is it luckier to buy tickets on the rich side of town?Prev TopicNext Topic

• Tucker Black

  

  Colorado
  United States
  Member #173,294
  February 25, 2016
  1,178 Posts
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  Today, 5:55 am

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  In response to FrostyGambling

  Quote: Originally posted by FrostyGambling on Jul 20, 2026

  "Some of those packs are immediately distributed to retailers, but not every pack is immediately sent out. Retailers reorder them when they get low and need to replenish what they have in their store."

  Yeah good point, it may be true that the roll that has the top prize may not be sent out yet. So I think not only buying from multiple locations but also buying throughout the game period as well could improve your chances of running into the winning scratch off ticket.

  It doesn't make any difference.

  To make the math easy, let's consider a game with one million tickets, of which one of them wins $1 million. All the others are losers.

  If all the tickets were available for sale (let's say you're the first person to buy a ticket), the probability of winning with one ticket is obviously 1 in 1 million. 

  However, let's say that 90% of the entire game's tickets are sitting in a warehouse and 10% of the tickets have been distributed to stores. Does this affect your probability of buying a winning ticket? Let's see...

   

  We will use what is known as conditional probability to break this down so we can calculate it. It goes as follows:

  The probability of you buying a winning ticket is:

  Prob(the winning ticket is sitting in a warehouse) times Prob(you buy a winning ticket from a store given that the winning ticket is sitting in a warehouse)

  PLUS

  Prob(the winning ticket is not sitting in a warehouse) times Prob(you buy a winning ticket from a store given that the winning ticket is not sitting in a warehouse)

   

  The probability that the winning ticket is sitting in a warehouse is 90%. The probability that you buy a winning ticket from a store, given that the winning ticket is sitting in a warehouse, is zero. This means the first part of the above equation is 0.9 times 0, which is 0.

  The probability that the winning ticket is not sitting in a warehouse is 10%. The probability that you buy a winning ticket from a store, given that the winning ticket is not sitting in a warehouse, is 1 in 100,000. The reason is that 10% of the one million tickets is 100,000 tickets, of which one of them is a winner. Thus, the second part of the above equation is 0.1 times 1 in 100,000, which is equal to 1 in 1 million.

  Add the two together, and you get 0 plus 1 in 1 million, which of course equals 1 in 1 million.

  So it doesn't matter whether all the tickets are available for sale or only a small fraction. The reason is because no one knows if the winning ticket is sitting in a warehouse or not. If it's not, then the probability of winning is much higher. But first you have to overcome the probability that the winning ticket is not sitting in a warehouse, and the two simply cancel each other out.

  Hope this helps.