Statistics 101
Walking through a casino is painful for a math major. Just about everyone there is trying to be "lucky." There's the lady who stalks the slot machines looking for the one that is hot. There's the guy at the roulette table with a pad of paper carefully taking notes. A math prof at Purdue always said, "The lottery is a tax on the mathematically challenged." A casino is full of people trying to "beat the odds." But do they even know what "odds" are?
- One roulette wheel spins 10 black numbers in a row. The other wheel spins alternating red and black for 10 spins. Which is more likely?
- A roulette wheel has landed on red 500 times in a row. Is red or black more likely on spin #501?
- What bet on a roulette table has the best odds to payout ratio?
Tricky? Not really. It's statistics. For questions 1 and 2, we'll ignore the two green spaces (0 and 00) on the wheel and say there is a 50/50 change of getting black or red. So for question one, both occurrences are equally likely, but how many people would be more surprised at the first one? For the second question, even though red has come up 500 times in a row, both are still equally likely on the next spin. Any one spin has nothing to do with any spins that come before it or after it. They are independent events.
For the third question, you may be surprised to know that almost all bets have an equal odds to payout ratio. Expressed another way, for almost any bet you make, the expected return on $1 is -$0.053. The only bet that is different is the 5 number bet (0, 00, 1, 2, and 3) which has a lower expected return of -$0.079.
Every single game boils down to statistics. Slots machines in Washington are required to pay out at least $0.75 for every $1 that is played. Blackjack is a game of statistics if you play with perfect strategy and you only hurt yourself if you "go with your gut." Roulette is a losing battle as we've discussed. Play any game long enough, and you're going to lose money.
The only chance you have is to quit if/when you are ahead. You can't beat the odds. Statistics will always win if given enough time.