Hi DrAgOnPoWeR,

The red exclamation mark means: suspected program use. 

Explanation:
Excerpt of FlyOrDie's Rules of Use: 
"Using a computer to decide your moves in a board game (specifically chess, checkers, reversi, gomoku, nine men's morris, go, four in a row, pente and backgammon) on FlyOrDie is allowed.

FlyOrDie members have the right to know if they are playing against a computer. 
Therefore FlyOrDie uses a system - including analysis of client computing environment - to detect suspected program use, which will be indicated on the concerned player's info screen with a small icon"   and a red exclamation mark.

Rules Of Use  -->> 

https://www.flyordie.com/games/help/moderation.html

   - see under 2 "Cheating"   

Best regards,
John Stewart

It’s not about “the number of games for it to disappear”.  FOD uses a system to detect if you use a program or not to determine your moves.

TIP:  Try to stop flicking between screens when playing 😉