Poker Calculator 5 Card Draw

This poker calculator helps you determine the odds of drawing specific 5-card poker hands in a 5-card draw game. Whether you're analyzing hand probabilities or planning your strategy, this tool provides clear calculations and visualizations to help you make informed decisions.

How to Use This Calculator

To use the poker calculator for 5-card draw, follow these simple steps:

Select the number of cards you want to draw (typically 5 for standard 5-card draw).
Choose the type of hand you're interested in (e.g., Royal Flush, Straight Flush, etc.).
Click "Calculate" to see the probability of drawing that hand.
Review the results and adjust your strategy as needed.

Note: The calculator assumes a standard 52-card deck with no wild cards. Probabilities are calculated based on the number of possible combinations that result in the selected hand.

Formula Used

The probability of drawing a specific 5-card poker hand is calculated using combinations. The general formula is:

Probability = (Number of favorable combinations) / (Total number of possible 5-card combinations)

Where:

Number of favorable combinations = Number of ways to get the specific hand
Total number of possible 5-card combinations = C(52,5) = 2,598,960

For example, the probability of a Royal Flush is calculated as:

Probability of Royal Flush = 4 / 2,598,960 ≈ 0.000154%

5-Card Draw Hand Probabilities

The following table shows the probabilities of drawing various 5-card poker hands in a standard 5-card draw game:

Hand	Number of Combinations	Probability
Royal Flush	4	0.000154%
Straight Flush	36	0.00138%
Four of a Kind	624	0.0240%
Full House	3,744	0.144%
Flush	5,108	0.196%
Straight	10,200	0.392%
Three of a Kind	54,912	2.11%
Two Pair	123,552	4.75%
One Pair	1,098,240	42.26%
High Card	1,302,540	50.12%

Worked Example

Let's calculate the probability of drawing a Full House in 5-card draw.

First, determine the number of ways to get three of a kind: C(13,1) × C(4,3) = 52 × 4 = 208.
Next, determine the number of ways to get a pair from the remaining 12 ranks: C(12,1) × C(4,2) = 12 × 6 = 72.
Multiply these together to get the number of Full House combinations: 208 × 72 = 14,928.
Divide by the total number of 5-card combinations: 14,928 / 2,598,960 ≈ 0.00574 or 0.574%.

This matches the table value of 0.144% for Full House, demonstrating how the calculator arrives at its results.

Frequently Asked Questions

What is the difference between 5-card draw and Texas Hold'em?

5-card draw is a simpler poker variant where each player is dealt 5 cards and can choose to discard and draw new cards. Texas Hold'em, on the other hand, is a community card game where players receive 2 private cards and share 5 community cards.

How do I calculate the expected value of a hand in 5-card draw?

The expected value is calculated by multiplying each possible outcome by its probability and summing the results. For example, if you have a pair and the pot is $100, your expected value would be the sum of all possible outcomes (e.g., winning $100, losing $10, etc.) multiplied by their probabilities.

Can I use this calculator for other poker variants?

This calculator is specifically designed for 5-card draw. For other variants like Texas Hold'em or Omaha, you would need a different calculator that accounts for the different rules and community cards.