying to let you see the answer, past your pride. Post again after you have done this, I would very much like to read what your teacher has to say.

P.S. to all, I may have some sp? in there; so for all of you out there, stay in school ;)

[Nuclear]

Here is what my math teacher stated. In wanting to get a sum of 2 on two dice. One would be better at rolling one die at a time, since knowing the result of the first die would allow one to determine the odds of getting the results that he or she wants. If your first roll was a 2 then you would have 0% of getting a sum on of 2 on two dice. Though if you get a 1 on your first die, you now know that you have a 1/6 chance of getting another one. Though if you roll two dice at the same time, you have no knowledge other than a 1/36 chance of determining the odds of getting the sum that you want. Therefore the chances of getting the desired result is slightly higher by rolling one die at a time. That is what he stated word for word.

[tactical]

Hmmm,
you answered awefully fast, did you accept my challenge and print out the thread, And show them to your teacher? Within 20 minutes?

Anyways, knowing what you rolled on your first die, absolutely does not affect the outcome of what your next roll will be.

[Nuclear]

If you are going for a sum on both dice, then it does. If I am going for a sum of 2 and roll a 3 on my first roll, I now have a zero percent chance of getting the sum that I want. And I asked my teacher two days ago.

[Vollick1979]

What do predicting sums have to do with Axis and Allies? For example I want to roll two 1's with my two attacking infantry. I want two 1's! But i'll take only a single 1! So first roll is a 5, dang i missed, now this doesn't affect the next roll! Sure i can't get 2 hits any more but I can still get a single hit.

I'm still scratching my head trying to figure out how the sums of the dice have any relevance here. Wanting two 1's on a dice is not the same as going for a sum of two. This i feel is the hang-up you're stuck on Nuke. Once you realize this you'll abandon the dark side, and come back to the light. (The good guys always win!)

[SCIPIO]

If you are going for a sum on both dice, then it does. If I am going for a sum of 2 and roll a 3 on my first roll, I now have a zero percent chance of getting the sum that I want. And I asked my teacher two days ago.

Now you are talking of a different thing! This thing with the sum had nothing to do with what you were preaching before.
Now you are right, in this case it is in fact different if you throw one dice and afterward the other dice. OF COURSE if you know the result of the first one it's easier to predict a sum, because you already know the first term of the sum.
BUT this as nothing to do with what you said before AND nothing to do with A&A, because in A&A you don't give a damn of the sum of the dice (maybe only if you are SBR :D but it doesn't affect the result if you can predict it!)

[Stephen]

I don't know what else to say, except:

Those who know, do.

Those who don't know, teach.

:D

[SCIPIO]

I don't know what else to say, except:

Those who know, do.

Those who don't know, teach.
:D

:D LOL Stephen :D

[Zero Pilot]

If you are going for a sum on both dice, then it does.Wow... just... wow!

Where in the world did that come from?

*puts on tin foil hat*

This should protect me from any stray nuclear emissions. ;) ~ZP

[Lt M Cotten]

My Calculas teacher has conformed me correct. Because when you roll them one at a time, you know what you just got, and therefore can determine the chances of getting what you want in the next roll. Your chances are slightly higher due to you knowing what you got on the first die.

If your teacher said that he needs his certification revoked! That is the biggest pile of crap I have ever heard. The results of one rolled die, CAN NOT effect anything else, unless you can move the die with your mind! :eek:
Odds are not any better whether you roll the die seperate or together, period.

We are not looking at the sums of dice, just individual rolls..

[Nuclear]

When you roll two dice, no matter how you like it or not, a sum does appear. You are saying that sums of the dice have no meaning or part to the game of Axis and Allies Revised. Yet they do. If you need to get a sum of 2 on both dies, that being a one and another one, your odds are slightly higher when rolling one die after the other. Because after you roll the first dice, the number that you got, cannot change, it is set in stone and therefore becomes a constant. Now working off of this constant we can take the constant times the next set of chances, to determine if our sum can be achived. Maybe I am not explaining this all right, or I am missing word some word, because my whole school's math department has agreed with me.

[pagan]

~(A differs from B), then A=B

....LET IT GO PEOPLE....

[Stephen]

When you roll two dice, no matter how you like it or not, a sum does appear. You are saying that sums of the dice have no meaning or part to the game of Axis and Allies Revised. Yet they do. If you need to get a sum of 2 on both dies, that being a one and another one, your odds are slightly higher when rolling one die after the other. Because after you roll the first dice, the number that you got, cannot change, it is set in stone and therefore becomes a constant. Now working off of this constant we can take the constant times the next set of chances, to determine if our sum can be achived. Maybe I am not explaining this all right, or I am missing word some word, because my whole school's math department has agreed with me.
They are agreeing with you, most likely because of the way you're explaining it, and it makes sense in the way that you are explaining it.

Let me try it this way. You're saying that the result of the first dice cannot change. That is true. And then you take a look at the odds for rolling what you want with the second die, and assume that the odds of the first die don't apply anymore to your success, which is not true.

Look at it differently. If you want to roll a sum of 2, and you roll a die and get a 1, you know have a 1/6 chance of getting the other 1, to get your desired sum of 2. But, what were the odds of you getting that initial 1? This has to be taken into account, and that is what everyone here is trying to say.

When you say, "Once you roll the first die, you know what you get" that is true, but you can't discount the fact that, before you roll any dice at all, you don't know what you're going to roll. The odds of you rolling what you want with the first die are as important, and statistically equal, as the odds of rolling what you want on the second die. By the same token, the odds of rolling all dice together are the same as rolling separately.

---------------------------------------------------------------
Now to separately address what I think you are saying, is that the excitement of dice rolling is increased, that dice rolling is more fun, when rolling individually, rather than together. So that, if you're attacking with 3 inf and you roll three dice together, you have one shot to get a hit. But, if you roll 3 dice separately, and you happen to miss the first roll, you think that, no matter what happened, you still have 1/6 odds on the next die, and therefore prefer to roll them separately. I recall doing the same thing once when, 2nd ed., I bought three dice for tech and rolled them separately.

The thing is, the mathematical odds don't change, it's just one of those things when it seems like it's different in your head. This shouldn't impact your enjoyment of the game. Just remember, every dice has a 1/6 chance of coming up with any one number, whether you roll one dice, 3 dice, 6 dice, or n dice. Odds for any single dice are always 1/6. Odds for multiple dice when considered together (sums, averages, etc...) are slightly different, but that's only when the results of the dice all depend on one another.
In A&A, the dice don't depend on one another (ie. a hit by any unit is considered a hit, and every unit can hit the same like any other unit). So every infantry's die is separate from any other infantry's die. So, in A&A (and believe me, this is gospel-truth), you can roll all your dice together and the statistical odds are the same as if you roll them separately.

If it still doesn't make sense, just point out what doesn't make sense. I have essays to write and exams to prepare for so I can use the diversion, and I accept the challenge of trying to clarify what must be really confusing! :)

[Lt M Cotten]

I am afraid I can't let it go. Wrong is wrong.

His concept of how the die rolling works is flawed. The die are NOT added together, ergo no sum exists. Whether I roll one die twice or two dice once the results will not be any different period, and no amount of filabuster will change that.

Hopefully Stephen, your explaination will show him the error of his ways... :D

[Blasherke]

When you roll two dice, no matter how you like it or not, a sum does appear. You are saying that sums of the dice have no meaning or part to the game of Axis and Allies Revised. Yet they do. If you need to get a sum of 2 on both dies, that being a one and another one, your odds are slightly higher when rolling one die after the other. Because after you roll the first dice, the number that you got, cannot change, it is set in stone and therefore becomes a constant. Now working off of this constant we can take the constant times the next set of chances, to determine if our sum can be achived. Maybe I am not explaining this all right, or I am missing word some word, because my whole school's math department has agreed with me.
Nuclear, PLEASE take the effort to read all previous posts, they are ALL right! I'm a very patient person, but if you would have been my opponent... And sums DO really have nothing to do with A&A! Even when you do need two 1's at a time ( who would attack then???), still the dice are NOT influencing each other! Tjeez, this is one of the most difficult threads ever!

Anyway, as always,
greetz,
Blash

[DocD]

The problem then is yours Lt M Cotten , not Nuclear's.

There comes a point when all youare doing is banging your head on a wall. Somepeople refuse to stop doing it. these are the more enlightened ones. What would you calla person who persists with the head banging? I would call that person as smart as the person from whom drives him to do it.LOL :D LOL

I have to agree Pagan! At some point you have to throw up your arms and just say "your funeral dude".
If a guy tells me he can jump from a plane at 10K feet without any parachute or other means of surviving the fall, and continues to argue (through some quantum physics equation) that he will be ok....what is a guy to do?

I think stephen has pointed out the error in plain king's english...if nuclear doesn't understand that........

[Nuclear]

Get this straight all, I understand what all of you are saying. Its just that my math teachers state otherwise.

[DocD]

How many math teachers do you have aboard said plane?

[pagan]

LOL... now THAT's funny !

[SCIPIO]

Get this straight all, I understand what all of you are saying. Its just that my math teachers state otherwise.

maybe your math teachers are explaining something else, maybe they are really no good, maybe they don't listen to you, maybe they got some private problems, maybe they are on DocD's plane, I DON'T KNOW!
BUT WHAT I KNOW FOR SURE, BELIEVE US PLEASE, IS THAT (as Stephen said):

in A&A (and believe me, this is gospel-truth), you can roll all your dice together and the statistical odds are the same as if you roll them separately.

[Nuclear]

I will not believe it until my math teachers do. Obvisiouly I cannot believe anyone side. The math teachers have a higher knowledge of math then the people here, while your arguement makes some sense, it does not seem to address a particler issue, which I cannot really explain.

[Stephen]

If anyone is already bored by this thread, don't read on and then say, "Oh, my, why can't we just stop?" If you don't care, don't read it. I won't cry :)
I will not believe it until my math teachers do. Obvisiouly I cannot believe anyone side. The math teachers have a higher knowledge of math then the people here, while your arguement makes some sense, it does not seem to address a particler issue, which I cannot really explain.
I'll quote your original post, and see if we can straighten this thing out :)
Most people do not realize that the pervious rolls have no effect what so ever over the next. A person could roll a one 50 times in a roll, and still would have a 1/6 chance of rolling a one again.
This statement is 100% true, and a very common mistake people make, most often called the "gambler's fallacy", or mistaken as some "law of averages". Each roll is independent of the one before it, and the one after it. The fact that you understand this concept is awesome. Let's go on:
That is why when I play; many people like to roll one die at a time, instead of rolling a bunch of dice. Each die still has a 1/6 chance of being a 1.
You're still right about each die having a 1/6 chance of being a 1. Moving along...
the odds for throwing three 1s on one roll is 1/216. Though if I through one die at a time each and every time I through the die, I have a 1/6 chance of getting a hit. Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776
The 1/7776 are the odds of getting all 5 hits with 5 inf. Nearly impossible! When you compare rolling individual dice with a 1/6 chance, you're not comparing the same things. You are comparing the odds of throwing 5 dice and getting 5 hits with the odds of throwing 1 die 5 times and getting any hits.

Let's take a simple example of two dice, since the math is easier to work with. You and I and Dr. Statistics could probably work with the 5 inf example, but we don't want to hurt the brains of anyone else on these boards :) If I can show that the odds are the same rolling 2 dice together or separately, the same principle should apply to 5 dice together or separately.

If I roll two dice together and want two "1"'s, the odds are 1/6 * 1/6 = 1/36.
If I roll the dice individually, the first die, the odds of getting a "1" are 1/6. When I roll my second die, the odds of getting a "1" are 1/6.

But, when I roll them individually, what are the odds of getting two "1"s? The odds of the first die rolled are 1/6, and then the odds of the second roll are 1/6. You multiply them together, and you get 1/36.

Now let's say we are rolling two dice together and are just happy to get a single "1". This is a bit more complicated mathematically, but we can still see how the independence of the rolls is true here.
Rolling 2 dice together, you're happy to get either:
a 1 with the first die, and a 2-6 with the second,
OR
a 1 with the second die, and a 2-6 with the first,
OR
a 1 with both.

The way this is calculated is by taking the odds of each scenario, adding them together and voila, we have our odds of getting at least 1 hit.

The odds of the first scenario are 1/6 * 5/6 = 5/36
The second, it's the same: 5/6 * 1/6 = 5/36
Now the last one is key: it's 1/6 * 1/6 = 1/36

I think this is where, conceptually, things should start to make sense now. the 1/36 is the same as we mentioned before, when you roll all the dice together and try to get all hits. But when we're happy to get ANY hits, you add the chance of getting at least 1 hit on any die to the chance of getting both hits! So in this case, with two dice, at least 1 hit, the odds are 11/36.

So, let's go back to what you stated earlier and see how this applies: (I'll add in my emphasis)
For example, lets say that I need a 1 on a die to score a hit, and I have 5 inf. If I roll all 5 on one turn, me probabilty of getting all five hits is as follows: 1/6 times 1/6 times 1/6 times 1/6 times 1/6, which is 1/7776. Well you are most likely going to say, well I only have 3 Inf, so it is not as bad, though the odds for throwing three 1s on one roll is 1/216. Though if I through one die at a time each and every time I through the die, I have a 1/6 chance of getting a hit. Therefore it is to your benfit to roll each die, one at a time. I certainly like rolling each die by itself and having 5 times to get a hit with each at a 1/6 chance. Compared to rolling all 5 on the same time which to get all five hits is 1/7776.
Does it make more sense now? Your math above is comparing the odds of getting *all 5 hits* with 5 dice rolled at the same time, to getting *any hits* with 5 dice rolled separately.

If you're still not clear, think about what you are rolling for when you go into a battle with 5 inf against say, 2 inf. When you roll, you're not hoping for all 5 hits! You only want 2 hits. So you're happy if any of your inf get a hit. Fortunately, as you know, each dice has a chance of 1/6 of getting a hit. You don't need 5 hits (1/7776). You just need at least 2 (1525/7776 or 19.62%).

So that concludes my bit for now. I know you said in a post just before this one that you agree but your teachers don't. Maybe they misunderstand the game. Maybe they misunderstand the goals when you roll. Who knows. But hopefully you can see more clearly that the odds don't change, and maybe you can figure out where your teachers have taken a wrong turn! Believe you me, there are many, many people in this world, students included, who are smarter than teachers, and you just might be one of them!

[series]

Who do I side with? The 200+ people who make sense, or the crazy guy speaking gibberish, probably because of radiation.

Of course, the latter.

Nuclear is getting his facts mixed up, however. Perhaps a game like Panzer Grenadier is what he is referring to. However, the logic applies here, just a very small impact, not what he suggests.

Ok, take a look at this chart, based on addition:

X 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 1011
6 7 8 9 101112

What number appears most on the sums of 2 dice? 7. It is a fact, because 7 has the most combinations. So let's say you have 2 armor attacking. You have a significant chance of rolling a total of 7. Why is that good to know? it almost garuntees a hit. How many ways can 7 be divided up without having a number 3 or less? Zero. This means that, since 7, the center line, and all the smaller results, garuntee hits, you have MORE than a 50% chance of getting one hit. Just look at it a couple of times, it makes sense.

Nuclear is suggesting that this logic impacts the results. I see where he is getting that from, but take another look- each side has a 1/6 chance of landing anywhere on that chart. So if you roll the dice at the same time, it does not really matter, it just provides a different way to look at it, really.

I know what i said isn't completely relevant, but I feel it is important to share.

[Nuclear]

Stephen I agree with you on all the mathmatical aspects of what you have posted. Like I stated before, I understand where you guys are coming from. I am now off to see where my teachers made a mistake, if any, which I highly think that they did make one.

[Lt M Cotten]

I would be willing to bet that it was just amisunderstanding in details not an actual error, at least I hope so... :D

[pagan]

The math teachers have a higher knowledge of math then the people here,...


This is definately NOT true when addressing me, unless they are dealing with electro-thermal Dynamics - counting little arrows to address the possibility of light's motions, or Quantum Mechanics.

And even in these, I know a bit.