Poker Odds Calculator (Texas Hold'em)

How this calculator works

Count the cards that complete your hand — or pick a common draw from the preset list — and the calculator turns them into exact probabilities: the next card, and (from the flop) the chance of getting there by the river. The rule-of-2-and-4 estimate sits right beside the exact number so you can see precisely how much the shortcut flatters big draws.

Add the pot and the bet you're facing, and the pot-odds line completes the decision: the price expressed as required equity, and whether your draw clears it — with the flop-street subtlety handled honestly. A call that sees both cards (an all-in) gets judged against the by-river number; a call that buys only the turn gets judged against the single-street number, with implied odds noted as what must cover any gap.

The formula

Unseen cards after the flop: 52 − 2 (yours) − 3 (board) = 47

P(hit the turn)  = outs ÷ 47
P(hit the river) = outs ÷ 46
P(by the river)  = 1 − (47 − outs)(46 − outs) ÷ (47 × 46)

Required equity  = call ÷ (pot + call)
Rule of thumb: outs × 2 per street, × 4 for both

Pure combinatorics — every unseen card equally likely — as taught in any probability course and applied to hold'em in MIT OpenCourseWare's 15.S50 Poker Theory and Analytics. The pot-odds framework is David Sklansky's The Theory of Poker. The preflop matchup equities below come from exhaustive enumeration of all possible boards — the standard computation every equity tool reproduces.

Worked example

You flop a flush draw (9 outs) and face a $20 bet into an $80 pot (the defaults):

1. Unseen cards: 47. Next card: 9 ÷ 47 = 19.1%
2. By the river: 1 − (38 × 37)/(47 × 46) = 1 − 0.650 = 35.0% (rule of 4 says 36 — close)
3. Pot price: 20 ÷ (80 + 20) = 20% required equity
4. Facing an all-in: 35.0% ≥ 20% — clear call
5. Facing one street of betting: 19.1% vs 20% — a hair short on direct odds, and implied odds (the money you win when the flush arrives) close the gap easily here

That last line is the whole craft in miniature: the same draw, the same price, and the answer turns on what your call actually buys.

Assumptions & tips

• Discount dirty outs before trusting clean math. A straight card that also completes an opponent's flush is not a full out. Exact probability applied to the wrong outs count is precision without accuracy.
• Memorize three numbers: flush draw 35%, open-ended straight 31.5%, gutshot 16.5% — all by the river. Most in-game arithmetic is one of these plus pot odds.
• Pot odds price the call; implied odds price the future. Deep stacks make marginal draws profitable; short stacks make them folds. The pot in front of you is never the whole pot you're playing for.
• The coin-flip table prices all-ins. Knowing that a dominated ace is a 3:1 dog changes how casually you call shoves with AQ — the preflop matchups are the tax table of tournament poker.
• The math is the entertainment budget's friend. Odds tell you the cost of your decisions; they promise nothing about tonight. Play stakes whose swings you can genuinely afford.

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