i understand the formula from that "combat explained" thread.
to break the 1.0 ratio point, your unit need 5 hits to kill your opponent, while your opponent needs 6 hits to kill your unit.
but if ratio point of 1.0, and your unit have 1 first strike. your still need 5 hit, and so does your opponent, but in his theory, u get 1 free hit, means actually, u only need 4 hits, but opponent need 5 hits.
from the hit ratios of 5:6, and 4:5, it does look like that 4:5 have an advantage over 5:6, but if first strikes are chances, then it is not 4:5, its 4.5:5 or 9:10, which is much weaker than 5:6.
but that person said if unit with same strength, first strike promotion > strength promotion, but it only work like that when it is 4:5, which means first strike = sure hit.
but he also said first strikes are chances, so if your unit have 5-8 first strike, when combat happens, it will randomly have 5-8 first strike CHANCES.
but that breaks his own formula.
any way, too much math, made me headache, if first strike are chances, then its much weaker than strength promotion in ALL cases, not to mention when you vs another unit with first strike, and vs units immune to first strike.
edit: the above were original post, but i'll like to re phrase it abit, so everybody understand.
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combat explaination thread
here are some quotes from that thread
First Strike
First strike round(s) are special. The number of them is determined by looking at the number of first strike rounds of the attacker and the defender. Whichever number is greater gets the difference of values in first strike opportunities. For x-y first strikes (possible first strikes), the math is still unknown.
A first strike round is like any other round, except that the first striker is the only one who can do damage. For example, if the attacker has two first strikes and the defender zero, the first two rounds have two possibilities – the attacker wins so the defender loses damage or the defender “wins” and nobody gets hurt. The odds in this round are just like any other.
here he said first strikes are chances.
1.01-1.25 62%-75%
1.0 50%
The final jump point is around an even battle. Even a tiny bit of strength makes a HUGE difference. Any stronger unit, by even .01, will have at worst a 62.3% chance of winning the combat. That’s because the stronger unit does 20 damage and the weaker only 19. 5 rounds to kill vs. 6 rounds to kill. That’s all there is to it. Going from a tiny bit stronger to a tiny bit weaker drops your chance of winning from 62.3% to 37.7%. A 40% chance of winning is impossible for fully-healed units(without first strikes).
this shows the winning odds with pure strength calculation
it means if you unit strength : opponent unit strength = 1.01, your chance of winning is 62%
If your unit is barely stronger with first-strike or barely weaker without first strike, then the first strike promotion is better than a strength promotion. This appears true out to about the 1.38/1.39 strength ratio barrier. If the strength ratio is outside 1.38, strength beats first strike. And if strength would change which unit is stronger, strength wins out. Exact calculations on this may come later.
i found his calculation unreliable.
assume you have an archer with 1 unspent promotion, fighting another archer with no promotion.
according to his "third law", that unit with similar strength will do better with first strike than combat promotion.
but
Two units with identical strength and equal first strikes each have a 50% chance of winning (YAY! Something that finally makes sense in this mess of math). Give 1 a single first strike, though, and the odds of that unit winning goes up to 56.8%.
but if you give that archer combat promotion, which adds 10% strength. and that 10% will surely break the 1.01 ratio, (1.1 ratio), and that means it will atleast have 62% chance of winning according to his "second law"
which prooves combat promotion beats first strike promotion in all cases.
the statement "if 2 unit with same strength, then first strike works better" will only be true if first strike = sure hit, which will result with 64% chance.
and i dont even know how he calculated the chances, my 64% is an estimate lol.
the way i calculate is by number of hits required.
for example, at 1.01 breakpoint, my unit need 5 hits, and enemy unit need 6, so my chance of winning is 6/(5+6) = 54.54%repeating
but with "sure hit", and 1.0 ratio, winning is 5/(4+5) = 55.55%repeating
if chance of first strike and 1.0 ratio, winning is 52.63% 5/(4.5+5)