11 on 11 is the last number where defender has advantage

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Postby Cronus on Mon Jun 25, 2007 5:53 pm

Bob Janova wrote:I think you get 3 dice fighting 3vx (even though you can only move 2 armies forward) so 5v5 would be the breakeven point.


what?

1. defender get max of 2 dice
2. it's not a thought, it is a fact that 11 on 11 is the break point. This isn't a debate.
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Postby Petrelli4Prez on Mon Jun 25, 2007 5:54 pm

Robinette wrote:
Can I get your thoughts on adjusting an air conditioner...
Do you turn it UP to mean RAISE the temperature????
Or do you go UP to go DOWN.... :-k

where is that ice cold margarita when I really need it?


I turn UP the AC for the temperature to go down. :mrgreen:
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Postby Atarihero on Fri Jul 06, 2007 11:51 pm

Robinette wrote:So is the glass half FULL, or half EMPTY ???

If half the container has water, I have water. :wink:
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Postby rsuttles58 on Mon Jul 09, 2007 9:08 am

I've got a question along these lines. It's about dice odds.

So I was playing a game with friends last night who aren't the best of players.

I lost THREE battles where I was attacked by someone that had less troops than I had defending the territory.

1. The first one was just asinine. The guy attacked me in a 3v7 situation and WON without losing a single troop. He took that territory and then attacked with his 2 troops and broke my bonus on a territory behind it.

2. The other notable one was in a situation where I had 25 troops defending a territory and a guy attacked me with 18 troops. He won with 6 troops left over.

Did I just have the luck of the Jews here or are the odds really THAT much in favor of the attacker? My friends tried telling me that their attacking armies had the favorable odds when attacking in these situations. I actually called my girlfriend to make sure I wasn't losing my mind.
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Postby AAFitz on Mon Jul 09, 2007 9:25 am

rsuttles58 wrote:I've got a question along these lines. It's about dice odds.

So I was playing a game with friends last night who aren't the best of players.

I lost THREE battles where I was attacked by someone that had less troops than I had defending the territory.

1. The first one was just asinine. The guy attacked me in a 3v7 situation and WON without losing a single troop. He took that territory and then attacked with his 2 troops and broke my bonus on a territory behind it.

2. The other notable one was in a situation where I had 25 troops defending a territory and a guy attacked me with 18 troops. He won with 6 troops left over.

Did I just have the luck of the Jews here or are the odds really THAT much in favor of the attacker? My friends tried telling me that their attacking armies had the favorable odds when attacking in these situations. I actually called my girlfriend to make sure I wasn't losing my mind.


the 3 to 7 attack is very rare, but it does occasionally happen, the 18 to 24 is a very wise attack to make if you have nothing to lose....id much rather make the attack than let the 24 butcher my 18...
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Postby Grisle on Sat Jul 14, 2007 3:02 pm

alex_white101 wrote:well then, how come i attacked a 35 on 35 and ended 3 vs 25?!?!?!


You should have never let your armies get that low.
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Postby rondosocal on Fri Jul 20, 2007 12:30 am

Thank you. Excellent bit of data.
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cronus....

Postby calkid on Tue Jul 24, 2007 5:19 pm

if you are good at figuring out odds, i would like a breakdown of the odds when there is the same amount of armie on each territory. include the extra dice for the attatcker and the tie(WIN) for the defender. i would like to see a breakdown from 1vs 1 TO 15 vs 15 instead of just stating the odds. i want to know how you come up with that.
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Re: cronus....

Postby TipTop on Sun Jul 29, 2007 12:25 pm

calkid wrote:if you are good at figuring out odds, i would like a breakdown of the odds when there is the same amount of armie on each territory. include the extra dice for the attatcker and the tie(WIN) for the defender. i would like to see a breakdown from 1vs 1 TO 15 vs 15 instead of just stating the odds. i want to know how you come up with that.



Just use this http://gamesbyemail.com/Games/Gambit/BattleOdds
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Re: 11 on 11 is the last number where defender has advantage

Postby Cynther on Wed Jul 11, 2012 8:10 pm

Robinette wrote:
chessplaya wrote:
alex_white101 wrote:well then, how come i attacked a 35 on 35 and ended 3 vs 25?!?!?!

:lol: :lol: :lol: :lol: :lol: :lol: :lol:

he said a 50.4% chance to succeed




Which is also a 49.6% chance of failure...



So is the glass half FULL, or half EMPTY ???

For me it all depends on what's IN the glass...
If it's an Ice cold margarita, the glass is half FULL :)
If it's a tepid beer, the glass is definitely half EMPTY :(

Go now, and apply this lesson to your Risk strategy!


Well if he says the situation ended with 3 vs. 25, technically he didn't fail. He still has a possibility of winning the territory. It's all about believing =)
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Re: 11 on 11 is the last number where defender has advantage

Postby Campin_Killer on Thu Jul 12, 2012 10:10 am

Nice necro-bump...xD
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Re: 11 on 11 is the last number where defender has advantage

Postby Viceroy63 on Thu Jul 19, 2012 9:01 pm

Cynther wrote:
chessplaya wrote:
alex_white101 wrote:well then, how come i attacked a 35 on 35 and ended 3 vs 25?!?!?!

:lol: :lol: :lol: :lol: :lol: :lol: :lol:

he said a 50.4% chance to succeed


Well if he says the situation ended with 3 vs. 25, technically he didn't fail. He still has a possibility of winning the territory. It's all about believing =)


Believe what? That 3 troops can defeat 25?

Now I believe that am losing my mind. Can I call on some one's girlfriend please. Or some one offer me a half filled keg gar of Margarita. =)
:lol:

I guess that "Gambit" site help me to lose my mind as well. I can't figure out like it reads there. Attackers = 3. Defenders = 2. Rolls = 7776! My god man! From what planet does this come from. And watch out if there is a split? Lol.

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Re: 11 on 11 is the last number where defender has advantage

Postby Eddygp on Thu Dec 27, 2012 11:10 am

It only states the number of possible dice roll combinations with attack and defense. It is 6^5 which is indeed 7776. Check your maths, in CC they are very useful. I have created a formula to know whether I have a region correctly defended. I will only mention it involves a square root.
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Re:

Postby ZeekLTK on Tue Jan 08, 2013 2:00 pm

Grisle wrote:
alex_white101 wrote:well then, how come i attacked a 35 on 35 and ended 3 vs 25?!?!?!


You should have never let your armies get that low.



What is a general rule for a "cut off" point then?

26v25 - attacker still has the advantage, obviously keep going

24v25 - one bad roll, still have the overall advantage - keep going

20v25 - "well, I got some bad rolls but odds are that it will even out and I can still win this" - keep going

16v25 - really bad rolls, but odds are that it will "even out" and I'll get some rolls where I take 2 and lose 0 - keep going

11v25 - now it's looking shitty but this isn't a good position to leave yourself in - let the other play attack you 25+reinforcements v 11? Gotta keep going... 3v25 - damn!

So when would you stop?
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Re: 11 on 11 is the last number where defender has advantage

Postby mr. CD on Tue Jan 08, 2013 2:27 pm

Dice don't even out, that's not how odds work. It all depends on the circumstances, if it's a spot that needs to be broken, you might want to go on a little longer, if it doesn't 20v25 might be the moment to stop.
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Re: 11 on 11 is the last number where defender has advantage

Postby Gilligan on Tue Jan 08, 2013 5:35 pm

This is actually very useful information.
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Re: 11 on 11 is the last number where defender has advantage

Postby ZeekLTK on Wed Jan 09, 2013 12:24 am

mr. CD wrote:Dice don't even out, that's not how odds work. It all depends on the circumstances, if it's a spot that needs to be broken, you might want to go on a little longer, if it doesn't 20v25 might be the moment to stop.


Yes it is. Over a number of rolls, the odds of just one player winning EVERY roll diminishes greatly.

Take a coin flip, the odds that Player A wins is 50%.

But do the flip again. The odds that Player A wins TWICE in a row is only 25% (.5 * .5)

The odds that Player A wins THREE TIMES in a row is 12.5%.

Etc.

So, since rolls are similar to a coin flip (albeit more complex), you have to figure that if you are going to roll X times, the odds are extremely small that you are going to lose every single roll, and thus if you've already lost a handful of rolls, statistically you should start winning a few (that it will "even out"). To lose 11 times in a row (as the guy who went from 25 to 3 did) is not very likely at all.
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Re: 11 on 11 is the last number where defender has advantage

Postby ZeekLTK on Wed Jan 09, 2013 12:35 am

I mean, that's the whole premise of this thread - that the larger the armies involved, the more likely that the attacker will win BECAUSE the dice will "even out" in favor of the best odds.

If it's 25v25 (as in our example) you can reasonably expect to lose a handful of rolls in a row but still expect to win the attack overall because, as pointed out, starting at 25v25 gives you the overall advantage (a slight advantage, but one nonethless).

So it is reasonable to assume that even if I've lost 4-5 rolls in a row, eventually I should start winning some because odds are that I'm suppose to win overall, and how else am I suppose to win unless I start winning some rolls?
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Re: 11 on 11 is the last number where defender has advantage

Postby Robinette on Wed Jan 09, 2013 12:52 am

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Re: 11 on 11 is the last number where defender has advantage

Postby Viceroy63 on Fri Jan 11, 2013 8:02 am

When you think about it that is also the main premise in Trench Warfare settings. If you have a large stack that has to be approached, that is to say that the surrounding regions of your large stack also belong to you with only 1's on them, then your large stack has the advantage of striking the approaching force first. And so if you have more than just 11 troops then you have the advantage in the defense.

In regular settings your defensive stack would not have that advantage as the sweeping stack can cut across the game map and simply wipe out all large stacks with the 54% odds in the attackers favor. But in TW games the defender is the attacker and can even retreat (if possible) in order to maintain that attacker odds advantage in the defense of the position.

ZeekLTK wrote:So, since rolls are similar to a coin flip (albeit more complex), you have to figure that if you are going to roll X times, the odds are extremely small that you are going to lose every single roll, and thus if you've already lost a handful of rolls, statistically you should start winning a few (that it will "even out"). To lose 11 times in a row (as the guy who went from 25 to 3 did) is not very likely at all.


Actually when it come to the coin toss, I for one, can make the coin come out the same way every time or most of the time by controlling the circumstances or conditions of the toss. Catching the toss in mid-flight for example, at precisely the same interval each time and the same way each time helps. The starting position of the coin, whether it be heads up or down should also be the same each time. The pressure used on the coin by the thumb, exactly the same in each toss. This takes practice but can be achieved.
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Re: 11 on 11 is the last number where defender has advantage

Postby ZeekLTK on Thu Feb 21, 2013 5:08 pm

Viceroy63 wrote:Actually when it come to the coin toss, I for one, can make the coin come out the same way every time or most of the time by controlling the circumstances or conditions of the toss. Catching the toss in mid-flight for example, at precisely the same interval each time and the same way each time helps. The starting position of the coin, whether it be heads up or down should also be the same each time. The pressure used on the coin by the thumb, exactly the same in each toss. This takes practice but can be achieved.


Okay, but I was using the coin toss as an example of the dice on this site (which can't be influenced). If you are going to attack 11 times with 3v2 dice, it is not reasonable to expect to lose every single roll. Therefore, if you have lost 4-5 rolls in a row, it IS reasonable to expect to win a few of the next rolls, because odds of losing 3v2 every single time is not very high (especially the more times you roll). That was my point.

So, in the example we were using, the 25v3... if you've rolled enough to get down to say 17v3, why should you stop attacking? What are the odds that you will lose ANOTHER roll 0-2 when you've already lost 4 in a row? They are not very high, so you should keep rolling and expect to win soon. Such as the coin toss odds - if you've already lost 4 in a row, odds of losing another (5 in a row) is 3.13%, which means odds are 96.88% that you should win the next one. In the example about the 25v3, the odds of losing 22-0 (11 in a row) are 0.49% (if you assume each roll is 50/50, which they aren't, but for simplicity). Which means over 11 rolls, he had a 99.51% chance of winning at least ONE roll. Very unlucky for him, but it also means he did the right thing to keep attacking because he had such great odds of winning.
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Re: 11 on 11 is the last number where defender has advantage

Postby Viceroy63 on Thu Feb 21, 2013 5:57 pm

I was re-reading one of my earlier post and saw the error of my logic or my keyboard does not type my thoughts correctly. LOL. I had wrote...

Viceroy634 wrote:And so if you have more than just 11 troops then you have the advantage in the defense.


Correction: one never has the advantage in the defense no matter how many troops. But I do agree with that 11 troops vs. 11 troops, the Defender does have the very good possibility that he won't be conquered by the 11 attacking troops.

While I have personally conquered 11 troops with just a stack of 4 the percentage is probably less than 1% of the times. So for the most part the defender does usually break even or fairs better in that situation.
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Re: 11 on 11 is the last number where defender has advantage

Postby agentcom on Fri Mar 01, 2013 9:09 pm

ZeekLTK wrote:
Viceroy63 wrote:Actually when it come to the coin toss, I for one, can make the coin come out the same way every time or most of the time by controlling the circumstances or conditions of the toss. Catching the toss in mid-flight for example, at precisely the same interval each time and the same way each time helps. The starting position of the coin, whether it be heads up or down should also be the same each time. The pressure used on the coin by the thumb, exactly the same in each toss. This takes practice but can be achieved.


Okay, but I was using the coin toss as an example of the dice on this site (which can't be influenced). If you are going to attack 11 times with 3v2 dice, it is not reasonable to expect to lose every single roll. Therefore, if you have lost 4-5 rolls in a row, it IS reasonable to expect to win a few of the next rolls, because odds of losing 3v2 every single time is not very high (especially the more times you roll). That was my point.

So, in the example we were using, the 25v3... if you've rolled enough to get down to say 17v3, why should you stop attacking? What are the odds that you will lose ANOTHER roll 0-2 when you've already lost 4 in a row? They are not very high, so you should keep rolling and expect to win soon. Such as the coin toss odds - if you've already lost 4 in a row, odds of losing another (5 in a row) is 3.13%, which means odds are 96.88% that you should win the next one. In the example about the 25v3, the odds of losing 22-0 (11 in a row) are 0.49% (if you assume each roll is 50/50, which they aren't, but for simplicity). Which means over 11 rolls, he had a 99.51% chance of winning at least ONE roll. Very unlucky for him, but it also means he did the right thing to keep attacking because he had such great odds of winning.


This is not how probability works
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Re: 11 on 11 is the last number where defender has advantage

Postby Viceroy63 on Fri Mar 01, 2013 9:20 pm

Would you please elaborate on how Probability works?

Because I sort of agree with what ZealTK wrote. I just don't like doing deep math. LOL. :lol:
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Re: 11 on 11 is the last number where defender has advantage

Postby Kaskavel on Fri Mar 01, 2013 9:31 pm

His logic is completely wrong.
"and thus if you've already lost a handful of rolls, statistically you should start winning a few (that it will "even out")."
Wrong
"Such as the coin toss odds - if you've already lost 4 in a row, odds of losing another (5 in a row) is 3.13%, which means odds are 96.88% that you should win the next one. "
This is more than being just wrong and shows a serious misunderstanding of maths, probabilities and gameplay. If you ve already lost 4 times in a row, chances you lose a fifth one is still 50%, not 3%
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