Prediction Streak

In a tournament, ten games of cricket would be played. Each game would necessarily have a winner (i.e., there are no draw or tied games). None of the games are played simultaneously. The outcome of each game is independent of the outcomes of any of the other games. Further, both the teams in a game have an equal chance of winning.

The organiser of the tournament announces a 'prediction contest' where a contestant has to predict the winner of each of the games. The first correct prediction would win 1 point and the second consecutive correct prediction will win 2 point and so on.

A wrong prediction will earn no points and the next correct prediction will earn only 1 point, irrespective of the number of correct predictions done earlier.

For the first four matches, predicting all results correctly will earn \(1+2+3+4=10\) points. However, if only the third prediction proves incorrect the number of points would become \(1+2+0+1=4\).

What would be the most common score of a contestant for the '10 match prediction contest'?


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