#### DeletedUser107795

##### Guest

I thought I would try out some math concepts to determine noble probability. I rooted around in the forums and found some half-assed math. Wouldn't surprise me if you could find this somewhere else. (Let me have my fun you trolls! I have feelings!!)

Anywho,

Using the fun-inspired central limit theorem. We can say that any random variable with n =+ 30 is normally distributed.

This means we can narrow down the average to a more realistic number.

Here's the results:

**Probability of a single noble hitting 25 or above = 70 percent**

Using the empirical rule, we know that 68% of the sample falls between 1 standard deviation of the mean. (95 within two, 100 within 3)

**there is an appox. 68% chance your noble will fall between (22.84 - 32.42)**

there is an approx. 27% chance your noble will fall between (18.24 - 22.84, 32.42 - 37.02)**

there is an approx. 27% chance your noble will fall between (18.24 - 22.84, 32.42 - 37.02)**

***This is slightly nonsensical for the game as it goes past noble boundaries. However you can assume there is*

roughly a 13% that you will be below 22.84 or above 32.42. (13.5+13.5=27)

roughly a 13% that you will be below 22.84 or above 32.42. (13.5+13.5=27)

So this is close, but not exact. Anyone got better?

**Want to check my math? Here we go!**

Pulling up Excel, I generated random numbers from 20-35. 30 rows X 100 columns to be safe. (Thats 3000 random numbers between 20-35)

Average(U): 27.44

STDEV: 4.6

So, Now we need our Z formula. (X-U/STDEV)

p(X>25)

=(25-27.44)/4.6

=-0.53

Pulling up our table of standard values, -0.53 = 0.2981

1-0.2981 = 0.7019

Therefore the chances your noble being above 25% is 70%

However, This isn't quite right as you need 4 nobles to equal 100+.

So, Using the empirical rule, we know that 68% of the sample falls between 1 standard deviation of the mean.

That means

27.44 - 4.6 = 22.84

27.44 + 4.6 = 32.042

So there is a 68% chance your noble will fall between (22.84 - 32.42)

there is a 27% chance your noble will fall between (20 - 22.84, 32.42 - 35)