3 Card Poker Payout Calculator

Brian Alspach

1. Three Card Poker Odds Calculator
2. What Is The Payout For 3 Card Poker
3. How Does 3 Card Poker Payouts

13 January 2000

Abstract:

For rules and strategy please see my Three Card Poker section. Questions and Answers See questions I’ve answered about Three Card Poker from my Ask the Wizard columns. The programming of this game was done by JB. Read More Read Less. Enter data and press 'Calculate' to analyze. This is a free online Keno odds calculator which will determine the return, house advantage and jackpot break-even point (if any) for a given Keno pay table. Enter the data into the relevant fields. Below is a description of what each field represents. A poker odds calculator shows you the exact odds of your hand winning in any scenario. For example, you can give yourself pocket Aces, opponent 1 pocket Kings, and opponent 2 pocket Queens. The poker odds software will then calculate how often each hand wins. Using a Poker odds Calculator. Want to know how far ahead or behind you are in a Texas Hold’em hand against one, two or more opponents? Our poker calculator is the perfect medium for finding out the odds in any given situation.

The types of 3-card poker hands are

• straight flush
• 3-of-a-kind
• straight
• flush
• a pair
• high card

The total number of 3-card poker hands is .

A straight flush is completely determined once the smallest card in thestraight flush is known. There are 48 cards eligible to be the smallestcard in a straight flush. Hence, there are 48 straight flushes.

In forming a 3-of-a-kind hand, there are 13 choices for the rank and4 choices for the 3 cards of the given rank. This implies there are3-of-a-kind hands.

The ranks of the cards in a straight have the form x,x+1,x+2, wherex can be any of 12 ranks. There are then 4 choices for each card ofthe given ranks. This yields total choices. However,this count includes the straight flushes. Removing the 48 straightflushes leaves us with 720 straights.

To count the number of flushes, we obtain choicesfor 3 cards in the same suit. Of these, 12 are straight flushes whoseremoval leaves 274 flushes of a given suit. Multiplying by 4 produces1,096 flushes.

Now we count the number of hands with a pair. There are 13 choices forthe rank of the pair, and pairs of the chosen rank.The non-pair card can be any of the remaining 48. Thus, thereare 3-card hands with a single pair.

Three Card Poker Odds Calculator

We could determine the number of high card hands by removing the handswhich have already been counted in one of the previous categories.Instead, let us count them independently and see if the numbers sumto 22,100 which will serve as a check on our arithmetic.

A high card hand has 3 distinct ranks, but does not allow ranks of theform x,x+1,x+2 as that would constitute a straight. Thus, there arepossible sets of ranks from which we remove the12 sets of the form .This leaves 274 sets of ranks.For a given set of ranks, there are 4 choices for each cardexcept we cannot choose all in the same suit. Hence, there are274(4³-4) = 16,440 high card hands.

If we sum the preceding numbers, we obtain 22,100 and we can be confidentthe numbers are correct.

Here is a table summarizing the number of 3-card poker hands. Theprobability is the probability of having the hand dealt to you whendealt 3 cards.

Three card poker is always played with one deck of 52 cards. There are a total of 22,100 different ways that three cards can be dealt. Using a bit of math we can determine the probability of each hand. The table below shows the ways, probabilities and odds for each hand.

What Is The Payout For 3 Card Poker

Notes

As you can see on the table above the straight in three card poker out ranks the flush. This is unique to the game as in every other poker game the flush always out ranks the straight. The reason for the change in rankings is the fact that there are more ways to make a flush with three cards than there are ways to make a straight.

How Does 3 Card Poker Payouts

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