Authored on October 31, 2000.

In Reply to: * Chances for Roulette Dozens, Columns to Miss 8, 9, 10, 11, 12 Consecutive Spins* posted by

: Ion, I've noticed that you are quite proficient in figuring odds on roulette. Could you please tell me the chances on a single and double zero roulette wheel of 1 column or dozen not showing for 8,9,10,11,12, and 13 times? If possible could you give the answer in 1 in a thousand or 1 in 87 or whatever it works out to be? Thank you for your help.

o Axiomatic one, I understand your question this way.

*What is the probability of one dozen or one column to SKIP N consecutive spins?*

In such a case, we work with the *complementary* event of one dozen/column. The probability for one dozen or one column to *appear* is 12/38 = 0.3158 (31.58%). The probability of the complementary event is p=(38-12)/38 = 26/38 = 0.6842 (68.42%).

We can use now this last number and raise it to various powers. Or, we can use SuperFormula, the *binomial distribution formula (BDF)* to automate the process.

Here are the results for one dozen/column to miss N consecutive roulette spins.

5 times in a row: p = 15% (it happens 15 times in 100 spins; 1 in 6.667 spins);

6 times in a row: p = 10.3% (1 in 9.7 spins);

7 times in a row: p = 7% (1 in 14.3 spins);

8 times in a row: p = 4.8% (1 in 20.8 spins);

9 times in a row: p = 3.3% (1 in 30.3 spins);

10 times in a row: p = 2.2% (1 in 45.5 spins);

11 times in a row: p = 1.5% (1 in 66.7 spins);

12 times in a row: p = 1.1% (1 in 90.9 spins);

13 times in a row: p = 0.7% (it happens 7 times in 1000 spins; 1 in 142.9 spins).

Good luck, Player(s)!

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