what formula would be correct to find the odds of rolling 2 dice "X" number of times without a seven showing. There are 36 combinations when rolling 2 dice with six sides. Im wondering how often one could roll 20 times. One person suggested 1-((5/6)26thpower). Another stated it would have to be 1-(5/6) * (1/6).

Also curious if this would be true... At times during the game the 'button' is 'off' and one could roll a seven without harm. If I wanted to count only the rolls when the button is 'on' wouldn't it be the same likelihood/formula? as in not counting the 'off' rolls. Trying to say a person rolled 6 times, then button was turned off for 3 rolls, then the person rolled another 14 times, wouldnt that be the same as odds of rolling 20 times at once?

what formula would be correct to find the odds of rolling 2 dice "X" number of times without a seven showing. There are 36 combinations when rolling 2 dice with six sides. Im wondering how often one could roll 20 times. One person suggested $\displaystyle 1 - \left(\frac{5}{6}\right)^{26}$. Another stated it would have to be $\displaystyle 1 - \frac{5}{6} \cdot \frac{1}{6}$.

Also curious if this would be true... At times during the game the 'button' is 'off' and one could roll a seven without harm. If I wanted to count only the rolls when the button is 'on' wouldn't it be the same likelihood/formula? as in not counting the 'off' rolls. Trying to say a person rolled 6 times, then button was turned off for 3 rolls, then the person rolled another 14 times, wouldnt that be the same as odds of rolling 20 times at once?