About

Miscalculating poker hand equity costs real money. A player holding AK suited against QQ pre-flop has roughly 46% equity - close enough to feel confident, far enough to bleed chips long-term without precise numbers. This calculator evaluates Texas Hold'em hands using a complete 7462-class ranking system covering every distinct 5-card hand. Equity is computed via Monte Carlo simulation across 10,000 randomized runouts from the remaining deck stub, producing win, tie, and loss probabilities accurate to approximately ±1%. The tool assumes a standard 52-card deck with no jokers and no knowledge of opponent holdings beyond dealt community cards.

Outs - the count of unseen cards that improve your hand to a stronger category - are computed exhaustively, not estimated. The popular "rule of 2 and 4" approximation (outs × 2 per street remaining) diverges from true probability above 8 outs. This tool reports exact probability from the hypergeometric distribution of remaining cards. Note: equity figures assume random opponent hands. Against a tight range, actual equity shifts significantly. Adjust conclusions accordingly.

Formulas

Each 5-card hand receives a rank R from 1 (Royal Flush) to 7462 (worst High Card: 75432 offsuit). From n available cards (5 ≤ n ≤ 7), the best hand is the combination with the lowest rank value:

Best = min R(h) over all h ∈ n5

Monte Carlo equity estimation runs N = 10,000 trials. Each trial deals random cards from the deck stub D to complete 7 total cards. A random opponent hand is also dealt. The equity is:

Equity = W + 0.5 ⋅ TN

where W = wins, T = ties, N = total trials. The outs count O is the number of cards c in the deck stub such that adding c to the current cards produces a hand with a strictly better rank class than the current best hand. The exact probability of hitting at least one out with s cards to come from d unseen cards:

P(improve) = 1 − (d − O)!(d − O − s)! ⋅ d!(d − s)!

For a single card to come, this simplifies to P = Od.

Reference Data

Hand Rank	Name	Example	Frequency (5-card)	Probability	Odds Against
1	Royal Flush	AKQJT suited	4	0.000154%	649,739 : 1
2	Straight Flush	98765 suited	36	0.00139%	72,192 : 1
3	Four of a Kind	QQQQ7	624	0.0240%	4,164 : 1
4	Full House	KKK33	3,744	0.1441%	693 : 1
5	Flush	AJ842 suited	5,108	0.1965%	508 : 1
6	Straight	T9876 mixed	10,200	0.3925%	254 : 1
7	Three of a Kind	555K9	54,912	2.1128%	46.3 : 1
8	Two Pair	AA88J	123,552	4.7539%	20.0 : 1
9	One Pair	JJA93	1,098,240	42.2569%	1.37 : 1
10	High Card	AQ963 mixed	1,302,540	50.1177%	0.995 : 1
Common Pre-Flop Matchups (Approximate Equity)
	AA vs KK	Overpair vs Underpair	81% vs 19%
	AKs vs QQ	Overcards vs Pair	46% vs 54%
	AKo vs 72o	Best vs Worst	66% vs 34%
	JJ vs AKo	Coinflip	57% vs 43%
	KQs vs AJo	Dominated suited	40% vs 60%
	99 vs AKs	Mid pair vs overcards	54% vs 46%
	65s vs AA	Suited connector vs aces	22% vs 78%
	TT vs AQo	Pair vs 2 overcards	56% vs 44%

Frequently Asked Questions

This tool simulates a single random opponent per trial. For multi-way pots, equity shifts because more opponents increase the chance at least one holds a strong hand. A pocket pair like QQ has roughly 80% equity heads-up against a random hand but drops to approximately 55% three-way. For multi-opponent analysis, the simulation would need to deal and evaluate multiple opponent hands per trial, which this version does not perform.

The rule of 2 and 4 approximates probability as outs × 2% per street remaining (or ×4 with two streets). This linear approximation diverges from the hypergeometric reality above approximately 8 outs. For example, with 15 outs and 2 cards to come, the rule gives 60% but actual probability is about 54.1%. This calculator uses exact combinatorial math from the remaining deck size.

Yes. The evaluator treats the ace as both high (in A-K-Q-J-T) and low (in 5-4-3-2-A). The wheel (5-high straight) is correctly ranked as the lowest straight, rank class 10 within straights. This applies to both straight and straight flush detection.

With 10,000 trials, the standard error of a binomial proportion near 50% is approximately √(0.25/10000) ≈ 0.5%. The 95% confidence interval is thus roughly ±1 percentage point. For most practical poker decisions, this precision is sufficient. Increasing to 100,000 trials would reduce error to ±0.3% but increase computation time by 10×.

The calculator requires exactly 2 hole cards to evaluate hand strength. Community cards are optional - with 0 community cards (pre-flop), the Monte Carlo simulation deals all 5 community cards randomly per trial. With 3 (flop), 4 (turn), or 5 (river) community cards, the simulation fills only the remaining streets.

Yes. Being suited adds approximately 2-4 percentage points of equity depending on the situation. For instance, AKs vs QQ is about 46% equity while AKo vs QQ is about 43%. The suitedness provides additional flush and straight flush outs that compound across streets.