The odds favour the attacker, if you play the odds right

[Fewnix]

There have been a lot of posts on CC about the odds favouring the attacker. The focus seems to be on scenarios where the attacker attacks a tert with two or more armies on it from a tert with at least four armies on it, so the attacker gets the equivalent of rolling three die while the defender only gets to roll two die, In the long run, say over a thousand attacks 3 v 2, td is the idea the attacker will succeed in taking the tert losing fewer armies, or possibly only a many armies as the defender, for a net gain.

What is missing from much of this analysis is that even when an attack starts 3 v 2 the odds often change. When the defender loses one or more armies in the first or subsequent attacks, we can have the equivalent of the attacker rolling 3 die while the defender only rolls 1. If the attacker loses armies in the first or subsequent attacks, we can have the equivalent of the attacker rolling only one or two die, while the defender rolls 2. Then many attacks, not only end, they start from a different set of odds than 3 v 2.


1) The best odds for taking a tert without loss of armies, or only losing as many armies as the defender, are attacking a singleton from a tert with at least four armies on it.The most likely outcome is the attacker will take the tert and the singleton army with the first attack army without losing any armies.

2) Starting from a tert with 4 armies attacking a singleton, there is a reasonable chance the attack will fail, you will not take the tert or the singleton army and will be out one army- a net loss for the attacker. You can try a second attack, where the odds are equivalent to rolling 2 die and the defender one. with the odds roughly even between the attacker failing to take the tert and losing two armies the defender none and the attacker taking the tert with the loss of only one army total and the defneder one army

3) By starting an attack on a singleton from a tert with 5 plus armies, the attacker has the option, if the odds don't break favourably on the first attack, of attacking a second time from the equivalent of rolling 3 die with the defender only gets to one. In this second atack scenario, the most likely outcome is the attacker takes the tert and the singleton army with the loss of only one army.

Conclusion: the best scenario for a winning attack , defined as taking the tert and losing less or just as many armies as the defender, is an attack on as singleton from a tert with at least 5 armies on it.
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The second best scenario for a winning attack, defined as taking the tert and losing less or just as many armies as the defender is an attack on a doubleton from a tet with at least 5 armies on it. that should be covered in a separate post. Comments welcome

[anonymus]

I'm sorry but that's just stupid.. In the conclution the best odds for winning would be taking a single terr with an attacking force of say 600 if the goal is just to win..
Attacking 3v2 is suicide as it will leave you 1v2 if you fail.. And don't forget defending dice gets the edge in the case of a draw..
Going 3v1 can be done but makes no big sence unless you will drop your opponent from 12 to 11, 15 to 14 or similar case (or clearing a key area making it safe)

4v3 is not great odds but dropping 1's on 3 of your regions adjacent to a 3 makes 2+2+2 2v2 rolls and makes some sense in case you need a card early in game (as opposed dropping 3 ona 3 getting 1 3v2+ 1 2v2 roll in case of fail)

Anyhow I don't know if I make sense with this I just felt your conclution attacking 1's with a lot of troops rather than 2's with Only some troops is a truism and really not much help to anyone reading your analysis.. If you want to see odds of a string of attacks to succed either download assume odds or crack out the old pen and paper and do the math..

(me I used to use assultodds but now go by experience/guts unless important game but I'm sure farang or cof would crack out the calculator (or guts/experience in normal games before making a move..) as would chuuuk or similar players before sweeping the board in a feudal game..

Conclution; I agree with OP that given the choose attack small stacks with big stacks, however I disagree with OP on the point where this article would actually help anyone..


Kindest regards
/

[Fewnix]

Hoping people find this thread amusing, if not instructive, I would like to continue with the argument that The second best scenario for a winning attack, defined as taking the tert and losing less or just as many armies as the defender is an attack on a doubleton from a tet with at least 5 armies on it.6 would be better.

To stat we should consider that an attack on a terr with 2 armies on it from a tert with only 4 armies on it is not likely to yield a good result- defined a taking the tert and/or losing fewer or as many armies as the defender.

There are three possible outcomes from a 4 v 2 attacks, each relatively equally likely.

1) the defender loses 2 armies the attacker none. giving us a clear win for the attacker taking the tert and the two defending armies without a single loss

2) the defender loses one army, the attacker one giving us a possible second attack from a tert with 3 armies on it on a tert with one 1. The odds are y equivalent to rolling two die against one, tie to the defender, which should mean roughly equal odds of the attacker succeeding or failing. Succeeding is taking the second, last army, for a net loss of only one army to take two and a gain of the tert. Failing is the attacker losing another army, for a net loss of two armies, having taken only one army and not taking the tert. T his failure leaves the attacker with only 2 armies on the tert, facing a defender with one army / A third attack would be equivalent to 1 v 1, tie to the defender. with the odds being the attacker would end up with a net loss of 3 armies, no tert and having taken only one army of the defender.So the second outcome of a an attack from a tert with 4 armies on it on a tert with 2 armies, is not a good one for the attacker.

The third, equal likely outcome of an attack with 4 armies on a tert v a tert with 2 is the attacker loses 2 armies and the defender none. This leaves a 2 v 2 situation where a second attack id equivalent to rolling one die against a defender rolling 2, tie to the defender- a losing proposition.

So of the 3 possible outcomes on a first attack from a tert with 4 armies on it to a tert with two armies, only one outcome - the defender loses two armies , the attacker none, looks good for the attacker.
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But see how the outcomes changes with the attacker having 5 against 2.

There is still the possibility of the defender losing two, attacker none, a clear victory.

But now the possibility of the defender losing one, attacker one ,gives us the attacker with 4 on the tert and the defender one, discussed in the first post as a good one for the attacker.The odds are the attacker can now, with the equivalent of rolling three die and the defender one, take the second, last remaining army without losing any more armies and take the tert with a net loss of only one army. to the defenders loss of two.

Of course there is still the third possible outcome of an attack on a doubleton from a tert with only 5 armies-the attacker loses two and the defender none leaving the attacker with a tert with 3 armies on and the defender 2. a second attack here would be equivalent to a 3 v 2 die, tie to the defender, and is not likely to succeed

Which lead to the conclusion that, second best to an attack on a singleton from a tert with 5 armies on it, is a attack on a doubleton from a tert with 5+ (preferably 6) armies on it. That is, if your goal is to take a tert losing fewer or at least only as many armies as the defender

If people find this amusing I would be willing to continue the by concluding that in attacking a tert with three or more armies on it, you are best off by starting with at least 6 armies and stopping when down to 3 armies- the "soft attack". That is, if your goal is to, over the long run, take terts losing fewer or at least as many armies as the defender.




.

[Wolffystyle]

I'd like to add even more strategy; please allow me.

14) Attacking with a spiked die will provide the attacker with his/her best outcome. When you roll dice with pointy spikes protruding, you have a much greater probability (43.3%) of defeating your opponent. Most of these defeats (79.4%) come in the form of scaring your opponent shitless followed by the forfeiting phrase; "I quit if I must play with someone who carries pointy dice in their pockets." 20.5% of the increase in winning likelihood results from rolling the pointy dice into your opponent's eyeball. Your opponent will no longer be able to see the board well and this will increase your odds of winning. The final .1% increase results from increased profits to pointy-dice manufacturers and wholesalers which leads to greater movements of commerce which leads to US politicians use of less political capital to push bills and use of more political capital to help you win your game.

78). Roll with 27 dice instead of 3. The odds will be more greatly in your favor if you roll 27 attacking dice instead of 3. I don't need to verify this with mathematical proof, just accept it as law.

122). Throw your attacking dice at your opponent's face. See rule 14, section 2. (use in conjunction with rules 14 AND 78 for best outcomes!)

414). Do not eat Italian hoagies while rolling your dice. You will be drawn into your sandwich and may forget about rolling entirely. Also, if you do remember to roll, the sandwich's oil may cause you to roll erratically.

[BYUwonder11]

I'd like to add even more strategy; please allow me.

14) Attacking with a spiked die will provide the attacker with his/her best outcome. When you roll dice with pointy spikes protruding, you have a much greater probability (43.3%) of defeating your opponent. Most of these defeats (79.4%) come in the form of scaring your opponent shitless followed by the forfeiting phrase; "I quit if I must play with someone who carries pointy dice in their pockets." 20.5% of the increase in winning likelihood results from rolling the pointy dice into your opponent's eyeball. Your opponent will no longer be able to see the board well and this will increase your odds of winning. The final .1% increase results from increased profits to pointy-dice manufacturers and wholesalers which leads to greater movements of commerce which leads to US politicians use of less political capital to push bills and use of more political capital to help you win your game.

78). Roll with 27 dice instead of 3. The odds will be more greatly in your favor if you roll 27 attacking dice instead of 3. I don't need to verify this with mathematical proof, just accept it as law.

122). Throw your attacking dice at your opponent's face. See rule 14, section 2. (use in conjunction with rules 14 AND 78 for best outcomes!)

414). Do not eat Italian hoagies while rolling your dice. You will be drawn into your sandwich and may forget about rolling entirely. Also, if you do remember to roll, the sandwich's oil may cause you to roll erratically.

As a member of EMPIRE along with Wolffy allow me to say that this is the best advice that could be offered, especially if #122 is used with the spiked die, deeper wounds emotionally and physically are produced with this. Also, I hear playing this game roaring drunk while not as efficient, long term makes this more enjoyable since you are not worried about the outcome of a few rolls since you won't remember them anyways

[Fewnix]

Thank you anonymus for your post. For this discussion, I define winning narrowly, as taking the tert attacked losing fewer armies than the defender or at least only as many armies as the defender . There is a totally separate discussion possible about situations where it might be worth losing a lot more armies than the defenderl loses, in order to take a valuable tert ( say one that gives you a bonus).


So by this definition the best play for winning attacks the best chance to take a tert losing fewer armies than the defender , are attacking singletons from terts with at least 5 armies and stopping if you are down to 3 armies and have not taken the tert. In the long run, say 100 times you attacked singletons from terts with at least 5 armies and stopped when down to three armies,, you would probalbly end up taking over half the attacked terts and over 50 defenders armies, losing less than 50 armies.

The second best play for winning attacks, by this definition, is attacking doubletons from terts with at least 6 armies and stopping if you are down to 3 armies and have not taken the tert. From 100 such attacks you should end up taking half the terts and . over 10 of the defenders armies , losing less than 100 armies.

I was going to do a third post about the best way to play attacks on terts with 3 or more armies on it.For now lets ust say that to take a tert with 3 or more armies on it, you are best to start from a tert with 6+ armies on ,stop when down to 3 and realize the odds are about even in the long run, yo and the defneder will probably lose about the same amount of armies. sepaarte discussion.

I'm sorry but that's just stupid.. In the conclution the best odds for winning would be taking a single terr with an attacking force of say 600 if the goal is just to win..
Attacking 3v2 is suicide as it will leave you 1v2 if you fail.. And don't forget defending dice gets the edge in the case of a draw..
Going 3v1 can be done but makes no big sence unless you will drop your opponent from 12 to 11, 15 to 14 or similar case (or clearing a key area making it safe)

4v3 is not great odds but dropping 1's on 3 of your regions adjacent to a 3 makes 2+2+2 2v2 rolls and makes some sense in case you need a card early in game (as opposed dropping 3 ona 3 getting 1 3v2+ 1 2v2 roll in case of fail)

Anyhow I don't know if I make sense with this I just felt your conclution attacking 1's with a lot of troops rather than 2's with Only some troops is a truism and really not much help to anyone reading your analysis.. If you want to see odds of a string of attacks to succed either download assume odds or crack out the old pen and paper and do the math..

(me I used to use assultodds but now go by experience/guts unless important game but I'm sure farang or cof would crack out the calculator (or guts/experience in normal games before making a move..) as would chuuuk or similar players before sweeping the board in a feudal game..

Conclution; I agree with OP that given the choose attack small stacks with big stacks, however I disagree with OP on the point where this article would actually help anyone..


Kindest regards
/

[firsal901]

This may seem as a small entry in your massive book, but do remember that if there is a tie, the defender wins, therefore making the odds even. It boils down to numbers and luck (1000 troops don't do anything if the dice screw you over).

[Timminz]

When given only two options: attack, or be attacked, it is always best to attack as long as you have at least 4 troops.

[firsal901]

When given only two options: attack, or be attacked, it is always best to attack as long as you have at least 4 troops.

That really depends on the situation, whether its getting a card or staying alive,

[Geger]

When given only two options: attack, or be attacked, it is always best to attack as long as you have at least 4 troops.

That really depends on the situation, whether its getting a card or staying alive,

I agree with Timminz, even to stay alive, it's better to attack (of course as long you have at least 4 troops).

Take a look at this example : You has only 1 region with 2 troops and your only neighbor has 3 troops (he failed to take you out in the last turn). Now is your turn and you can drop 3 troops. You know the neighbor will attack you in the next turn and he can add 5 more troops (because he has more regions). What would you do, attack him or only drop? And 1 addition : behind the region with 3 troops he has only 1's.

[Timminz]

When given only two options: attack, or be attacked, it is always best to attack as long as you have at least 4 troops.

That really depends on the situation, whether its getting a card or staying alive,

In the situation I outlined, it only depends in a very small number of possibilities. For example, if you've got 4, next to a 1 or 2, and there's a large stack just behind it that wouldn't otherwise be able to attack you, my advice does not apply.

Other than that case, I stand by my earlier statement.

[firsal901]

I agree with Timminz, even to stay alive, it's better to attack (of course as long you have at least 4 troops).

Take a look at this example : You has only 1 region with 2 troops and your only neighbor has 3 troops (he failed to take you out in the last turn). Now is your turn and you can drop 3 troops. You know the neighbor will attack you in the next turn and he can add 5 more troops (because he has more regions). What would you do, attack him or only drop? And 1 addition : behind the region with 3 troops he has only 1's.

Hmm.... now that you put it that way, what if YOU lose the attack, you'd be screwed. If you don't attack, there's still a chance you will survive (like 10%, but theres a chance).Plus, in games, there is no "Post- war" effort , so you cant just screw with him at the end, cause it wont matter. I'd rather defend.


But, attacking all the way to the 1's may keep me alive, but more often than not, that is not the case.

[Geger]

I agree with Timminz, even to stay alive, it's better to attack (of course as long you have at least 4 troops).

Take a look at this example : You has only 1 region with 2 troops and your only neighbor has 3 troops (he failed to take you out in the last turn). Now is your turn and you can drop 3 troops. You know the neighbor will attack you in the next turn and he can add 5 more troops (because he has more regions). What would you do, attack him or only drop? And 1 addition : behind the region with 3 troops he has only 1's.

Hmm.... now that you put it that way, what if YOU lose the attack, you'd be screwed. If you don't attack, there's still a chance you will survive (like 10%, but theres a chance).Plus, in games, there is no "Post- war" effort , so you cant just screw with him at the end, cause it wont matter. I'd rather defend.



But, attacking all the way to the 1's may keep me alive, but more often than not, that is not the case.

Correct, the chance to eliminated would be bigger if the attack failed. But the chance to fail is only 33,58%. What if you win or split. Let's do a little math. We can use this http://gamesbyemail.com/Games/Gambit/BattleOdds as a tool :

Drop Only
Next turn : enemy has 8 troops (7 troops to attack) and we have 5. The chance being killed is 73,64%. Or we can say the chance being survive is 26,36% (more than you tought)

Attack as long we have at least 4 troops
a)Attack fails. Chance = 33,58%. Next turn enemy has 8 troops, we have 3. The chance being killed : 90,99%. Also total : 30,55%

b)1st attack draws, 2nd attack fails. Chance = 29,26% * 33,58% = 9,83%. Next turn enemy has 7 troops, we have 2. The chance being killed : 93,40%. Also total : 9,18%

c)1st and 2nd attack draw. Chance = 29,26% * 29,26% = 8,56%. Next turn enemy has 6 troops, we have 3. The chance being killed : 76,94%. Also total : 6,59%

d)1st attack draws, 2nd attack wins >> capture the region, split the troops to 2,2. Chance = 29,26% * 37,17% = 10,88%. Enemy has now 5 troops to attack these 2 regions. The chance being killed : 51,24%. Also total : 5,57%

e)1st attack wins, 2nd and 3rd attack fail. Chance = 37,17% * 34,03% * 34,03% = 4,30%. Next turn enemy has 6 troops, we have 3 (like case c). The chance being killed : 76,94%. Also total : 3,31%

f)1st attack wins, 2nd attack fails. 3rd attack wins >> capture the region, split the troops to 2,2. Chance = 37,17% * 34,03% * 65,97% = 8,34%. Enemy has now 5 troops to attack these 2 regions (like case d). The chance being killed : 51,24%. Also total : 4,28%

g)1st and 2nd attack win >> capture the region, split the troops to 2,3. Chance : 37,17% * 65,97% = 24,52%. Here the chance being killed only 38,27%. Also total : 9,38%

Those are all possibilities. And we can add all together and become the chance being killed = 68,86%. Or the chance to survive is 31,14%. See, 5% better than drop only.

CMIIW with my calculation

Note : this case we can find in 1vs1 doodle earth no spoils

Drop only is only good in the case like this, if we have more than 1 neighbor.

[firsal901]

Correct, the chance to eliminated would be bigger if the attack failed. But the chance to fail is only 33,58%. What if you win or split. Let's do a little math. We can use this http://gamesbyemail.com/Games/Gambit/BattleOdds as a tool :

Drop Only
Next turn : enemy has 8 troops (7 troops to attack) and we have 5. The chance being killed is 73,64%. Or we can say the chance being survive is 26,36% (more than you tought)

Attack as long we have at least 4 troops
a)Attack fails. Chance = 33,58%. Next turn enemy has 8 troops, we have 3. The chance being killed : 90,99%. Also total : 30,55%

b)1st attack draws, 2nd attack fails. Chance = 29,26% * 33,58% = 9,83%. Next turn enemy has 7 troops, we have 2. The chance being killed : 93,40%. Also total : 9,18%

c)1st and 2nd attack draw. Chance = 29,26% * 29,26% = 8,56%. Next turn enemy has 6 troops, we have 3. The chance being killed : 76,94%. Also total : 6,59%

d)1st attack draws, 2nd attack wins >> capture the region, split the troops to 2,2. Chance = 29,26% * 37,17% = 10,88%. Enemy has now 5 troops to attack these 2 regions. The chance being killed : 51,24%. Also total : 5,57%

e)1st attack wins, 2nd and 3rd attack fail. Chance = 37,17% * 34,03% * 34,03% = 4,30%. Next turn enemy has 6 troops, we have 3 (like case c). The chance being killed : 76,94%. Also total : 3,31%

f)1st attack wins, 2nd attack fails. 3rd attack wins >> capture the region, split the troops to 2,2. Chance = 37,17% * 34,03% * 65,97% = 8,34%. Enemy has now 5 troops to attack these 2 regions (like case d). The chance being killed : 51,24%. Also total : 4,28%

g)1st and 2nd attack win >> capture the region, split the troops to 2,3. Chance : 37,17% * 65,97% = 24,52%. Here the chance being killed only 38,27%. Also total : 9,38%

Those are all possibilities. And we can add all together and become the chance being killed = 68,86%. Or the chance to survive is 31,14%. See, 5% better than drop only.

CMIIW with my calculation

Note : this case we can find in 1vs1 doodle earth no spoils

Drop only is only good in the case like this, if we have more than 1 neighbor.

First off all, i don't get the math, but i get the fact its better to attack that to defend.
Second, I do remember that in TIES, the defenders win. Did you put that into account?

[Dukasaur]

First off all, i don't get the math, but i get the fact its better to attack that to defend.
Second, I do remember that in TIES, the defenders win. Did you put that into account?

Yes, that was already factored-in to the basic numbers he posted.

[firsal901]

Then I stand corrected

[Commander62890]

When given only two options: attack, or be attacked, it is always best to attack as long as you have at least 4 troops.

Exactly.