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Poker Odds
Playing the game of Poker has become in many ways a mathematical science, with television broadcasts providing instant probability analyses for players' different card combinations. Unfortunately, this information is not available to the players at Poker games, whether they are physical ones or games played at online Poker rooms.
Players learning to play Poker should have a basic idea of how likely it is to get high-ranking hands, and what the odds are to make their hand during games.
Dealt Hands
First, what are the chances of being dealt five cards from a fresh, shuffled deck in a physical Poker game and getting the following possible hands?
Making a Texas Hold'em Hand
In the game of Texas Hold'em, when players are initially dealt two facedown cards, what are the chances of making a hand, before and after the Flop? Let's take a look at the odds:
A Quick Lesson in Calculating Odds
When playing Texas Hold'em, players frequently need to quickly calculate the probability that their missing card will turn up either in the Turn or the River.
The term outs refers to the number of cards in the deck that will improve your hand (and includes the unseen cards held by other players).
An easy example of how to calculate your odds:
You start with a pair of Jacks, but the Flop doesn't contain another Jack. What is the probability that a third Jack will turn up on the Turn?
To figure this out, determine the number of outs and divide it by the number of cards left in the deck.
Holding two Jacks, there are two remaining Jacks - or outs.
For the Turn, the poker odds of seeing that third Jack are therefore two divided by 47 (you've already seen 5 out of the 52 - your pocket and the 3 cards of the Flop).
The probability of getting that third Jack at the Turn are 2/47 = 0.426, or close to 4.3%.
If that third Jack didn't show up on the Turn, what is the probability of it showing up on the River?
For the River, the odds of seeing that third Jack are therefore two divided by 46 (you've already seen 6 out of the 52 - your pocket, the 3 Flop cards, and the Turn).
The probability of getting that third Jack at the River are therefore 2/46 = 0.434, or still close to 4.3%.
Combining these two calculations, we can conclude that the probability of getting that third Jack at either the Turn or the River is 8.42%, or 10.9 to 1 against making Three of a Kind.
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