Interesting roullette outcomes...too interesting?

Hello, Mr. Shackleford and everyone else interested in the numbers behind the games. I want to share an experience that I had at a casino a few months ago, and see what you guys (and gals) think. In Arizona we don't have live roulette tables, we have the automated wheels where you place your bets on a touch-screen. When I sat down, someone else at the wheel was getting pretty animated because the wheel had just hit two 5's in a row. Then it hit 5 again. Then immediately after the three 5's, it hit three 27's in a row. I walked away after 2 more spins (neither were 5 or 27), thinking there was something a little suspicious about the wheel. I played blackjack for a while and won back a little more than I had lost on roulette (thanks for the youtube videos, Mike). Then I decided to play a little more roulette on the casino's other wheel. In the first 6 spins on this wheel, 5 and 27 both came up. I only go to the casino once or twice a year, and I didn't think I would ever come across such a statistical anomaly in real life. So, what do you wizards of the odds think? What are the chances that a casino having roulette wheels with no bias will show 3 of any number in a row, followed immediately by 3 of any other number in a row, and that within the next 8 spins that you play, both of those numbers will appear again? Thanks for your input.

After an unlikely event happens is a bad time to declare bias or cheating. Unlikely things happen all the time because there are a lot of them. Any given three-spin sequence of roulette is just as unlikely as 5-5-5. For example, 3-32-19 is just as unlikely as 5-5-5, but as humans our hunter/gatherer evolution causes us to zero in on false patterns all the time.

The time to test for bias or cheating is before something happens. That way you won't be telling narratives to yourself after the fact to explain what is most likely randomness.

Quote: MindOverMatter

What are the chances that a casino having roulette wheels with no bias will show 3 of any number in a row, followed immediately by 3 of any other number in a row, and that within the next 8 spins that you play, both of those numbers will appear again? Thanks for your input.

It wasn't even the same wheel. Just coincidence.

File it under "Shit Happens".

Will EvenBob be descending upon this casino to play 5 and 27 all day long?

*In response to SodaWater* I agree completely with the concepts that you describe here, and I thank you for your reply. However, you are not addressing the scale of how rare this type of event actually is. When I sat down and the guy at my table was yelling about two 5's showing in a row, I knew he was an idiot because there is a 1/38 chance at all times that the current roll will match the previous roll. At that point, what are the chances of hitting 5 again this time? Another 1 in 38 chance. However, that has little to do with my question. Let me first mention: when the first five showed, if I was to hypothetically say "I think it will hit the same number twice more in a row" the chances of this happening are 1/38^2 or 1/1444. After the next spin, if I say "I think it will hit the same number twice more in a row" the chances of this wager are also 1/1444. The chances of this type of sequence are at least 1/1444*1444 or 1 in 2,085,136. This does not even include having not one but both of those same numbers appear within the next 8 rolls I witnessed. Do you remember in June 2012 when a roulette wheel hit the same number 7 times in a row in Las Vegas? It was headline news on Yahoo for days, the odds against it were stated as 3 billion to 1, and it turned out in the end that the story was actually based on a picture of a non-action wheel that was being tested by the casino. You may not like my "narrative" style, but facts are facts...and numbers don't lie. So I ask all of you (and Mike probably has the best answer) at what point do odds of millions or billions against 1 become so improbable that they should be considered suspect? And does anyone have the algorithms needed to state the odds of what I saw as a simple, numerical value? Any knowledgeable input is appreciated.

*In response to AceofSpades* I started playing 5 and 27 after they showed up 8 times (4 times each) in 14 rolls. No such luck though, and I moved on after a few rolls that missed. I went back to blackjack and pulled ahead a second time. I've noticed that a lot of people will try to tell you that they are long-term winners in their local casino. They are almost always full of crap, with the possible exception of live poker players or skilled sports bettors....maybe even 6-9 Jacks Or Better, but those machines are hard to find here. The only reason why I almost always win is because I'm happy with walking away with a profit that is only 25% of my original bankroll. Good luck, and good gambling