/sci/ - Science & Math

[Anonymous No.6310737]

Dear Mathfags,

In this computer game the developers have introduced a "guaranteed reward system" for chance based rewards. The idea: instead of a fixed chance for a reward at every kill, your chance increases with every attempt so that eventually it becomes impossible to fail. When you succeed, your accumulated chance is reset to 0.

I'm investigating the relation between the chance increments and the overall average success through simulation. Pic related.

Does a system like this have a name? Is there an easy formula to go from chance increment to average success?

[Anonymous No.6310742]

>Is there an easy formula to go from chance increment to average success?

it's called "integration", look it up.

[Anonymous No.6310749]

This could a priori be arbitrary complicated.
Are the increment values deterministic? Do they only depend on the current probability (Markov chain)? Are them maybe even constant (in which case you split the paths in two, restart or current probability +shift, to get the probability over attempts)

[Anonymous No.6310763]

Define f(n) to be the probability that it takes n kills to get a reward. Now, take <span class="math"> \sum_{n=1}^{\infty} n \cdot f(n) [/spoiler] to obtain the average number of kills required to get a reward.

[Anonymous No.6310766]

>>6310749
They are constant, yes.

>you split the paths in two, restart or current probability +shift, to get the probability over attempts
That is pretty much how I'm running the simulation.

[Anonymous No.6310849]

>>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)

[Anonymous No.6310951]

It's called pseudo-random Distribution. It's used in games like Dota 2 for things like critical chance and dodge chance.

[Anonymous No.6311055]

>>6310951
http://www.youtube.com/watch?v=yR7BcWfBCsc
my life is a lie

[Anonymous No.6311076]

>>6311055
This is not even wrong

[Anonymous No.6311377]

Say they looked at gene x. How did they know gene x codes for the protein that leads to the color of someones' hair? Did they isolate the gene and actually make a protein with it? What process did they use? How did the human genome project know what each gene was for?

[Anonymous No.6311387]

>>6311377
>How did they know Gene X codes for the protein that leads to someone else's hair?

We look at mice or other organisms and knock out that gene. If mice with the defective gene start growing white hair, that's one way to know.

Also, we look at people's genomes and do statistical tests with their phenotype. If people with different sequences in X all tend to have different hair colors, and there's a high statistical probability that they're correlated, then we're pretty sure that X codes for hair color.

>How did the human genome project know what each gene was for?

It didn't. In fact, we STILL don't know the function of every gene or protein. The Human Genome Project just told us what all the genes were, not what they did.

[Anonymous No.6311397]

>>6311055

but that's retarded. it effectively lets you charge your crits.

that game sounds stupid as shit.

[Anonymous No.6311422]

>>6311397
>it effectively lets you charge your crits
You can try, but I don't think you've ever played dota. In a real game you don't decide when an engagement occurs, and when it happens you won't have time to charge anything.
Trying to have it charged at all times means you can't farm creeps, losing out on gold.