Numbers, numbers everywhere....

Greetings and salutations to all my Number Nerds--I'm hoping this article will find its audience!

Mark Twain said, "There are three kinds of lies: lies, damned lies, and statistics." Well, according to Real Mah Jongg, Bubbe has now "won" 200 games on the 2026 card, and I've received lots of detail about which hands and how often. Oh, I also had 87 Wall games, but it doesn't say which hands those were. 

The biggest problem is, I'm not sure how useful any of this is if I don't know how many games I actually PLAYED--the big "denominator" in the equation. Since I don't know how many of each hand I tried, it doesn't tell me which hand choices were the easiest to win. I will also add that by airing my history, I'm giving a huge leg up to those who will play me for the rest of the year. "Past performance does not guarantee future behavior," to sort-of quote investment advisors--but it's pretty likely that I will continue to have the same biases going forward. 

Be that as it may,  having reached the significant milestone of 200 wins, I am going to share my extrapolations from the statistics at RMJ. Your mileage will most assuredly vary--you may LOVE this year's Quint or 369 sections. Spoiler alert: I have not been winning with those hands as much. 

First of all, as I said, I have won 200 games. Not sure whether that was 200 of 287 total games (yeah, right). 400, 1000? Perhaps that statistic will be included next year.

For scoring purposes, I am going to consider that there were 72 different hands. Some were simple; others had variations, e.g. a one- and three-suited version, or a hand at the lower and upper ends of the number line, or like W1, you could choose which Wind couple appeared as kongs and pungs.

Here is the percentage distribution for total hands vs. hands I won, by section:          

 

	PERCENT OF HANDS,BY SECTION
	ON CARD		MY WINNERS
Year	5.5		6.5
Even	12.5		10.5
LN	4.25		8.5
Quints	4.25		1
CR	18		36
Odd	22		12
Winds	14		15.5
369	11		7
S&P	8.5		3
	100		100

In other words, I won a LOT more times using Consecutive Runs hands than any other section, nearly twice their 'fair share' on the card, and didn't use Odd or Singles and Pairs hands nearly as often as they appeared on the card. As I said, we can't completely understand this without knowing how many total attempts I made at the CR section....but we have to start somewhere. 

Another issue is the distribution of types of hands on the card. 18% of the hands on the card are concealed, but they were very poorly represented among my winners: only 5.5% of my winning hands were concealed, and nearly half of those were the White Whale (SP3). That's a perfect example of selection bias: I kept trying for some hands more than others.

On the other end of the spectrum, 26% of the hands on the card don't require any singles or pairs: every meld can use jokers, every meld can be exposed. Do you think Bubbe won with this kind, more often than the concealed ones? Yup, although I was surprised: they were less represented among my winners than I expected (only 23%).

As for specific components that I favored more than the average distribution: 

FLOWERS: I've been saying one of the reasons this card feels easier to me is that PUNGS of Flowers are a lot easier to attain than pairs or kongs. The pairs actually appear more frequently: Flower pairs appear in 21% of all hands, vs. (at least one) Flower pung appearing in 17%, and sextets appearing in only 3%....but I love the pungs. Among my 200 wins, 35.5% had at least one pung of Flowers. Just as seen with my preference for the CR section, I won twice as often as expected with Flower pungs.

DRAGONS: Dragons in ANY form appear in 32% of all hands, including singles, pairs, pungs, and kongs. I seem to like Dragon hands; 41% of my winners included at least two dragons (either two singles or a pair, at minimum). One very interesting statistic is that, like the Flower pungs, I seemed to like Dragon kongs--they appear in 12.5% of all hands on the card, but 25.5% of my winning hands included at least one foursome!

LIKE-NUMBER KONGS: Just like Dragon kongs, at least two like-numbered kongs (or quints) appear in 12.5% of all hands. Personally, I again leaned heavily on this type of combination. 21% of my winners fell into this category!

Overall, the hands I won with most often were, indeed, CR hands with three Flowers: specifically, I used CR2.1/2.2 ("Choose Your Chow"), CR5.1 and CR5.2 ("Madame DeFarge"), often switching between their one- and two-suit options; between them, 22% of ALL my winning hands were among these four. 

I won an additional 7% of all hands playing O5 and 369 #3 which are basically "cousins" of CR5.1 (Flower pung and dragon kong, with a consecutive pair, pair, pung). In O5 the pair/pair/pung combination is 135 or 579 instead of three consecutive numbers. 369 #3 slightly flips the order: it's pair/pung/pair (33 666 99). My theory is that 6's are very hard to get this year, so they decided to give us a break and let the 6's be the pung, with the ability to use jokers and/or call for exposure.

I guess the shortest, non-statistical way to say all of this is, I have an affinity for the hands that use a pung of Flowers and a kong of Dragons. (I won another 2% with W5!)

I try very hard to learn every section of the card, but honestly, sometimes I just gravitate to certain tiles. In previous years I said I was "a sucker for a Soap," wanting to play the Year hand, but my stats show I'm only at 1% above the expected amount for the 2026 section...and I haven't tried for SP6 yet! Then again, it IS only May...

What about you? Do you find yourself favoring certain hands or sections? Write me at Bubbefischer@gmail.com and tell me which hands you've been winning with....

 Talk to you soon!

 

Bubbe