Jokers, Jokers, Jokers

Greetings and salutations from Bubbe, here to reveal the truth about jokers!

I know what you all are saying, around the table: “Uch, does this set even come with jokers?” “I can’t get a joker to save my life.” And for the Scooby-Doo fans among us, “I would have made that hand, too, if it weren’t for my never getting any jokers!” The flip side, of course, is when you finally settle on a beautiful Singles and Pairs hand and suddenly pick a joker…or two. Only when you DON’T want them, amirite?

Bubbe likes to empirically test her ideas, and the ideal time to test them is when playing in tournaments. As I wrote in a previous blog, I played 29 hands in less than 24 hours and kept stats on each of them. Besides my win/wall percentage (just over 20 percent each), I also kept stats on jokers: specifically, “How many jokers did I have from the deal? How many did the winning hand use?” In looking at those numbers, I was hoping to see whether jokers actually DO play as important a role as we all think. Of course, I am not nimble enough to write about how many jokers get exchanged (if I’m taking too many notes, I can’t PLAY)—but looking at the deal and the winning hand is, at least, a start.

We all understand that eight of the 152 tiles are jokers—that’s a little over five percent of the tiles. On a very unsophisticated level, having 13 tiles in a normal deal (14 when you’re East) means that you have a 65-70% chance of getting dealt at least one joker. In other words, in two out of three games, you should start with one joker—or maybe in one game you are dealt two jokers, and none in two other games. In 29 games, getting 13.25 tiles per deal, my hypothesis is an expectation of being dealt approximately 20 (20.22) jokers: sometimes two, sometimes one, sometimes none. 

How did this bear out? Well, I actually received 21 jokers over the 29 games. Sounds like an accurate sample. What’s a little more interesting is the distribution of these jokers. Remember how I said sometimes you might get one, or two, or none? I actually received two jokers FOUR times, and in one deal I got THREE jokers! That’s 11 of the 21 jokers that I received. In other words, of the remaining 24 games, I only received a joker ten times. In 14 of the 29 games I played, I wasn’t dealt ANY jokers—that’s 48.3%, just under half of all games. 

Ok, fine. Half the time I didn’t start with a joker. Makes sense, even though we like to kvetch that we NEVER do…but is it that important to start with a joker? What if you pick a bunch, isn’t the FINAL result the most important? How many jokers did the winning hands have?

First of all, as I said before, 20.7% of the games were wall games—that’s six of the 29. How many of the winning hands were Singles and Pairs, or even regular hands that turned out to be jokerless? It turns out that no one at the tournament tables that I played at won a Singles and Pairs hand, which makes me think this is not a perfect testing ground. In this specific, limited sample, only ONE of the 23 winning hands was jokerless: the first 2468 hand with the four Flowers. That is only 4.3% of all winning hands. Sounds statistically significant to me.

How many jokers were involved in the other 22 winning hands? Consider that we pick and throw tiles throughout the game but generally hold onto our jokers, so they should be present in most hands by the end of a game. However, not every game gets to the end of the last wall. Since there are only eight jokers, the average number of jokers per player by the end of each game should be somewhere under two jokers apiece, but I’m going to hypothesize that the winner would have at least two jokers: in other words, better than just random distribution of jokers.

How did this one bear out? There were 56 total jokers among the 23 winning hands, including the one jokerless win. That averages out to 2.43 jokers per winning hand. That’s about a half a joker more, per hand, than the “just under two apiece” that would be expected when a game ends. 

And what was the distribution of these jokers among winners? As I said, one winning hand was jokerless. Four of the 23 hands had FOUR jokers; five had three jokers. Only ONE other hand ended with a single joker; half of the winning hands (12/23, or 52%) used two jokers. Again, I wish I’d kept track of exposures/exchanges, and whether these hands had used jokers that were later exchanged…

But the evidence is clear. Jokers absolutely, in this small sample of 29 games, made a BIG difference. I can only expect, on average, about .65 jokers per deal, and in half the games I started with none. The winning hand had a higher than “random chance” number of jokers, by almost half a joker per game.

Just thought you’d like to know your kvetching is well-founded!

If you have any questions or comments, feel free to email me at bubbefischer@gmail.com ; I love hearing from you!

Talk to you soon.

Bubbe