Open Face Chinese Poker Card Draw Probability Calculator

Open Face Chinese Poker is a popular card game where players can see all cards in the community pool before making their decisions. This calculator helps you determine the probability of drawing specific card combinations in this game.

Introduction

Open Face Chinese Poker is a variation of Texas Hold'em poker where all community cards are dealt face up. This open format changes the probability calculations compared to traditional poker games where some cards are hidden.

The probability of drawing specific card combinations depends on several factors including the number of cards already in the community pool, the number of cards remaining in the deck, and the specific combination you're interested in.

How to Use This Calculator

Select the number of cards already in the community pool
Choose the specific card combination you want to calculate
Click "Calculate" to see the probability
Review the result and interpretation

Note: This calculator assumes a standard 52-card deck with no jokers and no cards removed from play.

Probability Formula

The probability P of drawing a specific card combination is calculated using the hypergeometric distribution:

P = [C(n, k) × C(N-n, K-k)] / C(N, K)

Where:

N = total number of cards in the deck (52)
n = number of cards in the community pool
K = number of cards needed for the combination
k = number of specific cards you want to draw
C(a, b) = combination function (a choose b)

For example, calculating the probability of drawing a pair in a 5-card community pool would involve setting k=2 (for the pair) and K=2 (since you need 2 cards to make a pair).

Worked Examples

Example 1: Probability of a Pair

If there are 5 cards in the community pool, what's the probability of drawing a pair?

Using the formula:

P = [C(52, 2) × C(47, 3)] / C(52, 5) ≈ 0.0475 or 4.75%

Example 2: Probability of Three of a Kind

If there are 3 cards in the community pool, what's the probability of drawing three of a kind?

Using the formula:

P = [C(52, 3) × C(49, 2)] / C(52, 5) ≈ 0.0211 or 2.11%

Probability of Common Combinations
Combination	Cards in Pool	Probability
Pair	5	4.75%
Two Pair	5	4.59%
Three of a Kind	5	2.11%
Straight	5	4.62%
Flush	5	5.09%

Interpreting Results

The probability results from this calculator can help you:

Assess the strength of your hand
Determine optimal betting strategies
Understand the odds of specific card combinations
Make more informed decisions during gameplay

Remember that poker is a game of skill as well as probability. While these calculations provide useful information, they don't guarantee outcomes.

Frequently Asked Questions

What is the difference between Open Face Chinese Poker and Texas Hold'em?: In Open Face Chinese Poker, all community cards are dealt face up, while in Texas Hold'em, only some cards are visible.
How does the number of cards in the community pool affect probability?: More cards in the community pool reduce the number of unknown cards, which changes the probability calculations.
Can this calculator account for specific cards already in the community pool?: This basic calculator assumes a standard deck with no specific cards already revealed. For more precise calculations with known cards, you would need a more advanced tool.
Why do the probabilities seem low for some combinations?: Poker probabilities are often low because you're trying to match specific combinations against a large number of possible outcomes.
How can I use these probabilities to improve my game?: Understanding the probabilities can help you make better decisions about when to bet, call, or fold based on the strength of your hand and the community cards.