Casino odds?

Question

I was just at a casino where black numbers came up on the roulette wheel twelve consecutive times. Can you calculate the odds of this?

This may be harder: what are the odds of the blackjack dealer getting a 10 (including all 10-value cards, King, Queen, Jack) or Ace as his first card 80% of the time? (If it matters, the casino uses four decks)

Let's say the dealer had 20 hands, 80% of which he got a 10, Jack, Queen, King, and Ace as his first card.

Also, is there a way to compute the odds of the dealer winning 80% of the time, regardless of his first card? (meaning, his hand beats everyone) I am trying to figure out how the seemingly impossible luck of the dealer is just random chance.

So far, I have to agree with Sanjay. Although I've heard that each spin is a separate event, unrelated to any other, I believe that is the wrong approach to take when calculating the odds. It is not close to 50/50 each time. Otherwise, it would be commonplace to see red or black come up many times consecutively. It does not. And when it happens, it is something remarkable, in the true sense of the word; it is so rare that you view it as something out of the ordinary.

Answer 1

Roulette:
Landing on black: 18/38 = 47.37%
12 straight: (.4737)^12 = .0001276

.012% chance


Can't answer part two without some kind of "number of hands" limit. The long-term (ie. fair decks used forever) chance is zero.

Answer 2

The two contributors above me have totally right mate:
Here's a quote from you:

So far, I have to agree with Sanjay. Although I've heard that each spin is a separate event, unrelated to any other, I believe that is the wrong approach to take when calculating the odds. It is not close to 50/50 each time. Otherwise, it would be commonplace to see red or black come up many times consecutively. It does not. And when it happens, it is something remarkable, in the true sense of the word; it is so rare that you view it as something out of the ordinary.

What you seem to be doing is trying to get a formula that would allow you bet on the chance of red coming in 7 times in a row, on a roulette table you can only bet on the next number and one number is no more likley to be spun than any other.

I have worked in casinos that have had up to a hundred roulette tables and getting long runs of numbers is quite normal.

Blackjack is a variable % game it can be as much as -6%.

Answer 3

Something lost on most people is that the odds of the wheel coming up black 12 consecutive times is exactly the same as it going RBRBRBRBRBRB or BBRBRRBRRRBB or any other random combination of reds and blacks. Don't get too emotionally invested in what the ball has done on previous spins. It doesn't remember where it went the previous times at all.

Answer 4

This can't really be calculated because each spin is a separate event, unrelated to previous events. This is also a very small sample, so any result would be skewed.

Answer 5

The odds are you are going to lose your money.