Need for predictable random generator

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 should be critical. The problem is I got very bad real life results — sometimes players get 3 crits in 5 hits, sometimes none in 15 hits. Battles are rather short (3-10 hits) so it's important to get good random distribution.

Currently I use PHP mt_rand(), but we are just moving our code to C++, so I want to solve this problem in our game's new engine.

I don't know if the solution is some uniform random generator, or maybe to remember previous random states to force proper distribution.

Solution 1:

That means, 1 out of 5 hits should be critical. The problem is I got very bad real life results - sometimes players get 3 crits in 5 hits, sometimes none in 15 hits.

What you need is a shuffle bag. It solves the problem of true random being too random for games.

The algorithm is about like this: You put 1 critical and 4 non-critical hits in a bag. Then you randomize their order in the bag and pick them out one at a time. When the bag is empty, you fill it again with the same values and randomize it. That way you will get in average 1 critical hit per 5 hits, and at most 2 critical and 8 non-critical hits in a row. Increase the number of items in the bag for more randomness.

Here is an example of an implementation (in Java) and its test cases that I wrote some time ago.

Solution 2:

You've got a misunderstanding of what random means.

Which of these is more random?

While the second plot looks more evenly distributed, the more random is actually the first plot. The human mind often sees patterns in randomness, so we see the clumps in the first plot as patterns, but they're not - they're just part of a randomly selected sample.

Solution 3:

Given the behavior you're asking for, I think you're randomizing the wrong variable.

Rather than randomizing whether this hit will be critical, try randomizing the number of turns until the next critical hit occurs. For example, just pick a number between 2 & 9 every time the player gets a critical, and then give them their next critical after that many rounds have passed. You can also use dice methods to get closer to a normal distribution -- for example, you will get your next critical in 2D4 turns.

I believe this technique gets used in RPGs that have random encounters in the overworld as well -- you randomize a step counter, and after that many steps, you get hit again. It feels a lot more fair because you almost never get hit by two encounters in a row -- if that happens even once, the players get irritable.