What is opening-hand probability?
Turn an opening into a measurable condition and compare deck ratios fairly.
Define a condition and a deadline
Opening-hand probability is the chance of meeting a user-defined starting condition by a chosen point. Replace “a good hand” with a testable statement such as “at least one starter-tag card in the opening hand” or “one copy each of A and B by turn two.”
A first-turn draw, required resources, and search order can change whether the same card is a usable opener. DrawState evaluates only the rules and effects that you enter.
Build a baseline from deck and hand size
For a simple condition, a smaller deck or larger opening hand makes the same target count easier to see. Three targets in a 40-card deck have a 33.76% chance of appearing at least once in five cards, but a 30.11% chance of appearing exactly once. Success and desired-copy rate answer different questions.
Extra draws only behave like a larger hand when no earlier action changes the deck. Model shuffles, bottoming, and searches in their actual order.
Compare deck versions
Record the success condition, target turn, play order, and mulligan rule. Change only the target or access-card count in the next version. If several variables change together, you cannot tell which one caused the result.
A higher success rate may also bring more duplicates or fewer hands at the desired count. Consider those outcomes and the opportunity cost of a deck slot together.
Know what the result does not claim
Opening consistency is not win rate. Matchups, decisions after the opening, follow-up cards, and time limits are separate. Save the settings summary and engine version so later comparisons keep the same definition.