Losing Your Marbles

You have a large jar filled with colored marbles. It contains 1001 $\color{#3D99F6}{\text{blue}}$ marbles, 1000 $\color{#D61F06}{\text{red}}$ marbles, and 1000 $\color{#20A900}{\text{green}}$ marbles.

You randomly draw two marbles out of the jar, then put one or two marbles in (decreasing the total number of marbles in the jar by one or keeping the number constant) using the following rule:

• If the two marbles are $\color{#3D99F6}{\text{blue}}$ and $\color{#20A900}{\text{green}}$, put a $\color{#D61F06}{\text{red}}$ marble into the jar.
• If the two marbles are $\color{#20A900}{\text{green}}$ and $\color{#D61F06}{\text{red}}$, put a $\color{#D61F06}{\text{red}}$ marble into the jar.
• If the two marbles are both $\color{#D61F06}{\text{red}}$, put two $\color{#3D99F6}{\text{blue}}$ marbles into the jar.
• If the two marbles are anything else, put a $\color{#20A900}{\text{green}}$ marble into the jar.

Repeat this process until one marble remains. What color is it?