There's a very common mistake, or rather misconception going around many gamblers'
heads – it's called the gambler's fallacy.
The gambler's fallacy's meaning is the idea that previous outcomes have a say on future
outcomes in a game of chance. Let's take an example – suppose you flip a coin 9 times
and they all turned out to be heads, the chance of the next toss being heads or tails is
still 50%. It's true that on average, the outcomes should be around the 50% mark, but
that idea only qualifies on a very large scale.

Let's take another example – the Roulette. Many Roulette tables have a scoreboard
that will tell you which numbers have turned up during the night. There are many
gamblers out there that will bet on numbers that haven't turned up all night because they
believe that because they haven't, they are bound to turn up any minute now.

An experienced gambler knows that it's all about statistics and odds when it comes to
gambling over a long period of time. When dealing with events on a small scale you
cannot expect the outcomes to always be around what they're supposed to when
thinking about the long term.
The Roulette or coin do not have any “memory” of the previous outcomes, and these
events have no effect on any of the future outcomes.

The gambler's fallacy can be quite destructive. Imagine placing large bets on a number
with a supposed higher chances of turning up. This bet has no different odds than any
other random bet, therefore it could put a big dent in your bankroll.

I have seen many gamblers make this mistake, sometimes they won, most of the time
the didn't. These bets carry no more weight than any random selection and shouldn't be
thought of as better.
With the overall atmosphere in casinos it's fairly easy to let go of any reason and just go
with the flow, and the alcohol doesn't help either. This is just one mistake of many, but
should be avoided nonetheless.