Poker Probability Calculator

Poker Probability Calculator

Enter the number of cards that will improve your hand (e.g., 9 for a flush draw, 8 for an open-ended straight draw).

Probability of Hitting:

On the Turn (next card):

" + probTurnPercent + "%

" + oddsTurnFormatted + " to 1

By the River (two cards to come):

" + probByRiverPercent + "%

" + oddsByRiverFormatted + " to 1

Understanding Poker Probabilities and Outs

In poker, especially Texas Hold'em, understanding probabilities is crucial for making informed decisions. While you can't predict the exact cards that will come, you can calculate the likelihood of improving your hand, which helps you decide whether to call, raise, or fold.

What are 'Outs'?

'Outs' are the cards remaining in the deck that will improve your current hand to a winning hand (or at least a significantly better hand). For example, if you have a flush draw (four cards of the same suit), any of the remaining cards of that suit in the deck are your 'outs'.

Common Examples of Outs:

• Flush Draw: If you have two hearts in your hand and there are two hearts on the flop, there are 9 remaining hearts in the deck (13 total hearts – 2 in hand – 2 on flop = 9 outs).
• Open-Ended Straight Draw: If you have 5-6 and the flop is 7-8-X, any 4 or 9 will complete your straight. There are four 4s and four 9s in the deck, totaling 8 outs.
• Gutshot Straight Draw: If you have 5-7 and the flop is 6-8-X, only a 9 will complete your straight. There are four 9s in the deck, totaling 4 outs.
• Set/Trips: If you have a pair in your hand (e.g., 7-7) and the flop is A-K-7, you have 2 outs for a set (the remaining two 7s).

It's important to count your outs carefully and avoid 'duplicate outs' (e.g., a card that completes both a straight and a flush should only be counted once for the combined probability).

How the Calculator Works

This calculator focuses on the probabilities after the flop has been dealt (meaning 5 cards are known: your two hole cards and the three community cards on the flop). It then calculates the chances of hitting one of your 'outs' on the next card (the Turn) or by the River (either on the Turn or the River card).

• Cards in Deck: 52
• Cards Seen (Flop): 5 (your 2 hole cards + 3 flop cards)
• Unknown Cards Remaining: 47

The calculations are based on the following formulas:

• Probability of hitting on the Turn: (Number of Outs) / 47
• Probability of hitting by the River: 1 - [((47 - Outs) / 47) * ((46 - Outs) / 46)]

These formulas account for the decreasing number of unknown cards as more cards are dealt.

The "Rule of 2 and 4" (Approximation)

For quick mental calculations at the poker table, many players use the "Rule of 2 and 4":

• After the Flop (two cards to come): Multiply your outs by 4 to get an approximate percentage chance of hitting by the river. (e.g., 9 outs * 4 = 36%)
• After the Turn (one card to come): Multiply your outs by 2 to get an approximate percentage chance of hitting on the river. (e.g., 9 outs * 2 = 18%)

While this rule is a good approximation, especially for a moderate number of outs, this calculator provides more precise probabilities.

Why are Poker Probabilities Important?

Knowing your odds helps you make better decisions regarding pot odds. If the pot offers you 4 to 1 odds to call a bet, and your chances of hitting your hand are better than 4 to 1 (e.g., 3 to 1), then calling is a profitable long-term decision. Conversely, if your odds are worse, folding might be the better play. This calculator is a tool to help you understand these crucial probabilities.