On New Year’s eve my older son was playing poker with his friends using 2 decks of cards – see if you can spot the oddity in the picture ðŸ™‚

This is the 11:30 pm text I got from my older son who is at a new year’s eve party with friends – lol – glad he’s h… twitter.com/i/web/status/1â€¦—

Mike Lawler (@mikeandallie) January 01, 2020

For today’s project we decided to explore some of the probability ideas around playing poker with 2 decks of cards. First we just looked at the possible hands and talked about some potential questions to ask:

For an introductory problem, we looked at the number of ways of getting a Royal Flush and then all types of flushes with a 5 card hand dealt from a single deck of cards:

Now we looked at how regular flushes could happen when dealt from a two decks of cards shuffled together. We also had a good discussion about whether or not it was more likely or less likely to get a flush in the 2 deck situation:

Finally, we went back to Mathematica to take a look at the numbers for a general flush with one and two decks. Here we are lumping all kings of flushes together – regular ones, straight flushes, and Royal flushes are all the same.

Compute the chances of various hands with 2-deck poker is a pretty fun math exercise for kids.