Mahjong Probability Calculator

ToolsProbability Calculator

Mahjong Probability Calculator

Find the chance of drawing the tile you need over your next few turns.

One tile starts with 4 copies (Jokers and flowers have 8). Take away the ones you have seen. If any of several tiles would help, add their copies together.

All 152 tiles minus the ones on your rack, in the discards and in exposed groups.

How many turns you expect to draw.

For example, 2 if you need two more of the same tile.

Your odds

Estimates based on the numbers you enter. Many in-person tables and online platforms do not allow outside tools during play, so use this for practice and review. Unofficial fan tool, not affiliated with the National Mah Jongg League.

Examples

The chance of drawing a tile you need is lower than most players expect, and it climbs slowly with each extra draw. These examples show the chance of drawing at least the number you need from the wall. Count the tiles left with our Tile Tracker, and see our intermediate strategy guide for how to use the odds.

SituationChance
One tile with 4 copies left, 120 tiles unseen, next draw3.3%
The same tile over your next 5 draws15.8%
The same tile over your next 10 draws29.7%
A tile with only 2 copies left, 100 unseen, 5 draws9.8%
Any Joker (8 left), 120 unseen, 5 draws29.6%
Two of a tile (4 left), 120 unseen, 10 draws3.4%

Probability questions

How is the chance calculated?

Drawing tiles from the wall is drawing without replacement, so the calculator uses the hypergeometric formula: the number of ways to draw what you need divided by the number of ways to draw any tiles from the unseen pile.

Why use unseen tiles, not the size of the wall?

Tiles in other players’ racks are as hidden from you as tiles in the wall, so from where you sit every unseen tile is equally likely to be your next draw. Use all 152 tiles minus the ones you have seen.

Does it include tiles I could call from the discards?

No. It only covers tiles you draw from the wall. A discard that gives you a call is an extra chance, so the real chance of getting a tile is a little higher.

How many copies of a tile are left?

Each Bam, Crak, Dot, wind and dragon has 4 copies. There are 8 Jokers and 8 flowers. Subtract the copies you have seen on your rack, in the discards and in exposed groups, or use the Tile Tracker to count them.

What if I need two of the same tile?

Set “How many do you need?” to 2. The calculator then gives the chance of drawing at least two of the matching tiles in your draws.

What if any of several tiles would help?

Add together the copies left of each tile that would help, and enter that total. The calculator treats them as one group of matching tiles.

Does it tell me the chance of completing a hand?

No. Completing a hand depends on every tile the hand needs, and this tool does not use the NMJL card. Use it for each tile you are waiting on, as a guide to which tiles are worth chasing.

Can I use this during a game?

Check your table’s rules first. Many in-person tables do not allow phones during play, and online platforms often do not allow outside tools. It is best for practice and for reviewing a game afterwards.

Count the tiles left

Tap tiles as you see them and get the numbers for this calculator.

Open the Tile Tracker

Play a full game online

Ready for a real table? Play online with friends.

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