MahjPhD CardLab · Methods
How CardLab measures a hand.
What the numbers mean, how they were made, how they were checked, and where they fall short. Written for players, not statisticians.
A careful computer player commits to one hand from the deal, plays it out against three other players in 100,000 simulated games, and CardLab counts how often it wins.
1 · How a hand is measured
Play the game, many times, and count.
CardLab doesn’t calculate odds with a formula. American Mah Jongg is far too tangled for that: the Charleston, calls, jokers and three other players all change what happens. Instead, it plays complete games, very fast, and counts the results.
- 1DealAll 152 tiles shuffled once. East gets 14, everyone else 13.
- 2CharlestonThe first Charleston, an optional second, and a courtesy pass.
- 3PlayDraws, discards, calls, joker swaps, until Mah Jongg or a wall game.
- 4Repeat100,000 games for every hand on the card.
- =Win rateWins ÷ games, plus speed, jokers and points.
The card, written as data
Each line on the card is typed in once as a precise pattern: its groups, suits, numbers, winds, dragons, and where jokers may and may not go. CardLab then lists every concrete 14-tile hand the line allows. The 2026 card’s 55 lines become 1,077 exact hands. The typed card is checked line by line against the printed card before anything runs.
The deal
All 152 tiles are shuffled once. This is exactly equivalent to building the wall and breaking it with dice, so it doesn’t change any result. East then receives 14 tiles and the other players 13.
One hand under test
In each game, one seat commits to the hand being measured from the deal: every pass, discard, call and joker swap serves that hand. The other three seats play whatever looks best to them. The committed seat rotates through East, South, West and North, so no hand gets East’s extra tile more often than another.
The same deals for every hand
Game number 1 deals the same tiles whichever hand is being tested, and so does game 2, and so on. Every hand faces the identical 100,000 deals. A lucky deal full of jokers helps nearly every hand, so comparing hands on the same deals cancels much of the luck and makes the comparisons sharper.
A steady, sensible player
The computer player is consistent, not brilliant. At every decision it asks, “How many tiles am I missing for each hand I could still make?” and favors hands that are close, with a mild preference for higher points and a penalty for concealed hands, which can’t call discards. Its settings were tuned once, then frozen: every published number comes from the same player.
What each number means
Reading a CardLab report.
Every number describes a hand when you commit to it from the deal.
| Measure | What it tells you |
|---|---|
| Win rate | How often the committed player makes Mah Jongg with that hand. Shown with a 95% range. |
| Typical turns | How many draws a winning game usually takes (the median). |
| Joker dependence | How many of the hand’s wins used at least one joker, and how its win rate changes with 0, 1, or 2+ jokers dealt. |
| Points vs. average | Points won or paid per 100 games, compared with an average hand on the card. Bigger is better. This balances a hand’s odds against its value. |
| Lab rating | 1 to 5, by win rate: the easiest fifth of the card is a 5. |
| Backup hands | Other hands sharing the most tiles with this one, so you can switch with few changes. |
| Families | Groups of hands built from the same tiles, each with its own Charleston advice. |
| Charleston guide | The tiles a committed player passes most often for each family, compared with the card as a whole. |
2 · How it was checked
Tested before it was trusted.
Before any results were used, the simulator was run on an earlier card (2022), where statistics from real online play are published. The tests and their passing marks were written down before the first run, so the results couldn’t be nudged after the fact.
| Test | What was checked | Passing mark | Result |
|---|---|---|---|
| Rules | 20,000 games, every tile tracked after every move; every win rebuilt from scratch | No rule broken | Pass No violations |
| Judgment | 20 games replayed move by move and read against the physical card | No rule errors | Pass None found |
| Calibration | 20,000 games compared with real online play: tiles left in the wall, jokers dealt or drawn per player | Within 25% | Pass Ratios 1.18 and 0.97 |
What CardLab doesn’t report
A fourth test asked whether the simulator’s players choose the same hands as people. They don’t, so CardLab doesn’t report hand popularity. Every published number describes how a hand performs when you commit to it, which the three tests above support.
The 2026 card
The 2026 card was typed and checked the same way, and the rules test was repeated on it with no violations. The same frozen player then ran 100,000 games for each of the 55 lines: 5.5 million games in all. No published human statistics exist yet for 2026, so the 2026 results rest on the 2022 checks.
Read the full validation story
The fourth test. It compared the hands that win most often in simulation with the hands that win most often for people, using a rank correlation. The passing mark, set in advance, was 0.6; the result was 0.35.
Why it missed. Concealed hands made up about 23% of computer wins but under 1% of human wins: people rarely go for concealed hands, while the computer happily does when the tiles fit. People also swap jokers about twice as often. The computer player was tuned to score points, and nothing in that tuning teaches it which hands people prefer.
Two attempts to close the gap. First, the player was nudged toward hands that actually finish; agreement rose to 0.57, but the calibration test then failed, so the change was set aside. Second, in a plan written down before running it, three settings were adjusted: a stronger penalty on concealed hands, more calling, and a bonus for flexible racks. The best version that still passed calibration reached 0.42. Pushing the concealed penalty hard enough to reach 0.68 broke calibration again.
The decision. The plan said in advance that if the popularity test still failed after a retune, the 2026 edition would be the narrower one: committed-hand results only, with no popularity figures. That is the edition being published. The popularity question stays open for future editions.
3 · Limitations
What the numbers can and can’t support.
Computer players aren’t people
- They never misread a hand and always know how close every hand is, so games end sooner: about 5 more tiles left in the wall than at human tables.
- They swap jokers about half as often as people do.
- The other three seats are computer players too, so table dynamics differ from a human game.
- The player is sensible, not perfect. Read win rates as a fair way to compare hands; a stronger or weaker player would see different levels.
Simplified rules (version 1)
- No blind passes in the Charleston: every pass comes from the player’s own rack.
- Dead hands aren’t modeled: a call that fits no hand on the card is simply refused.
Sampling error
- With 100,000 games per hand, a typical win rate is accurate to about ±0.14 percentage points (±0.22 at the widest).
- Hands closer together than that aren’t ranked apart.
The benchmark
- The comparison data come from online play on one card year, which may include some computer players.
- There is no second, independent test card yet; a planned check on another year was skipped once the popularity test failed.
4 · FAQ
Questions people ask.
Why doesn’t CardLab show the hands?
The NMJL card is the League’s copyrighted work, and buying it each year supports the organization that keeps the game going. CardLab never reproduces the card. Every hand is named by section and line (S5L2 means section 5, line 2), so keep your own official card beside the report.
Real players switch hands. Why measure a hand by committing to it?
Committing is the only way to compare every hand fairly: each one gets the same deals, the same seats and the same player. It answers a practical question: “If I go for this hand, how often will it come together?” The backup-hands and family tables help with switching.
Why are the win rates so low?
Only one of four players wins each game, some games end with no winner, and committing to a single hand from the deal is harder than choosing freely. On the 2026 card, an average hand wins about 1 in 18 games when you commit to it from the deal.
Why “points vs. average” instead of raw points?
A committed player wins only a small share of games and pays in most of the others, so raw points per game come out negative for nearly every hand. Comparing each hand with the card’s average makes the useful part visible: which hands earn more than a typical choice, and by how much.
So should I always play the top-rated hand?
No. Your rack matters most. The joker and flower tables show how the best choices change with what you’re dealt, and the RECoRD Method is about reading your tiles every turn. CardLab tells you how hands tend to behave; your tiles tell you which one to play today.
Why doesn’t CardLab say which hands are most popular?
Because the simulator’s players choose hands differently from people, so popularity figures from it would be misleading. CardLab reports how each hand performs when you commit to it instead. See “How it was checked” for the full story; this may change in a future edition.
Will the numbers change?
The 2026 results are final: the runs are frozen and checksummed. Each new card gets a new edition, run the same way, about 10 days after the card arrives.
Is CardLab connected to the National Mah Jongg League?
No. MahjPhD CardLab is independent and is not affiliated with or endorsed by the National Mah Jongg League, Inc.
Can the results be checked?
Every simulated game can be replayed exactly from its random seed, and the simulator passes more than 450 automated tests. Questions about the method are welcome: ask here.
Ready to see the numbers?
The full 2026 edition opens February 1, 2027.
MahjPhD CardLab is an independent project and is not affiliated with or endorsed by the National Mah Jongg League, Inc. Analyses refer to hands by section and line number; the NMJL card itself is not reproduced.