Time magazine asks, What is the probability of rolling a pair of dice 154 times continuously at a craps table, without throwing a seven? Their answer: 1 in 1.56 trillion.
Patricia Demauro, a New Jersey grandmother,had a 154-roll lucky streak, which lasted four hours and 18 minutes, broke the world records for the longest craps roll and the most successive dice rolls without "sevening out."
But there's actually some path dependence, and a stat professor who really knows gambling estimated it as 1 in 5.3 billion.
So, 1 in a trillion, or billion. Both are beyond our intuition, but the extra 3 zeros matter.