In a certain magical game world each player spawns with $1000$ health. If a player's health drops under or is $0$, they are erased from existence and reborn. The developer of the fantasy game adds a feature that allows players to decrease the health of others and erase them from existence. This feature, a wand, does $n$ damage, a certain number between $1-100$, inclusive.

Oron and Jonathan decide to play this game. Jonathan casts a spell with the wand and hits Oron. However, Oron drinks a pink potion that decreases the health by $-\lfloor \frac{\left(n-m\right)^3}{420}\rfloor$, where $m$ is a certain number from $101-200$, inclusive.

What is the probability that Oron is able to survive after Jonathan casts the magic spell?

Question

In a certain magical game world each player spawns with $1000$ health. If a player's health drops under or is $0$, they are erased from existence and reborn. The developer of the fantasy game adds a feature that allows players to decrease the health of others and erase them from existence. This feature, a wand, does $n$ damage, a certain number between $1-100$, inclusive.

Oron and Jonathan decide to play this game. Jonathan casts a spell with the wand and hits Oron. However, Oron drinks a pink potion that decreases the health by $-\lfloor \frac{\left(n-m\right)^3}{420}\rfloor$, where $m$ is a certain number from $101-200$, inclusive.

What is the probability that Oron is able to survive after Jonathan casts the magic spell?