Your hat is irrivlent to the game, the dice are. Dice can be hot or cold and while there is nothing wrong with wanting to have lucky dice, actively staring at them is not good sportsmanship. A hat meanwhile subjectly can't influence a game and there isn't anything wrong with wanting to wear a particlar garment as a hat is a subject seperate from the game, a outside factor. For me the two subject matters are complelely different. Staring at a dice is intending to cheat, wearing a hat isn't. I don't understand how the question at hand can be interpreted in any other way.
How about staring at your opponents dice. Come on blanks, blanks, blanks...oh wait I guess that's cheating hahaha.