Rehashing that good ol' Attack and Defend Odds thing.

[stonebergftw]

As opposed to the complicated discussion http://www.majorcommand.com/forums/threads/1707-Attack-and-Defend-odds, let's assume a couple things and go from there:

1) There are no special circumstances, such as busting an opponents bonus, or completing a continent bonus for yourself.
2) Optimal strategy when attacking, is to attack with >3 attackers and to stop when your attackers <4.

Agree with point 2 or not, for the sake of argument, lets roll with it.

I'm going to write a program to simulate 100,000 rolls and post the results of the following 2 things:
1) The statistical chances of the following cases happening with an infinite number of attacking and defending troops, to give raw data on any single dice rolling sequence.
1a) 0 attacking armies die and 2 defending armies die
1b) 1 attacking army dies and 1 defending army dies
1c) 2 attacking armies die and 0 defending armies die

and 2) The statistical chances of x attacking armies completely taking over a territory with y defending armies, up to a variation of 50 armies in each territory, keeping in mind rule #2. *Note* I probably can't do 100,000 rolls for each of these scenarios. I have no idea how fast my PC is going to kick this data out, no matter how simple the program might be.

3) Same thing as the last, but disregarding rule #2.

I'll try to complete this by the end of the weekend and post the results. No promises on time frame though, as I have a project launch on the 15th, and a ton of work to do on it before then.

 

[Evan]

If you want, you can get 25k+ real roll combinations from MC historicals here:
http://www.majorcommand.com/DiceLog.csv

 

[Robinette]

ohhhh.... nice...
can't wait to see what you come up with stoneberg...

 

[giuppi]

If you want, you can get 25k+ real roll combinations from MC historicals here:
http://www.majorcommand.com/DiceLog.csv

That's a minegold!


EDIT: i see only games 307-439 in there. are the others available as well?

 

[stonebergftw]

The results for 4 or more attackers vs 2 or more defenders are in as follows: (3 dice vs 2 dice)

After 250,000 rounds of dice rolls, the following took place:
Attacker Killed 2, Defender killed 0: 92786 times or 37.1144 of the time.
Attacker Killed 1, Defender killed 1: 83817 times or 33.5268 of the time.
Attacker Killed 0, Defender killed 2: 73397 times or 29.3588 of the time.

I'd have run a million, but it maxed my server's PHP processing time of 30 seconds. At any rate, after running, and rerunning the test, the percents never change by more than a tenth of a percent, meaning that with such a giant result set, you can once and for all state the case that the percents to the hundredth place are certainly non-essential Robinette.

More results to come. Also, source code will be linked up for anyone interested when I'm done.

 

[giuppi]

I'm going to write a program to simulate 100,000 rolls and post the results of the following 2 things:
1) The statistical chances of the following cases happening with an infinite number of attacking and defending troops, to give raw data on any single dice rolling sequence.
1a) 0 attacking armies die and 2 defending armies die
1b) 1 attacking army dies and 1 defending army dies
1c) 2 attacking armies die and 0 defending armies die

without running the simulation, I expect:
1a) 37.17% (or around 37,170 out of 100,000 rolls)
1b) 33.58%
1c) 29.26%


As for point 2, I created the attached table long time ago, it's just a subset of what you want to do, but it gives the idea.


And apologies for making the other thread too complicated...



EDIT: if anybody's wondering, those percentages come from here, which is the same link Incandenza posted in the other thread. Just look at the first row of the table at the bottom of the page, where it says "Basic Battle Odds", right hand side.

 

[Badorties]

If you want, you can get 25k+ real roll combinations from MC historicals here:
http://www.majorcommand.com/DiceLog.csv

dude! you are giving away our secrets!

 

[stonebergftw]

The next part, where I run odds of complete takeover depending on armies in each country, will be pretty tight. I'm still finding time to do it though.

 

[Robinette]

The results for 4 or more attackers vs 2 or more defenders are in as follows: (3 dice vs 2 dice)

After 250,000 rounds of dice rolls, the following took place:
Attacker Killed 2, Defender killed 0: 92786 times or 37.1144 of the time.
Attacker Killed 1, Defender killed 1: 83817 times or 33.5268 of the time.
Attacker Killed 0, Defender killed 2: 73397 times or 29.3588 of the time.

I'd have run a million, but it maxed my server's PHP processing time of 30 seconds. At any rate, after running, and rerunning the test, the percents never change by more than a tenth of a percent, meaning that with such a giant result set, you can once and for all state the case that the percents to the hundredth place are certainly non-essential Robinette.

and now, let's make this even MORE simple...

Using your numbers above, we can calculate that for every 13 attacks one should only expect a ONE army advantage over the enemy. lol, "An ARMY OF ONE"

In other words, instead of there being 13 casualties on both sides, ONE enemy troop will die in place of one attacking troop every 13 rolls.

suddenly the attacker advantage doesn't look so large...

 

[stonebergftw]

and now, let's make this even MORE simple...

Using your numbers above, we can calculate that for every 13 attacks one should only expect a ONE army advantage over the enemy. lol, "An ARMY OF ONE"

In other words, instead of there being 13 casualties on both sides, ONE enemy troop will die in place of one attacking troop every 13 rolls.

suddenly the attacker advantage doesn't look so large...

Like in poker, you have to remember that a 4% advantage usually means that in the long run, it's the right move to put you're chips in. Though small, it seems that it is always the correct move to attack and NOT defend, IF you are positive that the enemy WILL attack you the next turn.

 

[Robinette]

Like in poker, you have to remember that a 4% advantage usually means that in the long run, it's the right move to put you're chips in. Though small, it seems that it is always the correct move to attack and NOT defend, IF you are positive that the enemy WILL attack you the next turn.

there is probably a greater statistical chance that your opponent will outright MISS his turn, lol...

and here is the full mathematical formula to prove what i'm saying:
4.0001% attacker advantage < opponent missing turn

hehee