These math tricks can make rare Pokémon appear out of nowhere

A technique that manipulates the video game's random number generator makes rare Pokemón appear, showing how it's not so random after all

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As a teenager, I spent countless hours playing Pokémon on the Game Boy. One of the game’s most popular goals is to collect as many coveted creatures as possible. Back then there were 151 of them—but some were extremely rare and almost impossible to find. You needed a lot of luck (or patience) to catch the most sought-after Pokémon. But you could give fate a little nudge with a few tricks.

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For instance, in the early 2000s it was possible to team up with other players and trade Pokémon. If you wanted to fill out your Pokédex, you had to: some Pokémon weren't available depending on the version of the game you played, so you needed a friend to trade with to catch those version-specific ones. Because Game Boys weren’t Internet-enabled, this was done via cable. The Pokémon trade was processed sequentially: first, I selected which Pokémon to send, and only then could the other player choose and transfer theirs. If I unplugged the cable after the first Pokémon had been transferred, the second part of the transaction didn’t happen. As a result, I still had my sent Pokémon, and the other person had it as well. This process allowed players to duplicate Pokémon as often as they liked.

Today, of course, you no longer need cables to trade, but there are other ways to influence the course of the game. One method exploits the weaknesses of a game’s random number generator (RNG) to obtain specific Pokémon; it’s appropriately known as RNG manipulation.

In fact, it’s random numbers that determine which Pokémon you encounter at seemingly random times during a game. Most experts prick up their ears as soon as randomness is involved because, surprisingly, generating random numbers is extremely difficult.

In everyday life, we perceive many things as random, but generating true randomness solely through a deterministic process like an algorithm is impossible. Instead we use what are called pseudorandom number generators. The number sequences they produce follow a fixed and theoretically predictable pattern, but their output is indistinguishable from a truly random sequence.

Pseudorandom number generators use values called seeds to achieve this: these are the starting values from which a seemingly random sequence of numbers is built. If the seed is known, however, the sequence of numbers can be predicted—which is where RNG manipulation in Pokémon comes into play. There are now dozens of different versions of the game, and each differs in its internal programming. Some contain pseudorandom number generators with rather simple seeds. In Pokémon Emerald Version, for example, the seed always has the value zero. In the fourth generation Pokémon games Pokémon Diamond Version, Pokémon Pearl Version and Pokémon Platinum Version, by contrast, the seed is derived from the date and time set on the console being used, as well as the time that has elapsed between booting up the game and hitting “Continue” on a save file.

The underlying algorithm that generates the random numbers in these third- and fourth-generation games is called a linear congruential generator. Such programs belong to the most common class of pseudorandom number generators. They are based on a linear equation and the principle of recursion. This means that the seed is initially used to calculate the first random number output by the linear equation. This output value is then substituted back into the linear equation to determine the next number in the sequence. In this way, a progressively increasing sequence of numbers is generated.

To ensure that the generated numbers only fall within a specific interval (for example, between zero and nine), a modulo operation is performed at the end of the equation: the result is divided by a number, such as 10, and only the integer remainder is retained. In this way, pseudorandom numbers can be generated, which, in the best case, are indistinguishable from truly random numbers.

Because the Emerald version of Pokémon always uses the same seed, the pseudorandom values can always be predicted. To prevent direct exploitation, the random numbers tick away in the background like an ultrafast clock, changing their value approximately 60 times per second. Therefore, as soon as a supposedly random event occurs—a player encounters a wild Pokémon, for example—where the generated random number is meant to determine the outcome, the rapid timing makes the action appear unpredictable.

Theoretically, if the same event occurs at the exact same time after the start of a game, the outcome will be the same. And this pattern can be exploited.

If you want to influence the random events of a game, you need, among other things, a precise stopwatch to execute an action at the right time. Furthermore, you need to know which random value is calculated within which time period and what that value encodes. Lists containing these data can be found online. These lists allow you to see which Pokémon can be expected to appear in which time frame after which actions.

Source: Read the original article on www.scientificamerican.com