Players are matched to a duel at random. There is a chance that the match will give more rewards than usual to the victor. The chance for a special match is increased by 20% for a player for each non-special match they play after their last match (their chance to get a special match immediately after their last one starts at 0%). A special match happens if either player "rolls" a success based on his chance, guaranteed if a player went 5 previous matches without a special match, unless the other player's last match was a special match.
Assuming an infinite number of opponents can be matched together, on average how many matches must one player play to get a special match?
Assuming an infinite number of opponents can be matched together, on average how many matches must one player play to get a special match?
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