Pick 2 probability, historical simulation and random selection answer different questions. This guide keeps the fair theoretical model separate from what the stored records happened to contain.
Theoretical outcome space
There are 36 FIRST possibilities and 36 SECOND possibilities, giving 36 × 36 = 1,296 ordered outcomes.
This is the theoretical probability for one exact ordered outcome under the fair model. It is not calculated from historical frequency.
Multiple exact selections
The Win Probability Calculator displays n / 1,296 for a user-entered number of exact selections.
This is exact only when n represents distinct exact ordered outcomes. The calculator accepts a count; it does not inspect the identities of the actual tickets. Duplicate selections do not create additional distinct coverage.
Historical Simulator
The Historical Simulator accepts one ordered pair per entered line and checks exact order against all valid loaded history. A reversal is not treated as an exact match.
It reports exact historical hits, retrospective hit rate, most recent hit, recent hit dates and draws, and the entered line with the highest historical count. It does not provide a selectable historical window.
The line with the highest recorded count is a historical result, not a prediction.
Historical simulation limits
The simulator does not calculate winnings, ROI, expected return or predictive validity. It answers how often the entered exact pairs appeared in the loaded records.
Random Number Picker
The standalone Random Number Picker uses browser cryptographic random values to generate FIRST and SECOND independently from 1–36. Doubles are therefore possible, and the generator does not use historical weighting.
The current source converts a random integer with randomUint32 % 36 + 1. Because 232 is not evenly divisible by 36, this creates a very small modulo bias. Browser cryptographic randomness is used, but the current implementation should not be described as perfectly uniform.
Analyzer selection modes
The Analyzer also provides Random, Hot, Gap and Balanced modes. The latter three use historical positional weighting; Random gives each FIRST and SECOND value the same selection weight within the interface.
These are research-oriented selection modes. The existing interface correctly notes that historical weighting does not change the underlying theoretical odds of any Pick 2 result.
Historical versus theoretical probability
Historical hit rate asks: “How often did this exact ordered result appear in the recorded data?” Theoretical probability asks: “What probability does the fair 36 × 36 model assign to this exact outcome?”
Those answers should not be merged. A historical count can describe the records without changing the mathematical probability of the next draw.