First Strikes

First Strikes

This not really a strategy article; more an objective description of first strikes. Hopefully it will address the most common questions people have regarding first strikes.

It should be approached as a supplement to the more complete guide Combat Explained, written by Arathorn. The linked article is very comprehensive but oddly the details on first strikes are mostly glossed over, and the assumption put forward that first strike chances have 50% probability is incorrect.


What's the difference between first strikes and first strike chances?

A Drill IV longbow has 4-7 first strikes. This means it has 4 first strikes guaranteed, and 3 first strike chances. If all of its first strike chances are converted into actual first strikes, it would receive 7 first strikes in battle. If none of the first strike chances were converted, it would receive only 4.

Before battle commences, there is a RNG roll that determines how many first strike chances will be converted. A common (but wrong) assumption is that each first strike chance has a 50% probability of being converted. Here is how it actually works...

Let #FSG be the number of guaranteed first strikes and #FSC be the number of first strike chances.

Then in battle, the unit will receive #FSG + rand(0,#FSC) first strikes, or equivalently rand(#FSG, #FSG + #FSC) first strikes.

rand(0,#FSC) returns a random number from the uniform distribution (all numbers are equally probable) with lowest value 0 and highest value #FSC. You can basically imagine it as a die with the numbers from 0 up to #FSC on it.

Going back to the 4-7 first strike Drill IV longbow, it would receive:

4 first strikes (25% of the time)
5 first strikes (25% of the time)
6 first strikes (25% of the time)
7 first strikes (25% of the time)

If it were true that each first strike had 50% probability of converting independent of the other first strikes, then the above numbers would have come from what's called a binomial distribution (not the uniform distribution), and they'd have been 4(12.5%),5(37.5%),6(37.5%),7(12.5%).


What do first strikes do?

When a combatant has N first strikes, it basically means that unit does not take damage in the first N rounds of combat, no matter how many times or with what force the opponent succesfully hits. If the first striker won the first N rounds anyway, the first strikes produced no benefit. If the first striker lost all the first N rounds, the first striker avoided taking damage N times because of his first strikes.

Because of the way first strikes affect combat (making first strikers immune to damage in the early rounds), it's possible to get some unusual situations when both combatants have first strikes.

Let's consider the example of two Drill IV longbows fighting. They both have 4-7 first strikes.

They both will always get at least 4 first strikes, so when they do fight the first 4 rounds of combat are always going to be completely pointless because both units will be immune to damage. The game might as well be rolling the RNG just for the fun of it (and if I'm not mistaken I believe the game really does roll the RNG in these cases), because neither unit will be taking any damage. Because of this, when two units both have guaranteed first strikes, they can be cancelled out. Obviously, the number of guaranteed first strikes that can be cancelled out depend on the unit that has the fewest guaranteed first strikes. In other words, you can only cancel out guaranteed first strikes until one of the units has none left.

First strike chances, however, can never be cancelled out. The example of the Drill IV longbows fighting is equivalent to two units each with 0-3 first strikes fighting, but not equivalent to two units with 0 first strikes fighting.

Another less common (but wrong) assumption is that units with first strikes somehow get free shots at the opponent. One must remember that even a unit with first strikes must still win combat rounds if it wants to damage its opponent. Avoiding damage in the first few rounds is not going to benefit a first striker much if it's going to take all the damage in every following round anyway. Even if you gave 10 first strikes to a warrior and made him attack an infantry, on average he'd only land about 1 hit on the infantry before dying, and that hit would only be worth 8HP.


How does one compare the value of first strikes with first strike chances?

It should be obvious to anyone who has been reading to this point, that first strikes are always going to be better than first strike chances. The question then becomes, how many first strike chances are worth one first strike?

There is no obvious answer to this, but a good rule of thumb that is used by many people is to say a first strike chance is worth half of one first strike. This rule of thumb turns out to be fairly useful because on average, only half of the first strike chances get converted.

Using this loose rule makes it interesting to compare the Drill 2 (+1 first strike) and Drill 3 (+2 first strike chances) promotions, because the two promotions appear to be the same value, and indeed they are pretty much the same value in all battles.

Technically having 2 first strike chances rather than 1 first strike makes both combatants slightly more likely to take more damage. The actual difference is so negligible in all battles that it is barely worth a mention, and there's definitely no point discussing it further.

With this loose rule in mind, we can roughly describe the four drill promotions as:

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

Here you can see Drill 1 is very weak compared with both Drill 2 and 3, and Drill 4 is arguably worth more than both Drill 2 and 3 combined.


What do first strikes not do?

• First strikes do not alter the damage dealt per successful hit nor the damage sustained during a losing hit, unlike most other promotions.
• First strikes do not alter the probability of winning each combat round.
• First strikes do not alter the XP earned by the first striker if he wins the battle.

A common (but wrong) assumption is that each first strike chance has a 50% probability of being converted.

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I had problems trying to buy that explanation as well. Thanks for clearing this up as I think this explanation is way over-due.

I also think 99% of civplayers go wrong with FS due to the name Firaxis chose. It really has nothing in common to the other promotions, but is a fancy term for Armour. It actually should be in its own separate category.

Thanks for starting an article on this.

When I think of free shot, I don't think of something that's necessarily going to hit. I think of it as a round where there is no risk of getting hit. In that sense, a first strike is a free shot.

Might be useful to add some guidelines on using first strikes. You're probably going to get more use out of them as a protective leader, as you don't have to actually spend a promotion on drill 1.

Another thing I'd be interested in is the interplay between battle odds, first strikes, R strength ratios, and exp for both attackers and defenders.

Nice article. Oromos ftw!!!

I have 2 questions though...

1) If the attacker and a defender have FS's, do they cancel out or does each one of them get a first strike at the opponent? An example would be a Keshik attacking a Longbowman - what would happen?

2) How do FS's figure into combat odds? Do they?!?

dankok8 said:

Nice article. Oromos ftw!!!

I have 2 questions though...

1) If the attacker and a defender have FS's, do they cancel out or does each one of them get a first strike at the opponent? An example would be a Keshik attacking a Longbowman - what would happen?

2) How do FS's figure into combat odds? Do they?!?

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1. You can always cancel out the guaranteed first strikes. I explained this above...

For example, if unit A has 4 first strikes and unit B has 2, then it's exactly the same as if A had 2 first strikes and B had 0. This is because for the first 2 rounds of combat, both A and B would be immune to damage, but in the following 2 rounds, only A is immune to damage. So the effect is the same as if only A had 2 first strikes.

First strike chances can never be cancelled out, but once they have been converted they can.

eg. Unit A has 4-7 FS. Unit B has 2-5 FS.

A rolls rand(4,7) and gets 5.

B rolls rand(2,5) and gets 4.

Unit A would be immune to damage in the first 5 rounds, Unit B only in the first 4 rounds.

2. First strikes definitely do figure into combat odds but the way combat odds are figured is very complicated. I'll be happy to show you how they're worked out, but I'll warn you there is a lot of maths and probability theory involved.

Tephros said:

Thanks for starting an article on this.

When I think of free shot, I don't think of something that's necessarily going to hit. I think of it as a round where there is no risk of getting hit. In that sense, a first strike is a free shot.

Might be useful to add some guidelines on using first strikes. You're probably going to get more use out of them as a protective leader, as you don't have to actually spend a promotion on drill 1.

Another thing I'd be interested in is the interplay between battle odds, first strikes, R strength ratios, and exp for both attackers and defenders.

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I'm not going to write about how to use first strikes here. I'm going to be writing about the drill promotions and how to use first strikes a bit later. See, my sig says coming soon.

I need to put this information out in advance, and I will refer to it in the next article rather than having to include all these details in the same piece.

PoM, I'm currently in a team-game where I am soon to have Drill IV protective longbows cranking right out of the gate. I actually can't wait, and I have free combat 1 promotion for all archers! I have to agree that the last Drill promo is the most important. Especially since all drills themselves get ignored by HA's, Knights, etc. But at the end you at least get that 20% bonus to mounted, so it covers ALL units. Ironically, cavalry get raped by Drill while Knights ignore it, haha! Another one of Firaxis' silly paradoxes.

Anyhow, it's been mentioned a few times about promoting to Drill because the AI keeps overestimating its chances in that case. That way you can get them to suicide a lot easier, even the AIs who have low attack courage. What input do you have to give on this?

obsolete said:

PoM, I'm currently in a team-game where I am soon to have Drill IV protective longbows cranking right out of the gate. I actually can't wait, and I have free combat 1 promotion for all archers! I have to agree that the last Drill promo is the most important. Especially since all drills themselves get ignored by HA's, Knights, etc. But at the end you at least get that 10% bonus to mounted, so it covers ALL units. Ironically, cavalry get raped by Drill while Knights ignore it, haha! Another one of Firaxis' silly paradoxes.

Anyhow, it's been mentioned a few times about promoting to Drill because the AI keeps overestimating its chances in that case. That way you can get them to suicide a lot easier, even the AIs who have low attack courage. What input do you have to give on this?

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I had never given much thought to the way the AI could be more likely to attack drill units. I'm not sure whether it's true but it definitely would not suruprise me if most basic calculations an AI did when comparing stack strengths was just considering the base strengths.

Note it's +10% bonus to mounted.

I don't intend to discuss much about strategy here, but when I do in another article, my number one rule will probably be: "Always use Drill IV units at ratio advantage." This either means only use them for defense in high defense terrain/cities. If using them on attack, it will usualy mean using siege first so the defending units have at least taken a hit or two already. In whatever role you use them, they're always strongest when the the ratio of attacker to defender (A : D) or A/D is less than 1 if defending or greater than 1 if attacking, the further from 1 the better.

Thank you for the explanation, though I did already read an article long ago talking a bit about it. Also, if I am not wrong, that article said that the AI does seem to ignore first strikes in the calculation when attacking a unit with first strikes...

Yes that's right, 10% not 20%. Anyhow, in today's continue I'm pressing drill to the absolute maximum right now. It was a lot of fun but I'll have to wait until Wednessday to kick up some more bloodshed. As the game is now, (thanks to vassalage) I have a couple cities cranking out bows with 6 promotions. Naturally I am mostly going hard core on drill still, but throwing in a few city-garrisons into the mix.

However, Snatty suggested today I try to get a few Guerilla III promos. That sort of startled me, while I don't mind that line up to level II, the III seems like a big waste. I'm not much into suicide promotions when I think the unit is the top of it's class doing the other thing.

But I don't know, maybe I will get one or two to EXPERIMENT a bit. What do you think? It's now or never.... unless I get the Celts of course.

obsolete said:

Yes that's right, 10% not 20%. Anyhow, in today's continue I'm pressing drill to the absolute maximum right now. It was a lot of fun but I'll have to wait until Wednessday to kick up some more bloodshed. As the game is now, (thanks to vassalage) I have a couple cities cranking out bows with 6 promotions. Naturally I am mostly going hard core on drill still, but throwing in a few city-garrisons into the mix.

However, Snatty suggested today I try to get a few Guerilla III promos. That sort of startled me, while I don't mind that line up to level II, the III seems like a big waste. I'm not much into suicide promotions when I think the unit is the top of it's class doing the other thing.

But I don't know, maybe I will get one or two to EXPERIMENT a bit. What do you think? It's now or never.... unless I get the Celts of course.

Spoiler :

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G3 doesn't synergize with first strikes particularly well given that first strikes are better when your strength ratio is high and you're outnumbered. If your catapults are seeing less than 50% odds of winning, the city has a single strong defender backed up by weak ones (making collateral irrelevant), and you're attacking a city on a hill, then sure G3 might make sense on a couple units.

I was thinking, would drill promotions be good for city attacking units? I'm currently playing a game as Japan and have experimented giving the samurai drill promos. The reason is this: if my seige units are doing their job, by the time my samurai actually start fighting, the defending units are down 25% or more of their total hp. Thus even without any promotions my samurai would still have good odds of winning each round of combat. If I give them city raider promotions the combat odds go up towards 95% or even higher. I could do that. Or I could give them more first strikes. By giving them more first strikes it seems that they win just as many battles as with city raider, but take less damage doing so, and they gain XP faster. So I've been thinking about what to do with gunpowder units. The city raider promotion to me is something to use to take down a really tough defender, and is very useful in the early game when seige is harder to come by. But if you have a ton of seige units, would it be better to give your attackers drill promos? Thoughts?

noto2 said:

I was thinking, would drill promotions be good for city attacking units? I'm currently playing a game as Japan and have experimented giving the samurai drill promos. The reason is this: if my seige units are doing their job, by the time my samurai actually start fighting, the defending units are down 25% or more of their total hp. Thus even without any promotions my samurai would still have good odds of winning each round of combat. If I give them city raider promotions the combat odds go up towards 95% or even higher. I could do that. Or I could give them more first strikes. By giving them more first strikes it seems that they win just as many battles as with city raider, but take less damage doing so, and they gain XP faster. So I've been thinking about what to do with gunpowder units. The city raider promotion to me is something to use to take down a really tough defender, and is very useful in the early game when seige is harder to come by. But if you have a ton of seige units, would it be better to give your attackers drill promos? Thoughts?

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What you have described here is very much in line with what I believe at the moment. However I haven't had much time to play these sorts of games out, only test them theoretically on the calculator. And unfortunately the games I do play are usually huge or large epic games so they take forever.

I believe drill troops (drill IV in particular) are very powerful when used as attackers if they are used in conjuction with siege. Since units with first strikes have a much easier time attacking when the defenders are damaged, it makes D4 the perfect promotion for your units that follow the siege units (or a couple CR units if there are very tough defenders still near full health). Samurais in particular are ridiculous, as at 10xp they can have 5-8 first strikes, more than any other unit in the game can have if I'm not mistaken. Navy SEALs and skirmishers also can achieve a high number of first strikes.

The fact the drill IV troops earn xp faster means they reach the even higher promotions so much faster. Once D4 is paired with further promotions (CR if using samurai ) like combat or pinch, the effect of the promos on each other is extremely potent.

hmm, I don't know if I'd choose drill over city raider for troops that attack cities, but maybe one or two samurai that go drill instead of combat. But mostly if you're attacking archers, not longbows/crossbows...

but when seige has already ripped the defenders apart, giving your samurai city raider makes the combat odds go from 95% to 99%...why bother? Giving them drill means they win battles without taking any damage! Still...I find drill more useful defensively most of the time. It is useful against collateral damage, but I wish Firaxis made it even more useful against CD

obsolete said:

I also think 99% of civplayers go wrong with FS due to the name Firaxis chose. It really has nothing in common to the other promotions, but is a fancy term for Armour. It actually should be in its own separate category.

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If it was armour then it wouldn't matter in what order damage is done. It wouldn't have to be the first attacks that get negated. If you think of first strikes as armour, then it's armour that stops working after the wearer makes successful attacks. Logically that doesn't make sense. The intended meaning does, where regular combat rounds can have damage on either side and first strike combat rounds where the first strikers can attack and the other side only defend.
Stoneskin in FfH2 is actual armour because it works for the first loses and not dependent on them happening before winning combat rounds happen.

obsolete said:

Yes that's right, 10% not 20%. Anyhow, in today's continue I'm pressing drill to the absolute maximum right now. It was a lot of fun but I'll have to wait until Wednessday to kick up some more bloodshed. As the game is now, (thanks to vassalage) I have a couple cities cranking out bows with 6 promotions. Naturally I am mostly going hard core on drill still, but throwing in a few city-garrisons into the mix.

However, Snatty suggested today I try to get a few Guerilla III promos. That sort of startled me, while I don't mind that line up to level II, the III seems like a big waste. I'm not much into suicide promotions when I think the unit is the top of it's class doing the other thing.

But I don't know, maybe I will get one or two to EXPERIMENT a bit. What do you think? It's now or never.... unless I get the Celts of course.

Spoiler :

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The G3ine could help you seriously rack up some xp. You can attack with a Drill4C1 longbow at worse odds than normal with a chance to retreat if things start going badly. If you get 3xp from attacking when the odds are slightly in your favor, imagine how many you get if the odds are against you. Though I would advance up the combat line. Especially since you have a free head start. With the same number of promotions you can get C3March. Though that is a LOT of xp. It might be interesting to try with Churchill though. But you can't count on getting the free combat1 for archers event every game.

Churchill of the Celts might be interesting for Guerilla 3 Drill 4 troops . . .

CivCorpse said:

The G3ine could help you seriously rack up some xp. You can attack with a Drill4C1 longbow at worse odds than normal with a chance to retreat if things start going badly. If you get 3xp from attacking when the odds are slightly in your favor, imagine how many you get if the odds are against you. Though I would advance up the combat line. Especially since you have a free head start. With the same number of promotions you can get C3March. Though that is a LOT of xp. It might be interesting to try with Churchill though. But you can't count on getting the free combat1 for archers event every game.

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You might get XP at lower odds but every time you retreat you're only taking 1XP. G3 is only going to be better XP-earning-wise if you are attacking at consistently bad odds, where using Drill would not be advisable anyway. But yeah, attacking with G3 at bad odds (eg. for 6XP or so) and flukishly winning occasionally could be pretty neat. If you try this at some point I'd be interested in hearing about its effectiveness.

Bandobras Took said:

Churchill of the Celts might be interesting for Guerilla 3 Drill 4 troops . . .

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lol great idea. Gotta try that sometime.

PieceOfMind said:

You might get XP at lower odds but every time you retreat you're only taking 1XP. G3 is only going to be better XP-earning-wise if you are attacking at consistently bad odds, where using Drill would not be advisable anyway. But yeah, attacking with G3 at bad odds (eg. for 6XP or so) and flukishly winning occasionally could be pretty neat. If you try this at some point I'd be interested in hearing about its effectiveness.



lol great idea. Gotta try that sometime.

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Haha, I played a game with this combo(Churchill and Celts) already in a highland map! Overkill? Nah, EVERY other AI had a random leader but was from the Celts!

It was a fun game, I loved it, I love G3, it is a funny promotion! I didn't get to use it that much though, everybody had their cities on hills...

I know this is an old thread but I imagine its viewed even still for its usefull info so I thought I would add something that ocurred to me while reading it just now.

I notice it is emphasized in red that each first strike chance does not have a 50% chance of occuring like many people may think, but yet the explanation of how it does work sounds to me like it is contradicting this comment.

As in the example of a dice where the dice has a side 0 plus however many sides as there are "FSC", I will make my own example that shows it to be the same as a 50% chance per strike.

Lets say the unit has 3 FSC. So we use a 4 sided dice with the numbers 0, 1, 2, 3.
In this example there is a 25% chance of any one of those 4 numbers occuring.

Now lets look at it in the supposed 'wrong' way where there is a 50% chance per strike:
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.

This outcome of a 50% chance for each FSC to occur is further supported in the original post where the poster says:

How does one compare the value of first strikes with first strike chances?...There is no obvious answer to this, but a good rule of thumb that is used by many people is to say a first strike chance is worth half of one first strike. This rule of thumb turns out to be fairly useful because on average, only half of the first strike chances get converted.

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So in other words the explanation of how it works does not go contrary to the supposedly 'assumed' 'wrong' outcome of 50% chance for each strike to occur.