>>6310766

Here's a way to implement it:

If the increment i in probability is constants, then given it must reach exactly 1 at one points, there is a maximal number M of kills you can go without reward. And then M*i=1, i.e. the increment is 1/M each kill. The probability to get a reward R after K kills is hence K/M.

Let's store the current number of kills K and the rewards R got so far in a vector indexed by (K,R), where K runs from 0 to M and R runs from 0 to how long you play t.

We have

(K,R) --> (0,R+1)

has probability K/M

and no reward

(K,R) --> (K+1,R)

has hence probability 1-K/M.

If you want to see the probability for R rewards after T time steps, use these probabilies to set up the (M*t) times (M*t) transition matrix

http://en.wikipedia.org/wiki/Transition_matrix#Example:_the_cat_and_mouse

Then you can get the probabilities by choosing some value R and summing over the K's of the vector. (Since the matrix is so sparse, you can do it on paper, probably)