Laying Coins on a Table

Last Problem:

What do the red letters have in common?

What do the black letters have in common?

ACTBYK

MDUEW

Answer:

The red letters are the capital letters in the alphabet that have only vertical symmetry. The black letters are the capitals that have only horizontal symmetry.

Today’s Challenge:

Two players take turns placing identical coins on a perfectly round table. The first player who cannot put a coin on the table without overlapping an existing coin loses.

Devise a strategy so that one of the players will always win, no matter how large the table is.