Odds Of Making Poker Hands

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The Players Guide To Video Poker Information

To calculate your poker equity - or how often you should win a hand, you can use a simple formula. Count how many outs you have. For example, if you're drawing to a flush, you have 13 suited cards, two in your hand, two on the board - leaves 9 outs. The chance of you hitting on the turn is 9.4 (+4) = 40%. Number of Poker Hands. Some of the techniques of combinatorics, or the study of counting, can be applied to calculate the total number of poker hands. It is important to note that the order in which the cards are dealt to us does not matter. Since the order does not matter, this means that each hand is a combination of five cards from a total. Pot odds in poker simply means the “price” that it costs you to continue with your hand. For example, if you’re in a hand where the pot is $100 and your opponent bets $50, you’re getting 3 to 1 pot odds to call. The pot is $150 (the $100 that’s already there plus the $50 bet) and it costs $50 to continue. Divide the $150 by $50 to get 3.

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One of the great features of video poker is the fact that the odds of each hand being dealt are the same on every machine (Games with 52 cards of course have different odds to those with 53). While the pays for the wins change the chances of getting the wins do not. Below we list the odds of many hands being dealt pat and the odds of winning on the draw for a 52 card game.

Initial Deal Odds

The table below shows the odds of getting any winning hand on the first five cards dealt on a game using 52 cards. Odds change if you are playing a game with an additional wild card such as Jokers Wild as there are 53 cards.

HandOddsHand Odds
Royal Flush 1 in 649740Straight : 1 in 255
Straight Flush : 1 in 72193Three of a Kind :1 in 47
Four of a Kind : 1 in 4165 Two Pairs :1 in 21
Full House : 1 in 694Pair J, Q, K or A 1 in 7.69
Flush : 1 in 509Any Pair 1 in 2.37

Odds On The Draw

As much as we would all like to see a pat hand dealt every time we hit the max bet button this is rarely the case. In reality less than 1% of hands played will result in you holding all five where over 60% of hands you will hold just two cards going into the draw. Knowing this lets look at some examples.
The table below shows the odds of getting a particular hand when holding one, two, three or four cards. Of course you have to be holding the right cards for the odds to be correct. For example for cards to a royal is made up of four suited cards in the 10 to Ace range. Four to a flush is four suited cards etc.
Royal Flush Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 178,3651 in 16,215 1 in 1081 1 in 47
Straight Flush Draw *
Hold 1 Hold 2Hold 3 Hold 4
1 in 59,4551 in 8,1071 in 360 1 in 47
Four of a Kind Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 3,4301 in 3601 in 23.24n/a
Full House Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 619 1 in 98 1 in 16 n/a
Flush Draw
Hold 1 Hold 2 Hold 3 Hold 4
1 in 3611 in 991 in 26 1 in 5
* The straight flush section has several variations that can change the odds that are displayed. These are primarily and inside draw or an outside draw. For example if you have 5h, 6h, 7h, 8h there are two ways to make the straight flush - either a 4h or a 9h will do it. However if you have an inside draw you have for example 2d, 3d, 5d, 6d. In this case only one card can make the hand (4d).
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The following Texas Holdem odds table highlights some common probabilities that you may encounter in Hold'em. It is not vital that you learn these probabilities, but it is useful to be aware of the chances of certain situations arising.

Texas Hold'em odds chart.

SituationPercentage OddsRatio Odds
Preflop Probabilities:
Dealt AA.0.45%220 to 1
Dealt AK.1.2%82 to 1
Dealt AKs.0.3%331 to 1
Dealt 72o.0.9%109 to 1
Being dealt AA vs. KK (heads up).0.004%22,559 to 1
Dealt a pocket pair.6%16 to 1
Dealt suited connectors.4%24 to 1
Flop Probabilities:
Flopping a pair.32.4%2.2 to 1
Flopping a set (with pockets).11.8%7.5 to 1
Paired Board:
2 players, probability of trips.17%4.8 to 1
3 players, probability of trips.26%3 to 1
4 players, probability of trips.34%2 to 1
5 players, probability of trips.43%1.4 to 1

How to use Texas Hold'em odds.

The odds in this Texas Hold'em odds table are unlikely to directly help your overall strategy, but they are pretty interesting nonetheless. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with.

Other poker odds charts.

For more useful odds charts that you can use for when you are working out whether or not to call when on a drawing hand, use the following tables:

Odds of making poker hands signals

Both of these tables give the odds for completing your draw depending on how many outs you have. You can find out more on how to work out odds and all that mathematical stuff in the article on pot odds.

Go back to the poker odds charts.

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