Combat Odds to Consider

[ethan]

I did some quick Excel simulations of combats to give a better sense of the "odds" of winning various combinations. I have found this quite surprising as what might seem small advantage often turn out to be quite significant when looking at the combat overall.

A 4 dice vs 4 dice combat with one side superior the other side average, no net POAs:

Superior Wins: 45%
Average Wins: 29%
Draw 26%

A 4 dice vs 4 dice combat, one side superior the other side superior with general, no net POAs:

General wins: 48%
Superior wins: 24%
Draw: 28%

8 dice vs 8 dice, one side superior one side with general, no net POAs

General wins: 51%
Superior wins: 29%
Draw: 20%

So what I took away is that what seems a pretty small advantage , re-rolling one extra number turns a 50-50 combat into a 3 to 2 or better advantage.

[dave_r]

And how long has it taken you to work this out?

[hammy]

It's not that hard Dave.

I have a spreadsheet that will let you work out all sorts of odds with a bit of work. The trouble is that while you can calculate the exact odds there really is little point and playing by gut feel works a lot better.

I played a game on Tuesday and one of my LH bow/sword BGs shot an enemy LH jav/lt sp BG disrupted. I could have shot again but it would have been an even fight and needed a long shot for me to even force a test (1 in 4 chance with 2 dice) so instead I trusted to close combat and my swordsman capability and charged. The enemy LH were less than 1 MU away so decided to stand.

One impact and melee round later my light horse were routing with a base missing

[babyshark]

8 dice vs 8 dice, one side superior one side with general, no net POAs

<snip>

General wins: 51%
Superior wins: 29%
Draw: 20%

Shouldn't this one turn out even, as the general gives the average (I presume) troops the same re-roll as the superiors?

Interesting results. Is the re-rolling worth more than a POA?

Marc

[ethan]

8 dice vs 8 dice, one side superior one side with general, no net POAs

<snip>

General wins: 51%
Superior wins: 29%
Draw: 20%

Shouldn't this one turn out even, as the general gives the average (I presume) troops the same re-roll as the superiors?

Interesting results. Is the re-rolling worth more than a POA?

Marc

Sorry if I wasn't clear it is a General+Superior vs. Superior (or Elite vs. Superior).

[philqw78]

Sorry if I wasn't clear it is a General+Superior vs. Superior (or Elite vs. Superior).

Then you also need to consider the chance of passing CT's, which can, in effect, turn a loss into a draw. Superior and generals add a lot to this.
But unfortunately not the death roll.
And then the chance that the general dies, doing the opposite and taking surrounding BG with him.

[ethan]

Sorry if I wasn't clear it is a General+Superior vs. Superior (or Elite vs. Superior).

Then you also need to consider the chance of passing CT's, which can, in effect, turn a loss into a draw. Superior and generals add a lot to this.
But unfortunately not the death roll.
And then the chance that the general dies, doing the opposite and taking surrounding BG with him.

Would be nice, but baby steps.

[dave_r]

It's not that hard Dave.

I have a spreadsheet that will let you work out all sorts of odds with a bit of work. The trouble is that while you can calculate the exact odds there really is little point and playing by gut feel works a lot better.

That's not what I meant. What I meant was the startling revelation that if you make troops better then they win more. My rule of thumb is that a quality advantage equates to half a POA.

I certainly surprised Spike the other week when my Knights charged his Poor Legionnaires behind Fortifications. Double minus at impact and evens in melee. I reckoned that I had a 1.5 POA advantage over the Wickedly Wascaly Woman's so would slaughter them. And so it proved.

[ethan]

That's not what I meant. What I meant was the startling revelation that if you make troops better then they win more. My rule of thumb is that a quality advantage equates to half a POA.

Fair enough, but how much better was really the question I was trying to answer. Looking at the troops in isolation on a per file basis does not give the big picture of the overall effect IMO.

Four dice of average needing 4s to hit will, on average, score 2 hits.
Four dice of superior needing 4s to hit will, on average, score 2 1/3 hits.

So the superior are (2 1/3)/(2) = (7/3)/(6/3)=7/6=16% better right? No they are twice as likely win. That to me at least was something I hadn't fully realize until I simmed it out.

Average fighting it out with one side having a POA gives something like:

POA Wins 56%, No POA Wins 20%, Draw 24%

So a full POA vs. even POAs and superior only gives about an 8% additional boost. Interestingly being Superior vs. Opponent with a POA (and average) doesn't help much the POA still wins about 51%.

Being Elite vs a POA gets it closer but the advantage is still with the POA. The POA wins 41%, Elite wins 29% and there is a Draw 30%

This all makes sense given that the side with more expected hits per die wins, it just gets magnified quite a bit when looking at actual outcome probabilities.

[spikemesq]

It was my understanding that there would be no math.

[babyshark]

Props to Spike.

/signed

John Cocktosten

[timurilenk]

Then you also need to consider the chance of passing CT's, which can, in effect, turn a loss into a draw. Superior and generals add a lot to this.
But unfortunately not the death roll.
And then the chance that the general dies, doing the opposite and taking surrounding BG with him.

These things are relatively simple to do.

Below is the odds of winning and losing together with base losses and cohesion drops for the cases Ethan cited. the cohesion drops take into account the factors from the combat with a zero modifier for other factors which I can add in

Size Reroll to hit coh Size Reroll to hit coh Win A Draw Win B Death A Death B Drop A Drop B
4 0 4 0 4 0 4 0 36% 27% 36% 18% 18% 21% 21%
4 1 4 0 4 0 4 0 46% 27% 27% 15% 25% 12% 28%
4 2 4 0 4 1 4 0 46% 28% 27% 18% 28% 9% 22%

Interesting to note that on a 4 vs 4 combat hitting on 4s there is a 20% chance that each side will drop at least one level.

Whilst superior does not help on the death roll, it means you will have to take less rolls so is a benefit overall.

I have not modelled generals dying but it can be done.

All very interesting - not sure how much they help in the actual game though

[ethan]

All very interesting - not sure how much they help in the actual game though

I personally find it quite useful in actual games or in order to understand how a situation is likely to play out.

I was originally motivated to do this when I had a line of heavy chariots facing off against another line of heavy chariots, but one side had a general. I figured there was an advantage but was unsure if it is was a big one? or a little one? I had a sense that was a big advantgae, but haven't seen it played out enough to really have a feel. Sure I had seen similar fights with one side getitng blow out, but was that just a fluke?

Turns out, it probably isn't a fluke and if you get a chance to try and smash an enemy line of Kn/Chariots with the only advantage to you of having a general it is a probably worth a shot.

[Scrumpy]

They help to explain why you made that incredibly stupid charge that cost you the game.... Well the odds suggested that my 6 knights should have beaten the mob.......

[timurilenk]

They help to explain why you made that incredibly stupid charge that cost you the game.... Well the odds suggested that my 6 knights should have beaten the mob.......

Well yes, I guess you could use it that way!

[sphallen]

This reminds me of poker. Any world class poker player knows the odds of winning with the cards he gets. It doesn't mean that he might not go against the odds, but he's at an advantage against someone who doesn't know the odds.

Of course in my case I'll just roll ones so it doesn't matter.

Steve

[grahambriggs]

All very interesting - not sure how much they help in the actual game though

I personally find it quite useful in actual games or in order to understand how a situation is likely to play out.

I was originally motivated to do this when I had a line of heavy chariots facing off against another line of heavy chariots, but one side had a general. I figured there was an advantage but was unsure if it is was a big one? or a little one? I had a sense that was a big advantgae, but haven't seen it played out enough to really have a feel. Sure I had seen similar fights with one side getitng blow out, but was that just a fluke?

Turns out, it probably isn't a fluke and if you get a chance to try and smash an enemy line of Kn/Chariots with the only advantage to you of having a general it is a probably worth a shot.

My logic tends to be as follows for combats with, say, equal POA 6 dice a side:

FoG is a chaos system - ie a small difference can be magnified. If, say, my general turns a 3-3 hit result into a 4-3 it's that's half a base lost and a decent chance of the enemy dropping a level - on balance one of those should happen (sometimes none, sometimes both). I'd be thinking there's a roughly 50:50 chance of him having that influence (a single reroll, 50:50 to hit).

There's also a protection effect. Say my opponent does three hits and I do two before re-rolls. So I've 4 dice that missed, making it more likely than not that I'll be hitting on rerolls (average of 1 and a third dice to reroll, hitting at 50%).

Of course the downside is the general might die or get tied up for ages.

So if he's influencing lots of dice on equal POAs or better my TCs tend to get chuck into combat. Melee's where I'm a POA down maybe not. There's not much improving you can do when hitting on 5 or 6, and that just tends to delay the inevitable. Maybe if it was a spear unit fighting sword guys and I really didn't want to disrupt at impact.

G

[dave_r]

So if he's influencing lots of dice on equal POAs or better my TCs tend to get chuck into combat. Melee's where I'm a POA down maybe not. There's not much improving you can do when hitting on 5 or 6, and that just tends to delay the inevitable. Maybe if it was a spear unit fighting sword guys and I really didn't want to disrupt at impact.

Or those combats you know are going to get better - Knights into spearmen for example, minus at impact, evens at melee. If you can survive the impact you are generally quids in to win the melee. You can of course get dead jammy and win the impact sometimes, which generally means end of spear unit.

You can also put a general with a unit and not fight in the front rank - which generally keeps the unit there for longer with much less risk and the general can always disappear if things get very terminal.

I generally agree with Graham - it is not worth commiting a general to a fight where you are a POA down (i.e. going to lose)

[marioslaz]

Why do you want to lost so much time with statistic calculation? I made too first times I want to explore the chances of a match up. Then I found it's very less time consuming to make a simple PC program to simulate a melee round (and also CT and death roll subsequent) and repeat this one million of times. After one million of such simulations, the average is very close to the chance calculated with mathematics formulas (error is under 0,1%). To repeat one million of times requires on my PC (Athlon 2600 2Ghz, a PC 3 years old) a few seconds. To write a such program it's very easy also for who isn't a great informatics expert and you can do it with freeware tools (I use Netbeans, but many other exist).

[ethan]

Why do you want to lost so much time with statistic calculation? I made too first times I want to explore the chances of a match up. Then I found it's very less time consuming to make a simple PC program to simulate a melee round

That is what I did, although I just used Excel to do it.