Probability Poker Texas Holdem

Introduction

This page examines the probabilities of each final hand of an arbitrary player, referred to as player two, given the poker value of the hand of the other player, referred to as player one. Combinations shown are out of a possible combin(52,5)×combin(47,2)×combin(45,2) = 2,781,381,002,400. The primary reason for this page was to assist with bad beat probabilities in a two-player game, for example the Bad Beat Bonus in Ultimate Texas Hold 'Em.

Probabilities in Texas Hold'em Introduction An understanding of basic probabilities will give your poker game a stronger foundation, for all game types. This article discusses all the important, and interesting, probabilities that you should be aware of. Probabilities in poker Probability means the degree of certainty that a possible event will occur. When we are dealt a hand in Texas Hold'em, we don't care whether we get the A first or the K first (which is what we just worked out), just as long as we get them in our hand it's all the same. There are two possible combinations of being dealt this hand (A K and K A ), so we simply multiply the probability by 2 to get a more useful probability. A good poker player knows that they have 3 to 1 odds of having a flush on the top, and 8 to 1 odds of having 3 of a kind. Pot odds Every good poker player knows how to calculate pot odds, as this is an essential factor in making decisions in poker. Pot odds are basically the link between the pot size and the size of the stake. Poker Math & Probabilities (Texas Hold'em) The following tables provide various probabilities and odds for many of the common events in a game of Texas hold 'em. Odds% Example Win% 330-to-1 0.30% JJ v 77 80% v 20% 220-to-1 0.45% 55 v AQ 55% v 45%. In Texas Hold'em, poker odds are THE probability tool you need as a poker player. In fact, you should always be thinking about poker odds - yours and your opponents' - when making decisions. In short, poker odds is the probability of you winning that hand, or the price it offers (pot odds).

For example, if you wish to know the probability of a particular player getting a full house and losing to a four of a kind, we can see from table 7 that there are 966,835,584 such combinations. The same table shows us that given that player one has a full house, the probability of losing to a four of a kind is 0.013390. To get the probability before any cards are dealt, divide 966,835,584 by the total possible combinations of 2,781,381,002,400, which yields 0.0002403.

Table 1 shows the number of combinations for each hand of a second player, given that the first player has less than a pair.

Table 1 — First Player has Less than Pair

Table 2 shows the number of combinations for each hand of a second player, given that the first player has a pair.

Table 2 — First Player has a Pair

Table 3 shows the number of combinations for each hand of a second player, given that the first player has a two pair.

Table 3 — First Player has a Two Pair

Table 4 shows the number of combinations for each hand of a second player, given that the first player has a three of a kind.

Table 4 — First Player has a Three of a Kind

Table 5 shows the number of combinations for each hand of a second player, given that the first player has a straight.

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Table 5 — First Player has a Straight

Table 6 shows the number of combinations for each hand of a second player, given that the first player has a flush.

Table 6 — First Player has a Flush

Table 7 shows the number of combinations for each hand of a second player, given that the first player has a full house.

Table 7 — First Player has a Full House

Texas Holdem Probability Chart

Table 8 shows the number of combinations for each hand of a second player, given that the first player has a four of a kind.

Table 8 — First Player has a Four of a Kind

Table 9 shows the number of combinations for each hand of a second player, given that the first player has a straight flush.

Table 9 — First Player has a Straight Flush

Table 10 shows the number of combinations for each hand of a second player, given that the first player has a royal flush.

Table 10 — First Player has a Royal Flush

Probability Poker Hands Texas Hold Em

The following table shows the number of combinations for each hand of player 1 by the winner of the hand.

Table 11 — Winning Player by Hand of Player 1 — Combinations

The following table shows the probability for each hand of player 1 by the winner of the hand. The bottom row shows that each player has a 47.97% chance of winning and a 4.07% chance of a tie.

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Table 12 — Winning Player by Hand of Player 1 — Probabilities

Understanding pot odds, like explained in the Texas Hold Em Poker tips paragraphs, can help you win more hands of poker and take home more money.

Poker, in its essence, is a game of probability. And the number one thing you need to remember when playing poker is this: you want to bet lots of money when you are probably going to win. Of course, there is always the chance your competition will pull a very lucky card and get the bigger hand, but with all things being equal, when there is a high probability you are going to win, bet your money.

A key thing here to remember is no one can control luck and you need to be playing your best all the time. You can't play poker with a fear of betting because the other guy might get lucky. If you put your money in when you are the favourite for the best hand, you do that enough times and you end up winning in the long run.

This is the first important thing to understand with pot odds, ok?

Texas Hold Em Poker Tips – Your Don't Have To Be A Maths Genius

Table 5 shows the number of combinations for each hand of a second player, given that the first player has a straight.

Probability Poker Texas Holdem Tournaments

Table 5 — First Player has a Straight

Table 6 shows the number of combinations for each hand of a second player, given that the first player has a flush.

Table 6 — First Player has a Flush

Table 7 shows the number of combinations for each hand of a second player, given that the first player has a full house.

Table 7 — First Player has a Full House

Texas Holdem Probability Chart

Table 8 shows the number of combinations for each hand of a second player, given that the first player has a four of a kind.

Table 8 — First Player has a Four of a Kind

Table 9 shows the number of combinations for each hand of a second player, given that the first player has a straight flush.

Table 9 — First Player has a Straight Flush

Table 10 shows the number of combinations for each hand of a second player, given that the first player has a royal flush.

Table 10 — First Player has a Royal Flush

Probability Poker Hands Texas Hold Em

The following table shows the number of combinations for each hand of player 1 by the winner of the hand.

Table 11 — Winning Player by Hand of Player 1 — Combinations

The following table shows the probability for each hand of player 1 by the winner of the hand. The bottom row shows that each player has a 47.97% chance of winning and a 4.07% chance of a tie.

Probability Poker Texas Holdem Rules

Table 12 — Winning Player by Hand of Player 1 — Probabilities

Understanding pot odds, like explained in the Texas Hold Em Poker tips paragraphs, can help you win more hands of poker and take home more money.

Poker, in its essence, is a game of probability. And the number one thing you need to remember when playing poker is this: you want to bet lots of money when you are probably going to win. Of course, there is always the chance your competition will pull a very lucky card and get the bigger hand, but with all things being equal, when there is a high probability you are going to win, bet your money.

A key thing here to remember is no one can control luck and you need to be playing your best all the time. You can't play poker with a fear of betting because the other guy might get lucky. If you put your money in when you are the favourite for the best hand, you do that enough times and you end up winning in the long run.

This is the first important thing to understand with pot odds, ok?

Texas Hold Em Poker Tips – Your Don't Have To Be A Maths Genius

So, how do you know you have the best hand? This is where the mathamagic comes in. Don't worry, understanding poker odds is just plain, basic math. Nothing fancy like logarithmic-hoodiggies or algabraic-catscratchers, just basic math.

Key point – you don't have to be a great mathematician to be a great poker player. That's the truth. You do however need a bit of a basic understanding of math to be a successful Texas Hold Em Poker player.

Texas Hold Em Poker Tips – How To Calculate Your Pot Odds

First things first, you need to be able to calculate your chances of getting ‘outs'. Outs are the cards you need to make the best hand you can, to hopefully win. These little guys are important because you need to win pots if you want to win money. You get the idea.

Texas Holdem Poker Probability Chart

So for an example. Say you have a pair of Kings and you are pretty sure your opponent has a pair of 10's. The four community cards are something like 3-5-7-2. You 강남홀덤 know that your opponent needs a 10 to win. There is one card to go, the river.

So for the calculation: There are 52 cards in a deck. Eight of the cards have been used; your two, his two, four on the board, so there are 44 cards remaining. Two of those cards help you, so you are at 22-to-1 odds.

Because only 2 of the cards in the deck will help your opponent, you are in fact a 22-to-1 favourite to win the pot, which puts your at a humongous advantage.

Texas Hold Em Poker Game

Understanding pot odds and outs, which is the probability you will get your best hand, is very important because it gives you information to make the correct moves. In the previous example you know, from pure probability, that you will win 21 times out of 22.

Texas Hold Em Poker Hands

So you can happily bet money and stay in the pot because overall, over the long run, you will win. You want the numbers to be on your side, that's the point this Texas Hold Em Poker tips trying to get at.