We are playing a version of Canasta.
Tonight we had 6 players and 4 decks. Everyone playing individually. The goal is to get the most points which is most easily achieved by getting a “canasta” - i.e. 7 of the same number including wild cards (2s and jokers). As you play, you lay down your sets (3 or more cards). So you typically know which card number someone is targeting for his/her canasta.
The question is whether adding a 5th deck speeds up the likelihood that someone will get a canasta faster.
Two competing hypotheses (which may both be wrong):
- it does not change anything because the odds for which cards you pull should not change when you add another deck that has the same odds. It will be more likely someone gets a canasta with more decks but it won’t change how fast it happens.
- it does change because there are more of each card (going from 4 decks to 5 decks means going from 16 to 20 of each number). Having more of each number means that more than one person can successfully get a canasta for the same number.
Does anyone have a model for how to think about this?