Need for predictable random generator

Question

I\'m a web-game developer and I got a problem with random numbers. Let\'s say that a player has 20% chance to get a critical hit with his sword. That means, 1 out of 5 hits

Answer 1

I agree with the earlier answers that real randomness in small runs of some games is undesirable -- it does seem too unfair for some use cases.

I wrote a simple Shuffle Bag like implementation in Ruby and did some testing. The implementation did this:

• If it still seems fair or we haven't reached a threshold of minimum rolls, it returns a fair hit based on the normal probability.
• If the observed probability from past rolls makes it seem unfair, it returns a "fair-ifying" hit.

It is deemed unfair based on boundary probabilities. For instance, for a probability of 20%, you could set 10% as a lower bound and 40% as an upper bound.

Using those bounds, I found that with runs of 10 hits, 14.2% of the time the true pseudorandom implementation produced results that were out of those bounds. About 11% of the time, 0 critical hits were scored in 10 tries. 3.3% of the time, 5 or more critical hits were landed out of 10. Naturally, using this algorithm (with a minimum roll count of 5), a much smaller amount (0.03%) of the "Fairish" runs were out of bounds. Even if the below implementation is unsuitable (more clever things can be done, certainly), it is worth noting that noticably often your users will feel that it's unfair with a real pseudorandom solution.

Here is the meat of my FairishBag written in Ruby. The whole implementation and quick Monte Carlo simulation is available here (gist).

def fire!
  hit = if @rolls >= @min_rolls && observed_probability > @unfair_high
    false
  elsif @rolls >= @min_rolls && observed_probability < @unfair_low
    true
  else
    rand <= @probability
  end
  @hits += 1 if hit
  @rolls += 1
  return hit
end

def observed_probability
  @hits.to_f / @rolls
end

Update: Using this method does increase the overall probability of getting a critical hit, to about 22% using the bounds above. You can offset this by setting its "real" probability a little bit lower. A probability of 17.5% with the fairish modification yields an observed long term probability of about 20%, and keeps the short term runs feeling fair.