# Probability same football square wins all four quarters

A local casino has a Super Bowl football squares promotion going on. All the 100 squares are guaranteed to be filled by the customers. The casino will pay a certain amount to the winner of each quarter and then is thinking of paying a large bonus if the same square wins all four quarters. I started thinking about estimating the probability that the same square will win all four quarters. See if you agree witH my analysis as follows: The first quarter score is guaranteed to be won since all 100 squares are filled. And that same first quarter square will win the second, third, and fourth quarters if and only if these other three quarters have a score of "0"(e.g., 0, 10, 20, 30 etc) for each of the two teams. Now, the probability a teams score in any given quarter will be "0" can be estimated by anamlyzing previous games. In all 49 previous super bowl games there have been 49x4x2 = 392 quarterly scores by the teams involved. The number "0" was scored in 105 of these 392 quarterly scores. Thus the (approx) prob that a team scores "0" points in a quarter is 105/392 = 0.2679. So, the approximate prob that quarters Two, three, and four will result in scores of "0" for each team for each quarter is 0.2679x0.2679x0.2679x0.2679x0.2679x0.2679 = .0004 . Thus the prob that the same square will win all four quarters is approx .0004

• Much about the situation you're describing is unclear -- indeed the second half I am not sure I followed at all. But even in the first half of the question it's not quite clear how the winning squares are obtained. (Are they equally likely to be winning squares, for example?) ... Could you edit your question to clarify how the thing works? Assume many of us don't know what these things are or how they work (I sure don't). – Glen_b -Reinstate Monica Jan 12 '16 at 0:44
• I agree with your analysis Burt - pretty unlikely!!! – MikeP Jan 12 '16 at 16:19