Here’s the straight dope on these questions:
The reason the casino doesn’t want you betting red and black at the same time simply has to do with their comp policies. A casino will sometimes give out coupons or $100 in chips, or whatever to new players as a promotion. By betting red and black at the same time, it allows you to lower your variance, which means you’ve got a better chance of keeping the money from those coupons. Look at it this way: If you take $100 and bet red only, the chance that you’ll get your $100 back is very slim. You may win a bunch or lose a bunch. If you put $50 on red and $50 on black, then you get exactly $100 back unless the wheel lands on 0 or 00, in which case you lose it all. Still, that’s only a 1/18 chance, so it’s an easy way to convert those pay-to-play coupons to cash. Of course, the whole point of the coupons from the casino’s standpoint is to hook you into playing more, so they won’t allow it.
The house still has a 5.26% advantage on your bet, since if you didn’t notice the 0 and 00 are not red or black, and if the ball lands in either one you lose both bets.
There is no combination of bets in roulette that will get you better than a 5.26% house advantage. It doesn’t matter if you bet a single number, a group of four, twelve, or red or black. In the long run, the casino gets 5.26% of all the money placed on the table. The only exception is the ‘5-way’ bet at the top of the board, which is even worse. There are no ‘hot’ numbers, or ‘cold’ numbers, or any combinations of bet amounts that change the fact that the house gets 5.26% of all the action. Roulette systems are for suckers (there are two exceptions - ‘biased’ wheels and computers. One is extremely difficult to do and the other is a felony).
In blackjack, the reason the dealer has to call out ‘Splitting tens’ is twofold - one, a sign of a card counter is someone who will split face cards when the count is high enough. If the pit is alerted when you split tens, they’ll start to watch your play. The only people who split them are card counters or idiots, and it’s pretty easy to tell which is which very quickly. If they decide you’re a card counter they’ll punt you out of the casino, refuse to let you play blackjack, or limit your bet spreads.
The other reason they call ‘splitting tens’ is because there’s a type of low-level scam that involves the player half-heartedly indicating a split, then claiming he didn’t want to if he gets a bad card. Since splitting tens is such an obviously bad move, they’ll argue that they aren’t that stupid and the dealer obviously misunderstood. In these cases the casino will usually cave in rather than make a scene, pay you off, and ask you to leave. By calling out ‘splitting tens’ they make it absolutely clear that everyone knows what is going on.
Forget about other players hurting your chances in blackjack by making stupid plays. Your expected win rate has nothing to do with how other players at the table play. Chances are, if you believe this myth your probably one of the bad players anyway, since the truly good players understand this.