# Poker Odds & Outs Calculator Calculate exact hypergeometric probability of completing a poker draw and compare it against the pot odds you are being offered. --- - **Canonical URL:** https://dothecalculation.com/calculators/poker-odds-calculator - **Category:** Hobbies & Leisure Utilities - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology --- ## Poker Odds & Outs Calculator Calculate the exact probability of completing a draw from your outs and the cards left to come, using real hypergeometric probability rather than the table-side 'rule of 4 and 2' approximation — then compare it to the pot odds you're being offered. A probability reference tool, not gambling advice. - Exact hypergeometric probability, not just the quick estimate - Compares your hand's equity against the pot odds you face - Shows the shortcut rule alongside the exact math so you can see the gap ## Quick Answer — What Are My Odds of Completing a Draw? The exact probability of hitting at least one of your outs is a hypergeometric calculation: **1 − (ways to miss every out ÷ total ways the remaining cards could come)**. This is more precise than the well-known 'rule of 4 and 2' (outs × 4 with two cards to come, outs × 2 with one card to come), which is a fast mental shortcut, not exact math. **Quick reference (probability of hitting, with two cards to come from a standard 47-card unseen deck):** • 4 outs (gutshot straight draw) → **16.5%** exact (rule of thumb: 16%) • 8 outs (open-ended straight draw) → **31.5%** exact (rule of thumb: 32%) • 9 outs (flush draw) → **35.0%** exact (rule of thumb: 36%) • 15 outs (combo draw, e.g. flush + straight) → **54.1%** exact (rule of thumb: 60% — this is where the shortcut breaks down noticeably) The rule of thumb tracks the exact math closely for small out counts but overstates your real probability as outs climb past about 8-9, which is exactly why this calculator computes the real combinatorial answer instead of the approximation. ## How to Use This Calculator This is a probability and pot-odds reference tool for the math taught in any poker strategy resource — it is not gambling advice, and nothing here encourages wagering more or chasing losses. Enter your number of outs (the cards remaining in the deck that would complete your hand), whether you're calculating with two cards to come (after the flop) or one card to come (after the turn), and — separately — the current pot size and the bet you're facing, to see the pot odds you're being offered. **Worked example — flush draw after the flop:** 9 outs, 2 cards to come, 47 unseen cards, facing a $20 bet into a $100 pot. Exact hit probability = 1 − C(38,2)/C(47,2) = 1 − 703/1,081 = **34.97%**. Pot odds: you need to call $20 to win a $120 pot (the $100 already there plus your $20 call), so required equity = 20 ÷ 120 = **16.67%**. Since your 34.97% equity clears the 16.67% you need, this is a **profitable call by a wide margin** — an equity edge of about 18.3 percentage points. **A second example — gutshot after the turn:** 4 outs, 1 card to come, 46 unseen cards, facing a $25 bet into a $50 pot. Exact hit probability = 1 − C(42,1)/C(46,1) = 1 − 42/46 = **8.70%**. Required equity = 25 ÷ 75 = **33.33%**. Here the math says **do not call** — your real equity (8.7%) falls well short of what the pot is offering you (33.3%), a losing decision by more than 24 percentage points. ## The Formula This Calculator Uses **Exact hit probability** = 1 − [C(Unseen − Outs, Cards to come) ÷ C(Unseen, Cards to come)], where C(n, r) is the standard combinations formula (n choose r). This directly counts how many ways the remaining unseen cards could arrive without any of your outs showing up, versus the total ways they could arrive at all. **Unseen cards** defaults to 47 (52-card deck minus your 2 hole cards and the 3-card flop) with two cards to come, or 46 (minus the turn card too) with one card to come. **Rule-of-thumb estimate** = Outs × 4 (two cards to come) or Outs × 2 (one card to come) — shown alongside the exact figure so you can see how closely the shortcut tracks reality for your specific out count. **Pot odds and required equity:** Required equity % = Bet to call ÷ (Pot + Bet to call) × 100. Pot odds ratio = Pot ÷ Bet to call. If your exact hit probability exceeds the required equity, calling is profitable on a single-street, no-future-betting basis — this calculator flags that comparison directly. ## Why the Rule of 4 and 2 Isn't Exact The 'multiply outs by 4 or 2' shortcut exists because it's fast enough to use at the table without a calculator, and it's a genuinely useful approximation for the outs counts (roughly 4-12) that come up in most real hands. But it's a linear approximation to a combinatorial (non-linear) probability, so it systematically overstates your real equity as the out count grows. The gap is small and mostly irrelevant for a 4-out gutshot (16% vs. 16.5% exact) but becomes meaningful for large combo draws — a 15-out hand (open-ended straight draw plus a flush draw) is only 54.1% to hit on the exact math, not the 60% the shortcut suggests. For a decision that size, using the exact figure instead of the shortcut is the difference between a marginal call and a clearly profitable one, or vice versa. The same combinatorial logic — counting favorable outcomes against total outcomes — underlies a lot of the math this site covers. The [combination calculator](/calculators/combination-calculator) computes the raw nCr values directly if you want to see the combinatorics for a different scenario, and if you enjoy probability distributions in a different game context, the [D&D stat roll calculator](/calculators/dnd-stat-roll-calculator) applies similar dice-probability reasoning. ## Reading the Pot Odds Comparison Pot odds answer a single question: what percentage of the time do you need to win this hand for calling to break even, based only on the money already in the pot and the bet in front of you? If your drawing hand's real equity is higher than that required percentage, calling shows a profit on this street's math alone. This calculator's 'equity edge' figure is simply your exact hit probability minus the required equity — a positive number means the call clears the bar, a negative number means it doesn't, on this street's information alone. **Important nuance this calculator does not attempt to model:** implied odds (extra money you might win on future streets if you hit) and reverse implied odds (money you might lose if you hit a draw but still lose the hand) can shift a borderline decision either direction. Treat this tool's output as the baseline single-street math, not a complete decision framework. If you track skill ratings across game sessions rather than single hands, the [board game Elo rating calculator](/calculators/board-game-elo-calculator) applies a similar probability framework to head-to-head match outcomes. ## Frequently asked questions ### Is this calculator promoting gambling? No. This is a probability and combinatorics reference tool — the same math taught in any poker strategy resource. It does not encourage wagering more, chasing losses, or treat the calculator as a way to win money; it simply computes exact drawing-hand probabilities. ### Why is the exact probability different from 'outs times 4'? The outs-times-4 rule is a fast linear approximation used at the table. The real probability is a combinatorial (hypergeometric) calculation, which the shortcut tracks closely for small out counts but increasingly overstates as outs climb — a 15-out draw is 54.1% exact, not the 60% the shortcut implies. ### What counts as an 'out'? Any remaining card in the deck that would improve your hand to a probable winner. For a flush draw with four cards of a suit, the outs are the nine remaining cards of that suit not yet visible to you. ### What is required equity, and how is it different from pot odds? They describe the same threshold two ways. Pot odds is usually expressed as a ratio (like 5-to-1), while required equity is that same relationship expressed as a percentage you need to win to break even on the call. ### Does a positive equity edge guarantee a profitable call? It means the call is profitable based only on this street's pot odds and your exact hit probability. It doesn't account for implied odds (extra winnings on future streets) or reverse implied odds (losing more even after hitting), both of which can change a real decision. ### Why does the number of unseen cards change between flop and turn? After the flop, 5 cards are visible (your 2 hole cards plus the 3-card flop) out of 52, leaving 47 unseen. After the turn, a 6th card is visible, leaving 46 unseen — one fewer card and one fewer card to come. ### Can I use this for games other than Texas Hold'em? The underlying hypergeometric math applies to any draw where you're counting outs against unseen cards, including Omaha. You'll just need to adjust the unseen-card count to match that game's structure. ## Related concepts - **Hypergeometric distribution** — The probability distribution for drawing a specific number of successes from a finite population without replacement — the exact math behind poker outs. - **Pot odds** — The ratio of the current pot size to the cost of a contemplated call, used to determine the minimum win probability needed for a profitable call. - **Implied odds** — Additional money you project winning on future betting streets if your draw completes, beyond what's already in the pot — not modeled by this calculator. ## Related guides - [Understanding Calculator Formulas: How DTC Turns Inputs into Results](https://dothecalculation.com/blog/site-guides/understanding-calculator-formulas) — Understand how Do The Calculation formulas are presented, what the explanation blocks mean, and how to verify calculator logic before using a result in a real decision. ## Related calculators - [Aquarium Volume Calculator](https://dothecalculation.com/calculators/aquarium-volume-calculator) — Calculate your exact fish tank capacity in gallons and liters based on length, width, and height for accurate water volume. - [Coffee-to-Water Brew Ratio Calculator](https://dothecalculation.com/calculators/coffee-brew-ratio-calculator) — Calculate the exact coffee-to-water ratio for pour-over, French press, drip, or cold brew, with gram and tablespoon results. - [D&D Stat Roll Calculator](https://dothecalculation.com/calculators/dnd-stat-roll-calculator) — Simulate D&D character ability score rolls and analyze probability distributions to build optimized tabletop characters. - [Epoxy Resin Mixing Calculator](https://dothecalculation.com/calculators/epoxy-resin-calculator) — Calculate exact resin and hardener volume and weight for tabletop pours, coasters, and river tables from your mold dimensions and mix ratio. - [Garden N-P-K Fertilizer Ratio Mixer Calculator](https://dothecalculation.com/calculators/garden-fertilizer-npk-calculator) — Solve custom fertilizer mixtures from multiple sources using a matrix equation solver to hit your exact target N-P-K ratio. - [Garden Plant Spacing & Soil Volume Calculator](https://dothecalculation.com/calculators/garden-spacing-calculator) — Calculate how many plants fit your garden bed and the exact soil volume needed based on spacing, bed size, and raised bed layout. --- _This calculator is a probability and mathematics education tool, not gambling advice. It computes exact drawing-hand probabilities and compares them to pot odds using standard combinatorics. It does not model implied odds, opponent tendencies, or future betting, and should not be used as the sole basis for wagering decisions._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/poker-odds-calculator). Quote freely with attribution and a link to this page._