I truly wrote some code to do that. The gist of it’s utilizing statistics to appropriate unfortunate streaks. The approach you are able to do that is to maintain observe of what number of instances the occasion has occurred and use that to bias the quantity generated by the PRNG.

Firstly, how will we maintain observe of the proportion of occasions? The naive approach of doing this could be to maintain all numbers ever generated in reminiscence and common them out: which might work however is horribly inefficient. After a bit pondering I got here up with the next (which is principally a cumulative transferring common).

Take the next PRNG samples (the place we proc if the pattern is >= 0.5):

Values: 0.1, 0.5, 0.9, 0.4, 0.8
Events: 0  , 1  , 1  , 0  , 1
Percentage: 60%

Notice that every worth contributes to 1/5 of the ultimate outcome. Let’s take a look at it one other approach:

Values: 0.1, 0.5
Events: 0  , 1

Notice that the 0 contributes to 50% of the worth and the 1 contributes 50% of the worth. Taken barely additional:

Values: [0.1, 0.5], 0.9
Events: [0  , 1  ], 1

Now the primary values contribute 66% of the worth and the final 33%. We can principally distil this all the way down to the next course of:

outcome = // 0 or 1 relying on the results of the occasion that was simply generated
new_samples = samples + 1

common = (common * samples / new_samples) + (outcome * 1 / new_samples)
// Essentially:
common = (common * samples / new_samples) + (outcome / new_samples)

// You may need to restrict this to, say, 100.
// Leaving it to hold on rising can result in unfairness
// if the sport attracts on endlessly.
samples = new_samples

Now we have to bias the results of the worth sampled from the PRNG, as a result of we’re going for a share probability right here issues are rather a lot simpler (versus, say, random quantities of injury in a RTS). This goes to be arduous to elucidate as a result of it ‘simply occurred to me’. If the common is decrease it implies that we have to enhance the possibility of the occasion occurring and visa-versa. So some examples

common = 0.1
desired = 0.5
corrected_chance = 83%

common = 0.2
desired = 0.5
corrected_chance = 71%

common = 0.5
desired = 0.5
corrected_change = 50%

Now what ‘occurred to me’ is that within the first instance 83% was simply “0.5 out of 0.6” (in different phrases “0.5 out of 0.5 plus 0.1”). In random occasion phrases which means both:

procced = (pattern * 0.6) > 0.1
// or
procced = (pattern * 0.6) <= 0.5

So with a purpose to generate an occasion you’ll principally use the next code:

whole = common + desired
pattern = rng_sample() * whole // the place the RNG offers a worth between 0 and 1
procced = pattern <= desired

And subsequently you get the code that I put within the gist. I’m fairly positive this all can be utilized within the random harm case state of affairs, however I have never taken the time to determine that out.

Disclaimer: This is all home-grown statistics, I’ve no training within the subject. My unit exams do move although.