Situation:
-You have access to all territories (3-5) to complete the bonus (+5 income), and it is protected from the enemy, meaning they don't have any access to the bonus or its borders.
-Neutrals are 2, Standard Luck Settings.
-You have enough income to cover filling out the bonus, but would rather expend your armies elsewhere (fighting, expansion, etc)

Question:
What is the most efficient way to fill the bonus, balancing getting the bonus with the fewest armies and least turns?

Observations:
-I've tried attacking 4v2 everywhere, but ultimately find that at least one of the attacks fails, making it as good as useless for the next turn.

See Table 1 for Percentage of Success when attacking X territories with 3 or 4 armies.

X

(Sorry, Misposted too early)

Table 1:
X 3v2 4v2 5v2
3 31% 66% 86%
4 21% 57% 82%
5 14% 50% 77%
6 10% 43% 74%

So, when attacking more territories, you success rate of filling the bonus goes down.

Tactic 1:
While going 5v2 everywhere has the highest odds, armies are scarce, and this often times leaves extra men behind the line, and for a +5 bonus, isn't worth leaving 5 men behind the scenes.

So, I've taken to going 3v2 everywhere. I find this wins over the majority of the territories and weakens the ones it doesn't take.

Then, Next turn, I finish off the remainder if I didnt' get it. I find that when attacking 5 territories to complete the bonus, I save 5 armies up front as a trade off of having a 50% chance to complete the bonus on turn one down to a 14% chance.



The floor is open for more tactics/observations to further develop this thought/strategy.

Well I don't know much about how the luck percentages work or anything like that, but I advise attacking each with 3, as most will be taken, and then next turn finish taking it, using other armies to fight elsewhere. If you are playing with 75% luck you can never try and secure a bonus, especially if you need to take more than 2 territories to finish it that turn.

It entirely depends on the situation. If you just had enough to do 4v2 or 5v2 then I would suggest doing 3v2s and get it in 2 turns. It's important that you don't lose turns to get the next bonus. If, however, you have more than enough I see no reason why not to go 4v2. Chances are higher and if you have armies left, you can use them after to delay turns which is crucial to some moves.
With 5v2 I don't know. Depends on the situation I guess. Usually not.

Sorry, by try and secure a bonus, I mean that you cannot count on it happening, because of the variety of luck you can never expect it to happen, just wish it works :D

For Luck Calculations, I just raise the $age of probability to the power of number of territories, using 68% for 3v2 and 87% for 4v2.

Example: 4 territories 3v2 probability = 0.68 x 0.68 x 0.68 x 0.68 = 0.21 = 21%

When am at war i use 3v2 and 4v2 and last territory however no war am in i use 4v2.

John, while that is the right way to do it, it has zero to do with luck percentage. The luck percentage impacts the initial percentage (the .68 in your example)

The listed examples are why I loathe 75% luck games and rarely if ever play them

I'm glad I'm not the only person with the solution of lowering the luck percent. With a lower luck percent the solution is to always go 3v2 in cases where there are lots of territories to grab and/or troops are needed elsewhere, and 4v2 is the go-to choice if troops are plentiful or there aren't many places to attack.

My biggest problem with 75% luck in this scenario is that you need something like 13 or 14 troops per territory to guarantee (and around 7 per territory to have an overwhelming chance to win each attack) that you get all of them. Going 4v2 or 5v2 are almost certainly going to leave you without the bonus if you need to attack more than 3 spaces. I would say that 4v2 still leaves you with an unacceptable failure rate for even going after 2-3 territories. I would go 4v2 on all of them, then go for the remaining ones the following turn, as necessary. 3v2 will, too often, result in cases where you lose 1-2 and kill 0, putting you right back where you were. Though this is possible with 4v2, it's less likely. Hopefully with 4v2, you can use leftover troops to hit the other spaces that you fail to take as well, to lessen the burden. If you are trying to save a certain number of troops to use elsewhere, then it might be prudent to 3v2 to territories you can hit with leftover troops the following turn.

If you don't care about how many turns it takes, it might make more sense to send in half as many larger groups of 7v2, which is reasonably close to guaranteed, and then followup from each of the newly conquered locations into the remaining.

75% sometimes is really cruel, made me lose a 8vs2 today :/

For a while about a year ago I was helping a guy with a variation that involved 75% luck and really high incomes. I lost more than one 10v2 trying to expand.

7v2 was the breakpoint where I didn't feel like the luck percent was really holding me back, but I still lost a fair number of those attacks. 6v2 or less and I lost an unacceptable number of attacks.

Meh attack 10 around and 5 southern