The model
Choose 3 distinct cards from 52, without considering deal order: 52 × 51 × 50 ÷ 6 = 22,100 hands. This model accepts 12 runs (A-2-3, 2-3-4 through Q-K-A), excludes jokers and counts every hand once.
Category frequencies
| Category | Hands | Share of 22,100 |
|---|---|---|
| Trail / Trio | 52 | 0.2353% |
| Pure sequence | 48 | 0.2172% |
| Sequence | 720 | 3.2579% |
| Color / Colour | 1,096 | 4.9593% |
| Pair | 3,744 | 16.9412% |
| High card | 16,440 | 74.3891% |
How the counts are built
- Trail: 13 ranks × 4 choices of 3 suits = 52.
- Pure sequence: 12 rank patterns × 4 suits = 48.
- Mixed sequence: 12 × (4³ − 4) = 720.
- Color: 4 × C(13,3) − 48 pure sequences = 1,096.
- Pair: 13 pair ranks × C(4,2) suit pairs × 12 kicker ranks × 4 kicker suits = 3,744.
- High card: subtract the other 5 counts from 22,100 = 16,440.
Frequency is different from strength
A pure sequence is slightly rarer than a trail, yet the classic rules place a trail above it. The ranking is a game rule, not a list sorted by probability. A hand’s frequency also says nothing about how many opponents remain or what they hold.
Use the numbers to learn
Expect ordinary high-card hands to be common in randomly dealt practice hands. Record the category of each of 20 practice deals, then compare your small sample with the long-run proportions. A short streak does not change the next fair deal.
Guide evidence record
| Parameter | Value |
|---|---|
| Enumerated hands | 22,100 |
| Card ranks × suits | 13 × 4 |
| Sum of category counts | 22,100 |
Editorial review: . Guide parameters and source measurements are separate from APK release specifications.