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With the world cup coming up, our office/yard is having an office sweep. Each person who buys a ticket randomly draws a team out of a hat/box. Because we don't have 32 people in these locations, generally the office people buy two random tickets then the people in the yard buy a single random ticket.

Let's assume 8 teams are more likely to win than the others, is there any difference in the odds of winning if:

A) The office people buy two tickets than the yard buy the remaining.

B) The office people buy a single ticket, than the yard people buy a single ticket, than the office buy another ticket.

I feel like the odds should change, because there is then less choices for the yards people in A.

I understand obviously the office staff have an advantage because they are buying two tickets. But does the order of buying them affect chances?

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Since each ticket has the same probability of being the winning ticket, the order of choosing doesn't matter. A person who buys $2$ tickets has a probability of $\frac{1}{16}$ of winning, no matter when he buys the tickets. Since all the tickets are drawn at random, the last ticket is just as likely to win as the first.

Imagine that no one is allowed to know what ticket he drew until after the World Cup is complete. On the Monday after the tournament, everyone meets and opens the envelope containing the name of his team. Now the winner is whoever happens to have the envelope with Argentina (or whatever). Clearly the order in which the envelopes were distributed doesn't matter -- all that matters is how many envelopes you have.

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  • $\begingroup$ Thanks, what if the teams performance does matter? Like lets say there are 8 teams with a high probability of winning? $\endgroup$ – Phalanx Jun 13 '18 at 0:00
  • $\begingroup$ @Phalanx Then obviously it is advantageous to be one of the first $8$ people who chooses. I would think that choosing early in the process would be more important than the number of tickets you get to buy, but in any event it wouldn't be fair to let the people who choose early also buy two tickets at that time. $\endgroup$ – saulspatz Jun 13 '18 at 0:06
  • $\begingroup$ Sorry, I don't think I mentioned that it's randomly chosen out of a box. So we don't get to pick which country $\endgroup$ – Phalanx Jun 13 '18 at 0:07
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    $\begingroup$ What's randomly chosen, the order of choosing or the team? Please edit the question to explain the rules fully, rather than clarifying them in comments. (That's the standard procedure for this site.) $\endgroup$ – saulspatz Jun 13 '18 at 0:10
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    $\begingroup$ Yeah sorry, the only office sweeps I've done have been random. So I made an incorrect assumption. I'll edit original post. $\endgroup$ – Phalanx Jun 13 '18 at 0:13

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