Hint: It’s a lot.
A lot of card games like to brag about how many combinations are possible in the game. But other card games don’t have the variety that Cheer Up! does. We’ve played the game for years and years and have never seen the same combinations! So we wanted to put a number to it. By dusting off the ol’ math machine (brain), playing with Excel (horribly), and doing some intense math (probably all wrong because we didn’t pay attention in AP Calc), we can put Cheer Up! to the test!
Let’s see how much variety there really is with math that is almost certainly misused beyond belief!
Alright, the first thing we have to do is list out all the Questions in the game and their requirements. Luckily, we already have such a list.
As you probably know, each Question has one or more requirements that correspond to A, B, or C answer cards, which are marked in their respective columns. Those that require two of the same cards (like B+B) are indicated by a “2” in the column there.
Now we need to figure out how many different combinations are possible for each question. We do this by using a Permutation formula (stay awake, this gets good!).
For the purposes of this experiment, we’re going to assume that the ORDER of the cards does NOT matter for the questions where two of the same answer card is required (like B+B). So we’ll use the COMBINATION formula. If the question requires B+B, there are 130 possible answer cards that could be drawn (all of the B cards, including the NSFG pack!). This formula then tells us how many ways a person can play 2 cards from that deck without repeating a combination. Remember, we are trying to find how many combinations are ultimately shown to the group, so we are ignoring the fact that you actually are supposed to draw four and then pick two. Hopefully that’s right.
So there we have it. There are 8,385 ways to answer to the question “What should I name my new dog(s)?” (and any other question that only requires one deck). Not bad. You probably will never see all those combos, but that’s not a HUGE number. However, adding in more required answer cards makes many more possibilities, and you start to really see a jump when we get to the A+B+C questions. Having three different possible decks brings us to over 2 million combos!
Totaling that we have over 18 million combos possible in the base game alone. If we’re playing with 7 players, we can multiply all those numbers by 6 (one person each round is the dealer) and then totaling that up gets us to a whopping 108,000,000 answer combinations.
Now we can add in the NSFG questions, which brings us to almost 122,000,000.
But wait, there’s more! We forgot the Rules! Every question can theoretically be paired with one of fifty possible Rules, so we can just multiply these guys by 50 to get the actual number of unique possible rounds in Cheer Up! Drumroll please…
If one person, alone in their room, presumably listening to Dave Matthews Band, went through the game and simply picked random answers for every Question and drew a random Rule each time, that version of the game would only be one of over a billion possibilities. Every time you play a 7-player game of Cheer Up! (all the way through, no less) your game is only one of 6 billion unique possibilities. That’s pretty awesome! That’s double the chance that three generations of your family were born on a Leap Day. You have 35 times more of a chance to win the Powerball than to see two exact same games of Cheer Up! (still not a good chance, so please don’t buy more tickets).
Now that we have the basic numbers, we can have some fun.
How about if we run two infinitely-long games of Cheer Up! at once? We can just multiply 6 billion by itself. The number of combinations is so big we need help pronouncing it.
If it takes about five hours to go through all the questions in a game (50 rounds), we can deduce that you’ll see approximately 60 answer combinations on average per hour, which is about 1/5 of a game (so 10 rounds x 6 players). Dividing our 6 billion possibilities by 60 brings us to the 101 million hours it would take to see every combo in the game.
That’s 11,500 years. If every single person who owns Cheer Up! as of this writing played continuously for 24/7 (which obviously some of you are already doing) and streamed the games online so that we could all watch them, it would still take 23 years for all of humanity collectively to see every single combo in the game.
And finally, this brings us to the most important metric of all…
We think that’s a pretty good deal! :)
P.S. We think this is pretty close, but leave us a comment if this math is way off because the dog ate our homework.
Get Cheer Up! on Amazon now! (Don’t worry, there’s no math in it!)