Equity, Ranges, Draws, and Outs
Learning objectiveDistinguish known-card probabilities from range-based equity estimates.
Understand the idea
Equity is the expected share of the final pot: wins plus the appropriate fraction of ties. Hand-versus-hand equity assumes both hands known, useful for post-game study but usually unavailable live. Hand-versus-range equity weights plausible opponent holdings; range assumptions matter as much as the calculation.
An out is a future card that improves your hand enough to win under the assumed opponent hand. On a flop with nine clean flush outs, the rough turn-or-river improvement chance is 1 − (38/47)(37/46) ≈ 35%. Some outs may be dirty or an opponent may redraw, so improvement probability is not identical to winning equity.
At the poker table
A flush draw may have nine apparent outs, but a paired board can give an opponent a full house even when the flush arrives.
Code and decision sketch
Pseudocodeestimated_equity = (wins + ties / players_in_tie) / trials
# Sample only legal unseen cards and plausible opponent hands.Common mistake
Do not count a card as a clean out without checking the opponent range and board texture.
Try it yourself
Explain why equity against one known pair differs from equity against a range containing sets and stronger draws.