Integer payout function (enter the "expected" value, print the distribution maximized for "fun")

Question

We have several examples in our game where we want to randomize the “payout" based on the expected exit value. For example, instead of rewarding “10 credits” each time, we would like to reward an average of 10 for a long time with some randomness thrown to make it more “fun”, making it a little unpredictable.

It’s easy enough to change it to a random amount or even make it normal, but it’s not very optimized for “fun”. The difference in utility for the user between 5 and 15 credits is relatively small, but if there is a chance that from time to time they will win 100 credits, which will be a big draw and something that you can hope for.

Is there an algorithm optimized for players? This is basically a super-simple slot machine - I would expect someone to do a study to determine what makes something like this fun and fun, but I don’t even know where to start looking for something like that.

Answer 1

I think that the lavin papers published a very interesting sound and it needs to be studied, but without knowing anything about the slot machine algorithms, I would suggest something simple. The simple thing is to just randomly choose from two different distributions:

  select a random uniform U on [0,1]
 if (U <= p) select a random normal from N (10,2.5)
 if (U> p) select a random normal from N (100,10) 

Here you simply set p for the probability of receiving a reward from a less exciting distribution (and the obvious 1-p is the probability that it comes from a more exciting distribution). You do not need to use normals for these distributions. More uniforms will also work fine.

Answer 2

Some of the algorithms used by slot machines are described in detail in this article , including the commonly used method for creating “close misses,” and “bonus mode” to make gambling more fun.

and this is another article . although you may need access to the full text for this university (if you do not want to pay for it).

I don’t know if anyone wrote a program that implemented these methods, but I hope that the ideas used in old machines still work somehow in the digital world.