The Exponential Beam Bug is a glitch from version 1.06 that primarily afflicted the Thunderhead Lance and perhaps other weapons. The game would, for reasons unknown, perform multiplicative damage boosts instead of the proper additive ones for the Thunderhead Lance. If the player had only one Thunderhead Lance, the bug would not manifest. However, if he had two or more, the damage would raise exponentially due to the bug. For two, normal would be 3+3 for 6, whereas the bug caused it to be 3*3 for 9. Adding more would result in 27 and 81 instead of 9 and 12, for three and four lances respectively (note the Thunderhead Lance now does 6 damage per hit). This resulted Thunderhead Lances becoming the most powerful weapon damage-wise in the game if the player could buy the maximum of four.
This bug was fixed by version 1.08. Windows users, who were stuck in version 1.06 until 1.09 was released, got to experience and abuse this bug for far longer.