### How to Play the Lottery

As should be obvious, there is no way to predict what numbers are chosen in a lottery. Any patterns that appear in winning numbers are simply due to chance. The numbers that people choose though, are most definetly not random. Therefore, the goal of playing the lottery should not be to guess the numbers, but rather to ensure that the numbers you choose have the lowest probability of anyone anyone else picking the exact same numbers.

#### Statement of the Problem

Although I have no idea if any actual lottery plays by these rules, the goal of this thought is to find those six two digit numbers (AA BB CC DD EE FF) such that

1. Each number is between 00 and 99 inclusive
2. The probability of a human randomly choosing these six numbers in this specific order is the lowest of any six two digit number sequence

To do achieve the goal, I need to answer the following questions:

1. Where does the data for this thought come from? Lotteries do not publish the numbers people choose except for the winning numbers (which are useless since these are effectively randomly chosen).
2. What is the "memory" of a human random number generator? That is, does the first chosen number effect the second chosen number (yes)? Does the first effect the third (yes)? Does the first effect the fourth (maybe)? At what point does the effect of the first number become indistinguishable from noise?
3. Depending on the answer to the memory question, what is the probability distribution of a human random number generator generating a two digit number? What is the probability distribution depending on the first chosen number? What is the probability distribution depending on the first and second chosen number? Knowing the answer to the memory question will tell me how many probability distributions I need to find.