If you have ever been to a casino and played Roulette, you may have had the urge, like I have, to put more chips on black if red has come up over and over. Now, we both know the odds are still 50% (Technically 47.37% because of the 0 and 00 but we'll ignore that for this blog) but it sure feels like you have a better chance.
I wanted to test this myself, but I didn't want to lose a fortune at the casino, so I programmed a virtual roulette table. It rolls the "ball" 2000 times and keeps track of of the results. I set it to only make a bet if the same color has come up at least 5 times in a row. If the next time the same color comes up again, it will make the bet again next time, and keep on doing so until it wins. Here is a link to the page:
As you can see the page re-calculates new rolls every time you load it. Also as you can see, betting after a color has hit 5 times still gives you a 50% chance of winning. You may want to refresh it a few times to see the results change with new data.
I think what causes your brain to want to believe it has a better chance of winning is 5 of the same color in a row happens far less frequently than 1, 2 or 3. Looking at the results though you can see each x color in a row happens about half as often as the x times in a row before it. So even though you have 5 in a row, half of the time the next roll will turn it into 6 in a row.
So save some money and don't put any emphasis on bets when getting the same color in a row many times. The same thing applies to coin flips or any event in which you have a 50% chance of something happening over and over. Even if you get that once in many lifetimes event in which someone has flipped a coin and come up heads 17,000 times in a row, there is still 50% chance the 17,001st time will also be heads.