Section Systems

Dear Mark, I know that there's no casino in the world that would purposely allow the odds to favor me, the player. However, when I was a young lad, I once discovered a roulette bet that, for the life of me, has fooled me and anyone else I've asked into believing that the odds are now more than 50% in my favor of hitting a number. I'm hoping you can find the error of my logic, so I don't fool myself into betting my life savings into something that I can't help but think is nothing short of a sure thing.
Take your average 38-number roulette table (1-36, plus the 0 and 00 squares). The table will not only allow you to bet on individual numbers, but also on large chunks, as the table can be split up into thirds, each third giving you 3 to 1 odds. If the table is numbered 1-36, and you bet on two of these thirds, you're betting on 24 of these 36 numbers, giving you a 66% chance that it will land on your choices. Even factoring in the additional 0 and 00 blocks, you still have a 50/50 chance of hitting a number.
Now, if you walk in the casino with £20, bet £10 on each of the two thirds, and you hit, you'll walk away with £30. So not only do you have the odds in your favor, you also profit!
Blimey, when I went to Vegas last November, I tried this out on a couple of bets, and even the dealer there commented, "Nice bet!" Now, sir, what are we all missing here? Robert M.
What's missing was possibly your gratuity to the dealer after the croupier's compliment, "Nice Bet." Seriously, Robert, your syllogism has a flawed premise: you are wrong in assuming a 3-to-1 payoff when betting sections, rather, the actual payoff is 2-to-1. Furthermore, you say that you factored in the 0 and 00, but did you? If either of those two numbers moons its ugly face, you lose both of your wagers, as neither (0, 00) occupies any section. Consequently, the player's failure to competently consider the 0 and 00, lifts the casino advantage automatically to 5.26%.
Here's the "rithmetic." If you bet a pound on any section, every 38 spins you will win an average of £24 (12 wins at 2 to 1 payoff odds) and lose an average of 26 spins for a net loss of £2. This gives you an average loss of £2/38 = 5.26 pence per pound bet, paralleling the house edge of 5.26%. No "section system" can muster any chance of survival against that hefty casino advantage.

Gambling thought of the week: "A gambler is a man who will pay his gambling debts even when he knows he has been cheated." Leo Tolstoy