## Statistics Question: Best chance of kill?

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irrevenant
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### Statistics Question: Best chance of kill?

I've found myself in the following situation a couple of times last game and would like to know which approach offers best odds:

There's an opponent with 6hp left.

I can attack him with either a 6-1 (60%) attack or a 3-3 (60%) attack.

Which has the best chance of killing him?

DimWit
Posts: 27
Joined: April 3rd, 2006, 6:01 am
3-3....

3 Hit...
3 miss... (40% chance)
3 Hit...

6-1
6 Miss... (40% chance)

Only diffrence is with 6-1 ya got 60% chance to kill him without taking damage...

WildPenguin
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As said, 6-1 could actually reduce received damage. However, the chance to kill is slightly higher (60% vs 65%) with 3-3 damage.

As to which is better depends whether +5% CTK is worth potentially higher damage received from retaliation.

Dragon Master
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really depends on what unit you're trying to kill. If it's dragonguard I would go with 6-1 to minimize damage. But something like a WC i would go with 3-3 just to kill it.

Chris NS
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OK, you win. I've been lurking for long enough and this statistical question has convinced me to register. Right, let's answer it:

The probability of a kill with a 6-1 (60%) attack is the probability of 1 successful hit out of 1, which is, needless to say, 60%.

The probability of a kill with a 3-3 (60%) attack is the probability of 2 or more successful hits out of three. This can be any one of the following:

Hit, hit, hit: Probability = 0.6 * 0.6 * 0.6 = 0.216

Hit, hit, miss: Probability = 0.6 * 0.6 * 0.4 = 0.144
Hit, miss, hit: Probability = 0.6 * 0.4 * 0.6 = 0.144
Miss, hit, hit: Probability = 0.4 * 0.6 * 0.6 = 0.144

Total = 0.216 + 0.144 + 0.144 + 0.144 = 0.648 = 64.8%

So a 3-3 attack has a better chance of a kill (unless the unit you are attacking might kill you before you finish attacking).

Doesn't Wesnoth calculate this for you though?

Liminiality2
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Doesn't Wesnoth calculate this for you though?
It does but it rounds to the nearest tens place I think
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Soliton
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Chris NS wrote:Doesn't Wesnoth calculate this for you though?
It does and in the newest version you also get pretty graphs to illustrate the damage distribution after the fight.
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irrevenant
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Liminiality2 wrote:
Doesn't Wesnoth calculate this for you though?
It does but it rounds to the nearest tens place I think
I'm pretty sure the percentage displayed is the chance for each attack to hit not the chance to achieve a kill. Otherwise it would be at 0% an awful lot of the time.

My math had come up with the same answer as Chris NS, but I didn't trust it so it's good to get it verified (thanks Chris!).

I hadn't thought about the issue of return damage, so it was helpful to have that mentioned too.

Thanks all!

WildPenguin
Posts: 161
Joined: September 6th, 2005, 10:41 pm
Location: Australia
Odds for the Chance to Kill and Chance to be Killed are actually available when attacking. The attack dialog does only display the chance to hit, however, currently within the Damage Calculation dialog (which is avaliable via the attack dialog) towards the bottom there are 3 numbers each separated with a "/". These numbers represent "Chance to Kill", "Chance to be Killed", and "chance that both units survive", respectively and are rounded to nearest 1%.

This is exceptionally useful in-game for quick estimations on optimising each attack. And as Soliton said, they will be replaced with quite nice looking hitpoint distribution graphs next release.