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An Explanation of Texas Hold'Em Odds

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Probability is the foundation of texas hold 'em poker. If you are good or if you like numbers, you have a small advantage. But if you do not like math, this is not really a big problem, as long as you memorize the fundamental odds that drives the game.

Poker is both maths and instincts, but you need to first understand the maths before trusting your instincts.

Poker players must use odds to determine their actions. For example, what are the chances of completing a flush or a straight draw, what are the odds to flop a set or what are the odds to face poker aces when you have pocket kings.

Knowledge of these statistics is a prerequisite for winning. Below is a short list of keys terms related to odds in poker lingo

Outs The number of cards left in the deck that will improve your hand.
"I had four of a kind jacks, but he beat me with one out to hit a straight flush at the river."
Pot Odds The odds you get when calling a bet given the money already in the pot.
"There's $500 already in the pot, and my opponent only bet $30, giving me excellent pot odds for drawing to my flush."
Bet Odds The odds you get as a result of evaluating the number of callers to a raise.
"With a 1 in 4 chance of hitting my hand, and knowing all five other players will call my bet, my bet odds are excellent."
Implied Odds The odds you get assuming more betting and calling will occur at later streets during this hand. "Since I am sure John will not fold to my turn and river bets, my implied odds justify me staying in this hand."

In Texas Holdem poker, the odds are based on the number of outs and the odds to reach a given hand. So have need to do a little bit of counting, but this is not hard, and if you play regularly, these outs will be second nature to you.

To take a simple example, if you have a set by the turn and your opponent has a full house, you need a four of a kind to beat him. Therefore you have one out, in other word only one card will lead to you winning this hand.

Both you and your opponent have two hole cards and four cards are on the board, so eight cards are out there and 44 cards are in the deck. So your odds are 1 one in 44 to hit your hand, or 2.3% chance. The math will not get harder than that in poker. Odds are 1:43, i.e. one good possible outcome versus 43 bad outcome.

Pot odds represent the odds offered by the money already in the pot. If there is $100 in the pot and you only need to pay $5 to participate in that hand, then you can play any hand where you have 1:20 odds or better. As if you win you will get 20 times your bet, you only need a one chance in twenty to win to break even over the long term by calling.

If your chance of winning is significantly more than the ratio of the pot size to a bet, then you have good pot odds. Otherwise you have bad pot odds and you should fold. A typical case would be a $2/$4 Texas Hold'em table with ten nine facing one opponent on the turn. You get an open-ended straight draw when the board comes J862 and only the river card remains to come.

Any king or eight will give you the straight, so you have 8 outs (four 8's and 4 Kings left in the deck) and there are 46 unplayed cards left. You have 8/46 = 17% chance, or about one chance in 6.

If your opponent bets $4 and if the pot is $80, then $80/$4 is 20, and you stand to make 20 time your bet if you win. As 1/6 is much higher than 1/20, the pot odds are very favorable to you and you should call.

On thing that new players tend to do is to factor in the bets they made at previous betting rounds. In the last example, you would have contributed a significant part of the $80 pot. This does not matter at all. The only thing that matter is if you have the correct odds to make a call based on the pot, how the pot was made has no impact on the income from a statitical standpoint.

The next step is to use bet odds and implied odds. That is harder as you must estimate future actions of the other players, and only experience will teach you how to make correct implied odds forecasts.

Say you have a four flush on the flop this time. An early player bets, and everyone else folds, leading to a $20 pot. Your chance of hitting the flush on the turn is 19.1% (about 1 in 5). You have to call a $4 bet in a $20 pot, which is a 10x payout in you win. As 1/5 is higher than 1/10 the pot odds are good, but you also need to consider your opponent's bet on the and river also.

So you are facing $10 more until the end of the hand. You need to consider the chances of hitting the flush on the turn or river, which makes it about 35%, but you have to invest $10 for a final $40 pot. $40/$10 is 1 in 4. Close.

If you do not make your flush on the turn, you still have a 19.6% chance of hitting the flush. Also if you hit the flush on the turn, you can raise and increase your profit. But he may fold, and then the earlier pot odds calculation were wrong.

It is only by playing that you can get comfortable with the odds, but overall the math is not difficult. You just must make sure that you correctly take into account all possible scenarios.

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