What are the odds of the game Mafia? long question.?

Question

My cousins and I were playing the game mafia, where everyone gets a card and the person with a jack is a character called mafia but no one knows which card people have until the end of the round. My cousin Teddy got mafia three times in a row. On the fourth time, my cousin Johnny said Teddy might be in the mafia. I said I didn't think so because he had mafia three times already. Johnny said it didn't matter because every time the cards were reshuffled the odds were all the same for everyone and it doesn't matter what people had earlier. I said not completely true. It is rare to get mafia three times in a row and the odds were even less to get mafia four times in a row so therefore the odds were not the same. Who's right in this pathetic fight and can anyone put numbers to it? There were 10 players: 2 mafia, one doctor, one detective, and 6 villagers. It doesn't matter the rules. I just want to know the odds to get mafia 3 times compared to 4 times.

Answer 1

With 10 players, and 2 mafia, the odds of getting the mafia in any given round is 20%. 2 rounds in a row and the chances drop to 4%. 3 rounds and it falls further to .8 %. Finally the odds of getting mafia four rounds in a row is a miniscule .016%, a virtually statistcal impossibility.

Answer 2

Johnny is right: the odds of being in the mafia are the same from game to game. It doesn't matter if Teddy was mafia three games in a row: his chances of getting it again are the same in each game. Now, it's true that three in a row is more likely than four in a row - but once you've had three in a row, it doesn't REDUCE your chance to draw a jack a fourth time.