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Last year my coworkers and I did bowl pickem in our office. Everyone picked the team they thought would win each bowl game.

After everyone made their picks, just for fun we flipped a coin for each game and put the coin's prediction up on the board next to our picks.

Much to our surprise, the coin predicted the first 11 games perfectly!

What is the probability of this happening?

1.) Is it simply 0.5^11 = 0.000488 = 1:2049 odds ???

OR

2.) Is the formula more complicated, such as

p = SUM [0.5 * p1_win + 0.5 * p2_win + 0.5 * p3_win ... + 0.5 * p11_win]

where, pn_win equals the probability that the coin's selected team wins the actual game, through 11 games.

This formula would be to calculate the probability of two independent events: 1) a coin flip, and 2) the outcome of the bowl game. So in essence it combines a coin flip with Vegas odds. For example, if the coin picked Alabama to beat Washington, and vegas says Alabama has a 70% chance of winning the game, the probability would be 0.5 * 0.7 = 0.35. Then sum for each of these games through 11 games.

OR

3.) Some other method I am missing?

Thanks!