Conquer Club

Hi there, while trying to spice up my gameplay with a bit of science, I noticed that there's a lot of confounding info about that and a lot of sub-par odds calculators out there.

So I decided to calculate everything myself - and in the process put together an article about all single-attack probabilities. The article shows a couple of formulaic expressions (and how they were derived) for fast dice odds computation, and summarizes the results for all the usual attack configurations (see the table at the bottom of the page).

Sadly, for some attack configurations I could not derive a formula, so I have determined the odds via an exhaustive lookup function. Both the formulae and the lookup function are also published in this script - should others want to try and replicate the results, or find out how odds would look like for different attacker or defender caps or dice side numbers.

Your formulas are too complex!

The chance the defender wins in :

• 1 dice vs 1 dice = (1+2+3+4+5+6)/6^2
• 2 dice vs 1 dice = (1^2+2^2+3^2+4^2+5^2+6^2)/6^3
• 3 dice vs 1 dice = (1^3+2^3+3^3+4^3+5^3+6^3)/6^4

Damn, this forum doesn't support latex, I could make them simpler

My formulas are exactly what you wrote there - only with a shorter notation and generalized for s dice sides and a attackers. The long part before the final expressions is just the way I derived them

Also, since the defender never makes the decision whether to be attacked, victory probabilities are better given for the attacker.

I also did a calculator using excel generation of random numbers for the dice rolls. My results showed an average 54.5 % advantage to the attacker. Then I got into the following situation which just about confirms my excel calculations:

I’m in a, what seems to be marathon, trench, escalating, no reinforcement game. The next set of cards is worth 143,495 troops! I’ve kept track of my last 15 “massive” attacks, and here are the statistics:

Average attack size: 108,398. Average loss 96,371
Average defend size: 163,546. Average loss 118,132
The lowest percentage advantage to the attacker was 51.23%, the highest was 58.48% and the average was 55.02%.

For small attacks of a hundred or so, anything can happen, at 100,000 or more the attacker always seems to have the advantage and on average the defender will lose 55 troops for every 45 troops that the attacker loses.

Pardon me while I jump on my soap box “again”!

This game is why I made a lot of posts in the Semi-Auto Assault suggestion thread, http://www.conquerclub.com/forum/viewtopic.php?f=4&t=195316, with no luck yet! When stacks get this large it is “impossible” to make strategic assaults. You can’t assault a large stack of 5,000 or more and try to knock it down to just a few troops while leaving a larger stack against it. An auto-assault will knock down the opponent to zero so you capture the region and unblock any other troops behind it. And you can’t make 5,000 single assaults in the 3,600 second time limit for a single move!

The original complex suggestion in that thread was made in 2006 for a complex fix to make it easier to do things. This was way before trench warfare which is what has created the “impossible” situations due to the larger escalating stacks in trench games. A simple suggestion was made in September 2013 that would solve the problem, but it has been ignores so far!

Again, this is not to make the game easier, it is to make impossible situations possible.

Would a cap on total troops work?