The Math

Bruteforcing is finding the fastest path between elements and then doing attempts with the hope of getting wanted order. "n-element map" is simply a map with n number of elements (Countries, Continents, Counties, States, etc). n - number of elements to click on m - number of attempts p - the probability of succeeding These formulas help to calculate:

What is the probability of succeeding in the n-element map after m attempts?

1-(1-(1/(n!)))^m = p

How many attempts are needed to have a certain probability p of succeeding on the n-element map?

log(1-p)/log(1-(1/(n!))) = m

As doing these operations is quite complicated and/or nearly impossible for human, I recommend using: https://www.mathsisfun.com/calculator-precision.html (for the first formula) or https://www.wolframalpha.com/ (for both)

Here's a simple calculator made by @saifo https://www.calconic.com/calculator-widgets/brute-force-percent-change-calculator/62508c2a25b5a3001f08357f?layouts=true

Examples

We want to calculate a probability of getting 7-element map after 1000 attempts: 1-(1-(1/(7!)))^1000 = 18.00%

now after 2000 attempts: 1-(1-(1/(7!)))^2000 = 32.76%

Now we want to calculate the number of attempts needed to have a 50% chance of getting the 6-element map: log(1-0.5)/log(1-(1/(6!))) = ~499 attempts

Now for 8-element map: log(1-0.5)/log(1-(1/(8!))) = ~27 947 attempts