The mathematics of assassination

[Defensor Pacis]

A simple question of maths, but unfortunately I've forgotten how to work it out. http://www.totalwar.org/forum/non-cgi/emoticons/gc-help.gif

If I have several assassins trying to kill someone, how do I work out the overall probability of a successful assassination?

For example, if there are 3 assassins each with a 15% chance of killing the target, what is the chance that the target will die?

Surely it can't be as simple as summing the individual probabilities, otherwise if there were 10 assassins with a 10% chance, the target would definitely die - and that's not correct. And it's not multiplicative, as that would be the chance of them all succeeding, which is silly in this case (unless it's Murder on the Orient Express).

Sorry to ask such a question but my maths is not too hot

Dunce http://www.totalwar.org/forum/non-cgi/emoticons/gc-party2.gif

[Somebody Else]

Just use the binomial approximation, with n as the number of assassins and p as their chance of success.

One would have to make assumptions such as independence of course...

5 assassins, each with 20%, probability that target dies is 67.23%

5 assassins, each with 40%, probability that target dies is... 92.22%

Ignore the rubbish I said at the beginning. To calculate this, find the probability that they all fail and subtract that from one.

Take my first example: 1-0.2 = 0.8. 0.8^5 (0.8*0.8*0.8*0.8*0.8) = 0.32768. 1-0.32768 = 0.67232 = 67.23%

In your example with three at 15%, the probability is 38.59%.

I can't believe nobody has tried to correct me yet - as I have nothing to base this upon except for my grasp of statistics and logic.

[Imperial Buffoon]

I haven't done any testing myself, although I remember someone doing that a couple of months ago so do a search just in case.
I think SE's calculation is OK. This said, I believe the probabilities you're given for each assassin only take into account the assassin's and target's valour, but not the presence of border forts/watchtowers or enemy agents in the province.
IIRC, a watchtower catches each assassin with some prob. (which i don't know) but it only applies to one. The easiest thing would be to use n-1 for the prob but that would understate it...

[mfberg]

I think watchtowers catch your assassins before they get the chance to try for a kill.

The assassination failure calculation is correct. Since more than one can fail, but only one can succeed that is the way to figure it.


mfberg

[Daveybaby]

@Somebody Else : the reason nobody has corrected you is because youre correct.

Take the chance to fail (1.0 - chance to succeed) for each assassin and multiply them all together to determine the likelihood that they ALL fail. Thus the likelihood that at least 1 will succeed = 1.0 - total chance to fail.

e.g.

1 assassin with a 35% chance to succeed (65% chance to fail)
1 assassin with a 10% chance to succeed (90% chance to fail)
1 assassin with a 50% chance to succeed (50% chance to fail)

Chance of all failing = 0.65 * 0.9 * 0.5 = 0.2925 = 29%

Chance for at least one to succeed = 71%



Of course, as imperial buffoon points out, the chance to succeed given to you by the game for each assassin doesnt take into account the likelihood of the assassing getting caught by border forts or enemy defensive spies, so to achieve this rate you need to perform the assassination on friendly territory, which, lets face it, isnt going to happen all that often http://www.totalwar.org/forum/non-cgi/emoticons/gc-dizzy2.gif


Does anyone have any stats/formulae for how likely an n-star assassin is to get caught by watchtowers, or a spy of a certain rank?

[Defensor Pacis]

Thank you Somebody Else: your grasp of statistics and logic is clearly greater than mine

Very grateful for this info. http://www.totalwar.org/forum/non-cgi/emoticons/bigthumb.gif

[Colovion]

Heh, I attacked the Doge of Italy with a 14% chance to succeed. I didn't have much reason to do it besides that I offered a daughter to him in Marriage and he didn't accept So I killed him http://www.totalwar.org/forum/non-cgi/emoticons/gc-devil.gif His heir took over but still. http://www.totalwar.org/forum/non-cgi/emoticons/biggrin.gif That'll teach them to accept my daughters when I offer.

[Oaty]

Quote[/b] (Colovion @ May 27 2004,16:11)]Heh, I attacked the Doge of Italy with a 14% chance to succeed. I didn't have much reason to do it besides that I offered a daughter to him in Marriage and he didn't accept So I killed him http://www.totalwar.org/forum/non-cgi/emoticons/gc-devil.gif His heir took over but still. http://www.totalwar.org/forum/non-cgi/emoticons/biggrin.gif That'll teach them to accept my daughters when I offer.
Did you take a good look at your daughter 99 percent chance she looked completely repulsive.

Another thing as soon as the turn begins an assassins success is determined instantaneously before you even give him a mission. So if the assassin does'nt succeed and you reload the game and try another target he still wo'nt succeed

[motorhead]

Quote[/b] ]Another thing as soon as the turn begins an assassins success is determined instantaneously before you even give him a mission. So if the assassin does'nt succeed and you reload the game and try another target he still wo'nt succeed

- I'm not too certain about this. I was doing some testing on spy valor and rebellions and noticed that if i just reloaded the game and hit end turn, the results/events on the next turn seemed almost identical. So I ran 20 straight reloads/end-turns without changing anything and 17/20 times the major events i saw looked identical, but 3 times something new happened. However, if i changed something else (move a unit/agent/ship) before i ended that turn, it introduced alot more randomness to the results/events on the next turn.
- also, did some tests on bribing. i wanted to see what would happen if i bribed the garrison of rebels in a castle besieged by my allies (end result - 20 attempts, and it never succeeded). If i just reloaded the turn and ended it, an assasin i sent to kill an english emissary always seemed to catch him, but when i added a few more emissaries to do the bribing, my assasin never caught up to him the next turn.

- So, if you are a reloader http://www.totalwar.org/forum/non-cgi/emoticons/gc-curtain.gif , move things around before you end the turn.

edit: completely off topic comment: on the main forum page, where it shows "Last Post Info", this topic shows up as "The mathematics of ass...". first time i saw it i thought "a pr0n thread in main hall?" http://www.totalwar.org/forum/non-cgi/emoticons/gc-2thumbsup.gif

[Defensor Pacis]

LOL motorhead http://www.totalwar.org/forum/non-cgi/emoticons/gc-smile.gif

Nice advice about reloading by the way.