Entropy Lost: Nintendo’s Not-So-Random Sequence of 32, 767 Bits

Abstract

Early video games didn’t have hardware support for random number generation, so developers used software-based RNG. We show that hundreds of games in the Nintendo Famicom / NES library regenerate the same pseudorandom sequence of 32, 767 bits, although the machine code for doing so comes in more than one hundred variants. We identified the disparate implementations using a simple regular expression that matches the following “fingerprint” of operations: LDA, AND, STA, LDA, AND, EOR, CLC, BEQ, SEC, ROR. These instructions implement a classic 15-bit linear feedback shift register associated with x15 + x7 + 1 (i.e., tap the 15th and 7th bits). However, many games devoted more memory to the LFSR’s state. For example, Donkey Kong (1983) used 8 bytes (or 8 · 8 = 64 bits), The Legend of Zelda (1986) used 13 bytes, and Super Mario Bros. 3 (1988) used 9 bytes. In each case, additional entropy is lost by a simple programming error: the bits are shifted in the wrong direction.