Hello. My name is Zach. I have one question. It is not for any homework/schoolwork/college assignment etc, just a personal question. Also please note that this question is not regarding any actual lottery, there are no item prizes, money, or anything of any value to win.

Assume for all intents and purposes to win the “lottery” the goal is to match a randomly selected 5 digit number. Rather than purchasing a ticket which already has numbers selected and hoping that you match the number, this lottery allows you to pick all 5 of the numbers yourself. The “grand prize” so to speak is obtained by matching all 5 digits exactly. The 2nd place “prize” is obtained by matching the last four digits. The 3rd place “prize” is obtained by matching the last three digits. The 4th place “prize” is obtained by matching the last two digits. The 5th place prize is obtained by matching the last digit. Any prize is better then no prize at all and multiple prizes would be preferred (obviously) however the virtual benefits of the prizes are quite far apart (meaning that winning the “grand” prize once would be far preferred to winning the 5th place “prize” 50 times.

Also there is no limit to how many prizes you can win. For example you could win a 2nd place and a 4th place prize, or you could win the 3rd place prize 4 times.

Obviously you could guarantee winning the 5th place prize by simply purchasing 10 tickets, and ending each tickets number with a different digit between 0-9. Because of this obviously you could also guarantee winning the 5th place prize 10 times if you entered 100 tickets and used a rotation of 0-9 for the final digit. (10 of each number between 0-9).

If I was to enter somewhere between 200-300 tickets into the drawing, what numbers should be selected on the tickets. For example should they all start with the number 1 and then only the last 4 digits changing, or should they all start and end with different numbers? What would the best numbers be to select for each ticket to maximize my odds of winning both the highest and the most amount of prizes possible.

Thank you for your consideration.

The quick answer is that if the numbers drawn are truly random, and the payoff for having a 1st prize ticket is always the same (that is, if you happen to get all 5 numbers correct on two tickets, your win twice as much as if you had only one winning ticket), then it doesn't matter what strategy you use - they all have the same expected return. However, most lotteries have a set amount of cash prize, so that holders of all winning tickets have to share the prizes. Under this scenario it doesn't make much sense to purchase duplicate tickets, so the only strategy that matters is to not buy duplicates - other than that it doesn't matter what other method you employ.