wolf rider vs heavy cavalry vs maths in WB

[Seraad]

szymraszyn

I'm affraid your calculations are wrong from the very beginning.
Please refer to wiki for information on how the calculations are made.

20/45 is NOT the probability of single hit str20 vs str25

Here are the right calculations for this example (for single hit):
0,2*(1-0,25)/((0,2*(1-0,25))+(0,25*(1-0,2))) = 42,857% (NOT 44,444% as in your case).

The slight difference make the case exactly opposite to your conclusions. It is the hc who have almost 51% chance to win (50,94%). Not the wolf.

[Seraad]

Of course the above is only pure math.

The battle is yet more complicated as there is only 100 dice which means the real battle probability is rounded to full 1% - in this case the wolf has only 42% to chance to hit when attacking, but 43% chance to hit when defending.

So the whole probability would slightly change accordingly.

[szymraszyn]

Thanks, Seraad
I am sorry, I used wrong formula that I get from someone without chcking on wiki. But still I think wolf is better for his bonuses:
Strenght: hc is a bit better
Hc 1:0 wr
Hc is a bit faster
Hc 2:0 wr
Terrain bonuses: morale is better than personal strenght
Hc 2 : 1 wr
Terrain movement bonuses: wr helps others
2:2
Money : wolf rider is much cheaper
Hc 2:3 wr

[smursh]

except that open terrain is by far the most common terrain on most maps. Hv calv also gets 5 str on ice so works well on maps featuring ice terrain. So as with any bonus it depends on the map and how the units are used, hv calv stacked with elephants are devestating on open terrain while wolves stacked with elves or orcs are effective cheaper units for forest/swamp.

personally I favor crusaders for mid strength units. 60% ward makes them nice cover from ambush units to protect hero stacks, they are 50:50 vs your hv calv but by dropping the ambush of the wolf down to just 6.4% they will win that fight more often than not. no terrain bonus but better for city fighting.

[fantastory]

...there is only 100 dice which means the real battle probability is rounded to full 1% - in this case the wolf has only 42% to chance to hit when attacking, but 43% chance to hit when defending.

Is it true?

There was a post about rounding and this was fixed for ruins:
viewtopic.php?f=3&t=2173&p=12061&hilit=skeleton&sid=0700e7016d93f925392d2e4775032111#p12061

So the defenders gets about 0.5% on each roll?

[tabanli]

All 2 turn units are equally desirable. It really depends on the map. I won so many games in open maps with HL-Valkyrie-6 cavalry deep city raze and plunder suicide missions. Same with Dwarf Engineer-Giants by staying on the mountains. Ranger-7 Wolf Riders stack is not equally desirable, you have to mix with other units for the hit power. HL-Scorpions for sandy maps-HL-Yeti for snow.

Cavalry goes with elephants, yeti goes with mammoth, scorpions goes with sandworms, wolfies and giants goes with unicorns as 3 turn units.

Most people prefer Wolfs just be cause of Barbarians.

[tabanli]

25 vs 20 is 60-40 HC wins 52%

2 Wolfies against 2 HC is worse

[tabanli]

Basic calculation is

Attacker Power Rate (APR)= Strength/(100-Strength)
Defender Power Rate (DPR) = Strength/(100-Strength)

Power Ratio (PR) = APR /DPR
Power ratio also gives approximate equivalence of units for larger battles
50 strength 2 hit unit is approximately equivalent to 4 units of strength 20 with 2 hits.

3 Hit unit against a 2 hit unit wins 90.3 % if power ration is 8/3 = 2.6666
2 Hit unit against a 2 hit unit wins 90.7 % if power ration is 13/3 =4.3333

[SoulMan]

Hmm, for me its:

1) 16% ambush
2) 84% usual fight 25 vs 20:
a = 0,25*0,8 / (0,25*0,8 + 0,2*0,75) = 0,571428571 - HC will hit
b = 0,2*0,75 / (0,25*0,8 + 0,2*0,75) = 0,428571429 - Wolf will hit
HC wins if no ambush: a^2 + 2*a^2*b = 0,606413994
to check, lets calculate Wolf wins if no ambush: b^2 + 2*b^2*a = 0,393586006
Seems correct (sum up to 1)
3) So HC wins: 84% * 0,606413994 = 0,509387755
and Wolf wins: 16% + 84% * 0,393586006 = 0,490612245.

Seraad was right.

And You can't simply say which unit is better, all depends on situation.