Hello Mathematics Guru's,

Can I first caveat this question by saying, I'm wholly aware the house always has a mathematical edge if you play long enough in Roulette, but i am interested to know the following all the same.

I would like to know the percentage chance of the following occurring playing Roulette.

I like to bet on 2 of the dozen bets, which pays 2:1. Specifically the middle column (13-24) and high column (25-36) at the time covering approximately 64.8% of the board.

So my question is, what is the percentage chance of the low column numbers (1-12) and the zero occurring, ie the numbers i'm not betting on hitting consecutively? Specifically, 6, 7 and 8 times in a row.

Many thanks


  • $\begingroup$ Can you figure out the probability of [that event] happening one time? $\endgroup$ – The Chaz 2.0 Dec 14 '18 at 15:11
  • $\begingroup$ Yes, the chance of the first dozen (1-12) or the Zero hitting is 35.1% probability. Any single no including the zero is 2.7% and any dozen is 32.4% $\endgroup$ – Keir Doubas Dec 16 '18 at 19:13
  • $\begingroup$ Great! Now raise that probability ($0.351$) to the power of 6, 7, or 8. $\endgroup$ – The Chaz 2.0 Dec 17 '18 at 8:04
  • 1
    $\begingroup$ Many thanks, i've worked it out! $\endgroup$ – Keir Doubas Dec 18 '18 at 10:51

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