Special Match Probability: "Players are matched to a duel at random...."

[Scibra]

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?

 

[tkhunny]

I'm not convinced this makes any sense as presented. I await your personal thoughts and clarifications.

 

[Scibra]

Sorry it's a bit of a mess. I'm trying to find the number of matches needed to get a special match if the chance of getting one increases when you don't get one, and the chance resets to 0 when you do get one.

 

[Steven G]

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?

So I have a question from freemathHELP.com. What question is what exactly do you need help with? Where are you stuck? Why do you think your method is wrong? Please show us your attempt(s) at solving this problem and I am sure that you will get help. Thank you.