I had 1/300 chance of winning, and then received 1000 entries. This gave me 1/194 chance of winning. After receiving another 200 entries, I had a 1/181 chance of winning. Then, after another 420 entries, a 1/159 chance. Assuming the pool remains constant, how many entries must I submit to take my chances from 1/159 to 1/4 or 1/2 chance in winning.

Thank you.