Friday, July 1, 2022

Published July 01, 2022 by with 0 comment

Mario Party's 'Hide and Sneak' is not Balanced

Are you consistently losing to a 6 year old and looking for an excuse. If so, you've come to the right place.
'Hide and Sneak' is one of the mini-games in Mario Party. The basic rules are that 3 people hide and 1 person finds them. In round 1, there are 4 hiding spots. In round 2, 3. In round 3, 2. 

Each player on the hiding team picks a spot to hide and the seeking player picks one spot. If a player is hiding in the picked spot, he's out.

If a player is out he doesn't participate in later rounds.

If any players remain on the hiding team after 3 rounds, the hiding team wins.

Is this game 50/50? Working through the math, start with 1 hider:

  • round 1, there's a 3/4 chance of not being found
  • round 2, there's a 2/3 chance of not being found
  • round 3, there's a 1/2 chance of not being found
Thus, for an individual player on the hiding team, there's a (3/4) * (2/3) * (1/2) chance of not being found. That's 1/4, or 25%.

Inverting that, the seeker has a 3/4, or 75% chance of finding a given player after 3 rounds.

Since there are 3 players and their hiding decisions are independent, the chance of the seeker finding all 3 players in 3 rounds is just (3/4)^3, or 27/64. That's only 42%. It isn't balanced at all.

Is there an obvious way to balance it? What if we did 4 rounds with 5 starting hiding spots. For one hider:

  • round 1, there's a 4/5 chance of not being found
  • round 2, there's a 3/4 chance of not being found
  • round 3, there's a 2/3 chance of not being found
  • round 4, there's a 1/2 chance of not being found
Multiplied out, that's a 1/5, or 20% chance of not being found so 4/5, or 80% success chance for the seeker. The chance that the seeker finds all 3 players in 4 rounds then is (4/5)^3, or 51%. 4 rounds is way more balanced than 3 rounds.



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