First Strikes

[kcd_swede]

So instead of one 4 sided dice we instead use 3 two sided dice, each dice having a side 0 and 1, which is 50% chance of that strike occuring. If you roll all 3 dice then the odds of getting a total of 0, 1, 2, or 3 between them is still 25% if I am not mistaken.

I think you are mistaken, but you ended up with the right answer anyhow.

Your possible equally likely outcomes are:
0-0-0 = 0
0-0-1 = 1
0-1-0 = 1
0-1-1 = 2
1-0-0 = 1
1-0-1 = 2
1-1-0 = 2
1-1-1 = 3

So that under this scenario your odds of getting 0 FS would be 1/8, your odds of getting 1 FS would be 3/8, your odds of getting 2 FS would be 3/8, and your odds of getting 3 FS would be 1/8.

Now if we average them... (1*0 + 3*1 + 3*2 + 1*3)/8 = 1.5 FS on average if you have 3 FSC... and 1.5 first strikes (on average) out of 3 FSC means that on average you will get only 50% of the first strikes as you have FSC's.

But you will never get 1.5 FS! You are equally likely to get 1 or 2 FS's, and much less likely to get 0 or 3 FS's. This is, intuitively how it should work in the game. But according to the OP it does not.

If you use a 4-sided dice the AVERAGE is still 50% of the number of FSC's, but then 0 FSc is as likely as 1 FSc is as likley as 2 FSc is as likely as 3 FSc. As I understand it from the original poster, this is how it works. Nice to know... but not critical for playing the game.

 

[PieceOfMind]

If you roll all 3 dice then the odds of getting a total of 0, 1, 2, or 3 between them is still 25% if I am not mistaken.

This is where you are mistaken and it is the source of the confusion.

Think of a similar example, if you toss a coin ten times in a row, you do not have a 10% chance of tossing exactly 0 heads and you do not have a 10% chance of tossing exactly 5 heads. (You are in fact much more likely to toss exactly 5 instead of exactly 0).

For your case,
1/8 chance of rolling 0
3/8 chance of rolling 1
3/8 chance of rolling 2
1/8 chance of rolling 3.

Think about it.
If you want to research it further, google "binomial distribution" or "Bernoulli trials".

Of course, the whole point of what I was saying in the OP is that the first strikes do not follow this binomial distribution but instead the uniform distribution. i.e. equal chance of each possible number of converted first strikes.

 

[Vimp]

Yeah I see now that I was mistaken. Thanks both for clearing that up for me.

 

[mfie]

I have an intelligent question:
When you attack you attack always the strongest unit of your enemy (compared to your unit) first (except some exceptions). How are first strikes calculated in this (and in the combat odds)

 

[PieceOfMind]

I have an intelligent question:
When you attack you attack always the strongest unit of your enemy (compared to your unit) first (except some exceptions). How are first strikes calculated in this (and in the combat odds)

The way first strikes are used while determining the best defender is unnatural to me so I can't explain it very well, but there is some discussion in the following thread about a modcomp that changes how the bestdefender code works.

SDK modcomp Lead From Behind

The following pdf is a very mathematical description of how first strikes are considered in calculating combat odds. It's not very easy to read but it at least demonstrates that including first strikes correctly in an odds calculation is far from trivial. No wonder in the earliest versions of vanilla they badly mucked up how first strikes went in combat odds.
Towards a general combat odds calculator for Civilization IV (BtS)

 

[VoiceOfUnreason]

Edit: no need to beat the dead horse.

 

[_alphaBeta_]

Drill 1: +0.5FS
Drill 2: +1FS, Suffers 20% Less Collateral Damage
Drill 3: +1FS, Suffers 20% Less Collateral Damage
Drill 4: +2FS, Suffers 20% Less Collateral Damage, +10% vs. mounted units

So a unit that "Suffers 20% Less Collateral Damage," what does that mean exactly? Does it suffer less damage when selected for collateral damage, or does it mean it has a 20% probability of avoiding it, if selected (similar to evasion).

 

[PieceOfMind]

So a unit that "Suffers 20% Less Collateral Damage," what does that mean exactly? Does it suffer less damage when selected for collateral damage, or does it mean it has a 20% probability of avoiding it, if selected (similar to evasion).

It suffers 20% damage less when it receives it, IIUC. Nothing to do with evasion.

 

[MarkJohnson]

Well, I was noticing my FS units were winning better than the combat odds were saying. So, a little later in game I decided to give my arty with 2 barrage bonuses already a first strike as I was losing about 2 out of 3 arty on an attack of a new city.

Well, after giving them first strike I was only losing about one on average, sometimes none, and rarely two, but never three. My combat odds were usually 53% on first attack. before using FS I was probably averaging 2 deaths. as I would lose only one occasionally, and lose three occasionally. but it sure helped me a lot and let me focus on city defenders instead of attacking units and I was soon able to have two full attacking SODs.

Thanks for the article, and i can see why it's so hard to predict exactly the effects of FS with any certainty.
-=Mark=-

 

[PieceOfMind]

Well, I was noticing my FS units were winning better than the combat odds were saying.

That's a bit hard to judge, but what version of civ4 were you playing? Vanilla or BtS? And with the latest patch?

 

[MarkJohnson]

I was playing BtS with the latest 3.19 patch. I also was using the Better BUG AI mod.

 

[PieceOfMind]

In that case I'm 99% certain the odds would have been accurate (because it's possibly but unlikely my code has been messed up in a merge of mods somewhere, I trust Fuyu and EmperorFool et al to be getting the ACO code correct). Any observed discrepancies would surely be coming from either some strange rolls from the RNG or from some observer bias.

I'm a little bit unclear on your explanation of what happened but it sounds like you're happy there isn't any problem?

 

[MarkJohnson]

It may have been a stretch of good luck. I just thought the FS may have affects if they hit just right in the beginning of battle. Most games I have played, if first strike hits it will decrease their power and improve my odds since they have been weakened. If my first strike fails miserably, then odds usually don't change much for the next round of combat.

How does combat resolution occur?

Some games I play have units with both attack and defensive power and FS doesn't affect their attack on me. but some only have one power number and first strike will lower their power when it's their turn to attack me. Also, is there an initiative phase to see who get first attack, or does attacker/defender always go first?

-=Mark=-

 

[PieceOfMind]

Arathorn's article Combat Explained pretty much covers everything except first strikes, which is why I started this thread.

But basically combat occurs as the 2 combatants facing off against each other in 'rounds'. Each round a weighted die is rolled to determine who gets hurt. If the loser of the roll still has first strikes left, he does not take damage.

There is actually no real effect of a combatant losing the first one or two rounds of battle other than the obvious lower hitpoints he now has to fight with. What I mean to say is the strength does not decrease as he becomes more injured during battle.

There is no initial phase of combat unless you wanted to describe a first strike phase like I did in the OP of this thread, where one or more of the combatants still have first strikes left.
I have not looked at how the graphical display of battles works (combat animations) but I'm pretty sure they show the individual rounds of combat one by one.

 

[Cadbro]

If you have a defender with, say, 3 first strikes and an attacker with 1, does the defender have a chance to get off free shots?

 

[Ataxerxes]

If you have a defender with, say, 3 first strikes and an attacker with 1, does the defender have a chance to get off free shots?

Yes. The first round doesn't count. On the next two rounds, if the defender loses the round he takes no damage.

I like to use first strikes for protective leaders (1 free) and tanks. By that time with my tech lead my tanks will often take no damage when attacking. In addition to not having to rest to recover the next turn they can still use their second attack this turn.

Also, first strikes are great for Privateers.

 

[TheMeInTeam]

I'm not sold on first strikes on tanks. IMO generally combat or CR is superior:

Tanks often encounter reasonably high-heath rifles or infantry in cities; with bomber support you can cut down the defenses and eventually half the unit HP, allowing the drill tanks to win and have a decent chance of emerging unscathed. However, that itself takes extra turns.

Alternatively, you can just hammer the cities with bombers w/o actually bombarding, and in many cases your tanks will still have 90% odds or better if you simply take combat promotions; which are more versatile in general. Healing is a matter of leaving the damaged guys back with a medic and pushing the offensive with less/not damaged ones. Regardless, the amount of time it takes to damage the defenders significantly enough where drill is the best bet on tanks (which have a hard time making drill IV) isn't realistic.

One could use nukes instead of air power, but rather than drill tanks I'd take paratroopers for that.

I like drill on gunpowder troops the most, in tandem with siege support. PRO gunpowder can hit drill IV pretty quickly and the attacks by definition are more slow moving, while siege can bombard + hit instantly if you have enough (it's easier to put enough siege at a point compared to air assets).

Drill is also useful on protective troops earlier in the game (and all archery units start with an inherent first strike), although usually not on the offensive pre-gunpowder. Still, stocking a city with multiple high defense longbows can tear AI stacks to pieces and set up a sweep through their lands, so it's not something to completely ignore.

 

[randomguy13]

I actually quite like first strikes, but only in certain situations, such as when I was playing a shadow game of dualdoc's deity OCC always war game, where if I didn't have samurais with 7-10 first strikes, I wouldn't have survived the stacks of one hundred units against me without getting the pass breached (only 5 units defending for me) if not for this outrageous amount of first strikes. Other than those special occasions, however, I rarely use them.