Pi is an irrational number with an unpredictable distribution of the numbers 0 to 9. Yet patterns do emerge. Can we say with certainty that there is some point in pi where there are a billion consecutive zeros? Is there any way to calculate the number of digits of pi that must be expanded to have a 50% probability of this occuring? Is this analagous to the statement that if you flip a coin long enough you will with certainty get one billion heads in a row ?