One word. Insurance. I don't know why, but no matter the argument, it's my LEAST favourite basic of BJ.
I'm not too sure about the odds on this, but for any kind of Black Jack that offers insurance, some systems say it gives you a slight edge and you should always take insurance if you don't have any 10s. But it's bollocks to me to insure to win 2/1 for a roughly over 2/1 event and so I simply play no insurance BJ.
Actually, the basic strategy move on insurance is to
never take insurance. The only way this ever makes sense is if you are keeping track of the cards, and there are
way more 10s left in the deck than not. In a 1 deck game, after a fresh shuffle, this would be equivalent to no 10s being dealt with 2 hands being played. Since most casino games are more than 1 deck, this situation comes up very rarely. If you don't count cards, it's best to never take insurance or request "even money." (In an online game, it never makes sense to take insurance.)
Don't change your bets too often. A highly varying bet is usually a sign that someone is counting cards - all it takes is for the pit boss to be counting cards too to be sure you're counting, and then you're out of there!
I find that if you stick to certain rules when changing bets, you won't get too much heat.
1) Never change your bet after a tie. (Unless you plan on taking a bathroom/smoke break.)
2) Rarely decrease your bet after a win.
3) Doubling your bet after a win or loss looks like a standard player move. (Martingale, let it ride strategies.) Just don't get crazy with it.
4) Eat, drink and be merry.