About

Professional poker relies heavily on mathematics rather than mere intuition. This Texas Hold'em Probability Calculator determines the equity of a specific hand against an opponent. Equity represents the percentage of the pot a player expects to win over the long run based on the current cards. Understanding these probabilities helps players make Expected Value (EV) positive decisions.

Accuracy in poker demands recognizing the difference between absolute hand strength and relative equity. A pair of Aces is strong pre-flop but vulnerable on a wet board. This tool utilizes a Monte Carlo simulation engine to play out thousands of random scenarios within milliseconds, providing a statistical approximation of your win rate, tie rate, and loss rate against a specific opponent or a random hand.

Formulas

Equity is often estimated using the Rule of 4 and 2 during live play, but exact calculation requires combinatorial analysis or simulation. The probability P of hitting an "out" (a card that improves your hand to a winner) is defined as:

P≈OutsUnseen Cards

When calculating expected value (EV) for a call, we compare the cost of the call to the pot equity:

EV = (Pwin × Pottotal) − Costcall

For Pre-flop combinatorics, the number of distinct starting hands is calculated from the 52-card deck:

C=52 × 512=1326

Reference Data

Matchup Scenario	Favorite Equity	Underdog Equity
AA vs Random Hand	85.2%	14.8%
KK vs Random Hand	82.4%	17.6%
AA vs KK	81.9%	18.1%
AKs vs QQ (Coin Flip)	46.0%	54.0%
JJ vs AKo	56.0%	44.0%
88 vs AKs	51.0%	49.0%
AA vs 87s (Suited Connector)	77.0%	23.0%
22 vs AKs	52.0%	48.0%
KK vs QsJs	78.0%	22.0%

Frequently Asked Questions

This tool uses a Monte Carlo simulation method. Instead of iterating through millions of possible remaining deck permutations (which would be slow for a web browser), it plays out thousands of random deal scenarios instantly. Minor variances of 0.1% to 0.5% are normal and statistically insignificant for strategic decision-making.

Suited cards (e.g., AKs) generally have 2-3% more equity than their off-suited counterparts (AKo) because of the added potential to make a flush. While this seems small, it significantly impacts long-term profitability.

Currently, this calculator focuses on Heads-Up (1v1) scenarios to provide the most accurate strategic baseline. Multi-way equity dilutes significantly; for example, Aces might have 85% equity heads-up but only 45% against 4 random hands.

If you leave the opponent's hand empty, the calculator assumes a "Random Hand". This simulates your equity against any two unknown cards from the remaining deck, which is useful for determining absolute hand strength in isolation.