In the cool chart of logical fallacies that Greg offered there is one, the Gambler's Fallacy, which I'd like to address. http://assassination.../Fallacies.jpg
As a statistician and Lottery Games professional there are long term and short term time-frames to consider.
"Believing that runs occur to statistically independent phenomena such as a roulette wheel spin."
Each spin is of course independent and carries with it the odds of any specific number coming up of 37 to 1 if played with one "0".
In the red/black example it is 18/37 for black and 18/37 red and 1/37 for green "0".
Over time, over a certain # of spins, these results will always pan out.
Now take your example of Red coming up 6 times in a row... while the very next spin carries with it these independent odds, the overall odds of occurrence will need balancing at some point.
As a quick illustration let's assume we get 37 spins. The first 6 are RED.
We now have 31 spins left yet only 12 should be RED, 18 should be BLACK and 1 GREEN.
While the independent odds say 18/37 or 48.6% is the chance for RED this spin,
getting a 7th RED in a row is something we are also looking to accomplish whose odds are .6% of happening. Eventually the number of occurrences MUST equalize.
The same is true in any game of chance and number choices. In Daily 3 a player picks 3 #'s 0-9. Each of the 3 #'s has a 10% chance of coming up in its position (1st, 2nd, 3rd) If a player notices that the #5 had not come up in the 1st position over many weeks the REAL ODDS of the long term event start to take over for the independent ones and a run occurs.
Final example... watching a basketball game... if King James goes 2 for 15 in the first quarter yet is shooting 50% overall for the season would you bet that by the end of the game he would have made up for that deficit even though each shot carries its own % of success of about 50%?
The rest of that great image are tactics related to strategies for causing problems without it appearing so. Not sure why the Gambler's is in there...
From what I've seen of applied statistics, it is poorly used and terribly misunderstood by those trying to prove something has a high probability of occurence.
In most cases they forget what you must excluded from the results to get to the true odds...
Anyway... just an FYI that stats and probability is, like 3d measurements on 2d images... something more difficult than it seems