TP MASTER LAB
State the model before the number
There are 22,100 unordered three-card combinations: 52 × 51 × 50 ÷ 6. We assume no jokers, no replacement and both A-2-3 and Q-K-A as valid endpoint sequences. Wraparound K-A-2 is excluded. The categories below do not overlap.
Choosing a different ace ranking changes which run wins, but not these category counts as long as the same twelve runs remain valid. A game with wild cards, a reduced deck or special exceptions needs a different model.
Exact category probabilities
| Category | Hands | Probability |
|---|---|---|
| Trail | 52 | 0.2353% |
| Pure sequence | 48 | 0.2172% |
| Sequence, excluding pure | 720 | 3.2579% |
| Colour, excluding pure sequence | 1,096 | 4.9593% |
| Pair | 3,744 | 16.9412% |
| High card | 16,440 | 74.3891% |
Reproduce the arithmetic
Trail: choose one of 13 ranks, then three of its four suits, giving 13 × 4 = 52. Pure sequence: twelve rank runs × four suits = 48. An ordinary sequence has 12 × (4³ − 4) = 720 combinations after removing the single-suit runs.
Colour: for each of four suits choose three of thirteen ranks, then remove twelve runs, giving 4 × (286 − 12) = 1,096. Pair: choose its rank, two suits, a different kicker rank and a kicker suit: 13 × 6 × 12 × 4 = 3,744. High card is the remaining 16,440 hands.
The downloadable site package includes an enumeration script that classifies every combination and checks that these counts sum to 22,100. This is a calculation about a defined deck, not an APK security or randomness audit.
What the percentages cannot tell you
The probability of receiving a pair is not the probability that a pair beats all other players. Opponent count, known cards, comparisons and table-specific rules change that question. Hands dealt from the same deck are dependent, so multiplying independent single-hand probabilities is not a valid shortcut.
A long run without a trail does not make the next freshly shuffled deal “due” to contain one. An app animation, a lucky session or a losing streak also cannot establish whether its shuffle is fair. That would require evidence about the actual implementation and suitable testing.
Use these figures to understand the card model. Do not treat them as staking advice, income estimates or a prediction service.