Poker Hand Probability & Expected Value Calculator

Introduction

Poker decisions are usually made with incomplete information, but the math behind many common spots is straightforward: you are paying a price to continue (the call), and you have some chance to win the pot (your equity). This calculator combines draw probability, pot odds, and expected value (EV) into one workflow so you can quickly check whether a call is profitable under your assumptions.

Use it for typical Texas Hold’em situations such as flush draws, straight draws, and marginal made hands. The goal is not to “solve” poker—real play involves ranges, position, and future betting—but to give you a reliable baseline for disciplined decisions.

How to use the calculator

1. Select your hand type (for context and the quick reference table).
2. Enter your outs (cards that improve you to a likely winner). If you’re unsure, start conservative.
3. Choose the game stage: flop (two cards to come) or turn (one card to come).
4. Optionally enter known dead cards (folded cards you saw, exposed muck, etc.).
5. Enter pot size and the bet you must call.
6. Enter your estimated equity versus opponents’ ranges (from experience, a solver, or another tool).
7. Click Calculate to see probabilities, required odds, EV, and a call/fold suggestion.

Tip: If you want to compare scenarios, change one input at a time (outs, bet size, or equity) and watch how EV and the decision margin move.

Formula and assumptions

1) Draw probability from outs

The calculator estimates the probability of hitting one of your outs on the next card and by showdown. It uses standard deck counts for Hold’em:

• On the flop, there are typically 47 unseen cards (52 minus your 2 hole cards minus 3 board cards).
• On the turn, there are typically 46 unseen cards (52 minus your 2 hole cards minus 4 board cards).

For the flop-to-river probability, it applies the complement rule (miss turn AND miss river):

It also shows the popular Rule of 4 and 2 approximation (outs × 4 from flop, outs × 2 from turn) as a quick mental check.

2) Pot odds (break-even equity)

Pot odds answer: “What equity do I need for a call to break even if there is no more betting?”

3) Expected value (EV) of calling

This page uses a simplified one-street EV model: you either win the pot after calling or you lose your call amount. With equity expressed as a percentage:

Interpretation: If EV is positive, the call is profitable under your inputs. If EV is negative, folding is better (again, under the simplified assumptions).

Worked example

Limitations

• Equity is an input: the calculator does not compute equity from ranges; it uses the equity percentage you provide.
• No implied odds or fold equity: future betting, bluffing, and the chance opponents fold are not modeled.
• Outs can be “dirty”: some outs may make you a second-best hand (e.g., completing a straight when a flush is possible).
• Multiway pots are simplified: player count is collected but not used in the current EV math; treat equity as already adjusted for the number of opponents.
• Card removal is simplified: “cards you know about” reduces the remaining deck size conceptually, but the probability formulas use standard 47/46 denominators as implemented in the script.

Quick concepts refresher (outs, odds, EV)

Outs are the unseen cards that improve your hand to a likely winner. Common examples:

• Flush draw: usually 9 outs
• Open-ended straight draw: usually 8 outs
• Set mining (pair to trips): 2 outs after the flop, 3 outs preflop (context matters)
• Two overcards: often 6 outs (but can be dirty)

Pot odds convert the bet size into a break-even equity threshold. EV converts that threshold into a dollar expectation per call under the model.