The home and toss advantage are pretty huge in test cricket at the moment. Here's my suggestion to negotiate that while still maintaining randomness and unpredictability till the last match of the series (unlike awya team always chooses or teams alternate methods).
For an n match series, make a pot with n home balls and n+1 or n+2 away balls. (The exact number can be formulated in any way).
Instead of the toss, draw one ball from the pot. The away team has a slight advantage, and if a team gets the advantage in one test, their probability goes down for next matches. So something like Root winning 5/5 tosses vs India becomes highly improbable (0.2% in this case vs 3.1% in usual toss scenario).
Interest to hear any flaws in this method.
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