Nineteen Coins and a Curse

A carnival sack holds $20$ tokens: $19$ gold coins and $1$ cursed token, thoroughly mixed. You draw tokens one at a time without replacement. Each gold coin adds $\$1$ to your pot, but drawing the cursed token ends the game and wipes out the entire pot. You may stop after any draw and walk away with the pot. What is the optimal stopping rule, and what is the game's expected value under it?