Poker Odds Calculator: Texas Hold'em Outs, Pot Odds and EV

Outs, pot odds and EV in Texas Hold'em: calculation and example

With 9 outs on the flop, the chance of hitting at least once by the river is 1 − (38/47 × 37/46), or 35.0%; on the turn it is 9/46 = 19.6%. The tool compares this exact probability with the equity required by the pot odds, call / (pot + call), and derives the expected value of the call. The rule of 4 and 2 is shown only as a mental cross-check.

The three calculations

• Hit probability: on the flop, 47 cards are unseen (52 minus your 2 and the 3 on the board). P = 1 − ((47 − outs)/47 × (46 − outs)/46). On the turn, P = outs / 46.
• Required equity = call / (pot + call), with the pot already including the opponent's bet. The odds shown are pot / call, e.g. 4.0 : 1.
• Expected value = P × pot − (1 − P) × call. The call is rated profitable when P reaches the required equity, which is the same as a positive EV.

Example: pot of 120, 30 to call, flush draw (9 outs) on the flop. P = 34.97%. Required equity = 30 / 150 = 20%. EV = 0.3497 × 120 − 0.6503 × 30 = +22.5: a profitable call. The same draw on the turn gives 9/46 = 19.57%, just under 20%: EV −0.7, so the tool says fold.

Presets: gutshot 4 outs, pair to set 2, open-ended straight draw 8, flush draw 9, flush + straight draw 15. The mental rule (outs × 4 on the flop, × 2 on the turn) overestimates with many outs: 60% for 15 outs against 54.1% exactly.

Assumptions and limits

• Every out is assumed to give you the winning hand; remove dirty outs yourself.
• On the flop, the probability covers turn and river, so it assumes you see both cards with no further bet, as when all-in.
• No opponent hand simulation and no player count: the tool does not compute hand-versus-hand equity.

Frequently Asked Questions

What are the odds of hitting a flush draw on the flop?

With 9 outs you complete the flush on the turn or river 34.97% of the time: 1 − (38/47 × 37/46). Seeing only the turn, the chance drops to 9/47 = 19.1%, and from turn to river it is 9/46 = 19.6%.

How does the rule of 2 and 4 work in poker?

Multiply your outs by 4 on the flop (two cards to come) and by 2 on the turn (one card) to estimate your percentage. It holds up to 8 or 9 outs; beyond that it overestimates, e.g. 60% instead of 54.1% with 15 outs.

How do you calculate pot odds?

Divide the amount to call by the final pot after your call: 30 to call into a pot of 120 gives 30 / 150 = 20% required equity, or odds of 4 to 1. If your chance of winning is above 20%, the call is profitable over time.

How many outs does a gutshot straight draw have?

A gutshot has 4 outs, against 8 for an open-ended straight draw. On the flop, 4 outs give a 16.5% chance by the river, which needs pot odds of about 5 to 1 to call.

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

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