Chances Of 4 Of A Kind In Texas Holdem
Introduction
- Chances Of 4 Of A Kind In Texas Holdem Tournaments
- Chances Of 4 Of A Kind In Texas Holdem Game
- Chances Of 4 Of A Kind In Texas Holdem Rules
- Odds Of Flopping 4 Of A Kind In Texas Hold Em
'Bad beat' is a term that can mean having an outstanding chance of winning a bet, only to still lose. The term can be used in any form of gambling but is most commonly applied to poker. Many poker rooms offer a progressive jackpot for very unlikely bad beats. Various other rules are added to ensure that only surprising bad beats win. Below I present tables of bad beat probabilities, starting with the most liberal rules, and ending with the most stringent. The most stringent rules, the 'Bad Beat Type 3', are the most common, in my experience.
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Following are the rules for a type 1 bad beat.
The chance of 4 or a kind in 7 cards is 594: 1. 9 players is 9 hands so roughly 65: 1 for a table of nine. Browse other questions tagged texas-hold-em odds hand.
- Both the bad beat and winning hand must be the best possible combination of five cards. In cases where the same hand can be created multiple ways (for example player has AK and the board shows AAKKQ) the player's hole cards will take priority.
- Both the bad beat and winning hand must make use of both hole cards.
- A full house must be beaten by a four of a kind or higher.
The rules for a type 2 bad beat are the same as type 1, plus any four of a kind, whether the bad beat hand or winning hand, must contain a pocket pair.
The rules for a type 3 bad beat are the same as type 2, plus a full house may not make use of a three of a kind entirely on the board.
Chances Of 4 Of A Kind In Texas Holdem Tournaments
In my experience, is the most common format for bad beat rules is type 3. The additional rule for type 3 makes very little difference, compared to type 2.
The following table shows the probability of each bad beat hand under all three types of rules. The table is based on a ten-player game in which nobody ever folds. The probabilities are for any pair of players meeting the qualifying rules. If you want to know YOUR probability of winning, you should divide the probability in the table by 10.
Bad Beat Probabilities
| Bad Beat Hand | Type 1 | Type 2 | Type 3 |
|---|---|---|---|
| Any full house | 0.00203329 | 0.00050305 | 0.00049508 |
| Full house, three 3's or higher | 0.00189512 | 0.00046978 | 0.00046204 |
| Full house, three 4's or higher | 0.00175159 | 0.00043444 | 0.00042728 |
| Full house, three 5's or higher | 0.00160333 | 0.00039706 | 0.00039028 |
| Full house, three 6's or higher | 0.00144965 | 0.00035741 | 0.00035145 |
| Full house, three 7's or higher | 0.0012936 | 0.00031767 | 0.00031266 |
| Full house, three 8's or higher | 0.00113492 | 0.00027775 | 0.00027355 |
| Full house, three 9's or higher | 0.00097379 | 0.00023772 | 0.00023445 |
| Full house, three T's or higher | 0.00081113 | 0.00019759 | 0.00019503 |
| Full house, three J's or higher | 0.00064763 | 0.00015708 | 0.00015509 |
| Full house, three Q's or higher | 0.00048533 | 0.00011838 | 0.00011682 |
| Full house, three K's or higher | 0.00032561 | 0.00008130 | 0.00008033 |
| Full house, three A's or higher | 0.00016964 | 0.00004608 | 0.00004579 |
| Full house, aces full of 3's or higher | 0.00016004 | 0.00004350 | 0.00004322 |
| Full house, aces full of 4's or higher | 0.00014986 | 0.00004080 | 0.00004052 |
| Full house, aces full of 5's or higher | 0.00013898 | 0.00003797 | 0.00003763 |
| Full house, aces full of 6's or higher | 0.00012749 | 0.00003504 | 0.00003469 |
| Full house, aces full of 7's or higher | 0.00011580 | 0.00003233 | 0.00003203 |
| Full house, aces full of 8's or higher | 0.00010347 | 0.00002957 | 0.00002925 |
| Full house, aces full of 9's or higher | 0.00009067 | 0.00002673 | 0.00002645 |
| Full house, aces full of T's or higher | 0.00007714 | 0.00002383 | 0.00002359 |
| Full house, aces full of J's or higher | 0.00006286 | 0.00002064 | 0.0000204 |
| Full house, aces full of Q's or higher | 0.00004793 | 0.00001738 | 0.00001721 |
| Full house, aces full of K's or higher | 0.00003230 | 0.00001408 | 0.00001402 |
| Any four of a kind | 0.00001601 | 0.00001086 | 0.00001081 |
| Four 3's or higher | 0.00001437 | 0.00000996 | 0.00000992 |
| Four 4's or higher | 0.0000127 | 0.00000900 | 0.00000902 |
| Four 5's or higher | 0.00001099 | 0.00000805 | 0.00000804 |
| Four 6's or higher | 0.00000934 | 0.00000705 | 0.00000707 |
| Four 7's or higher | 0.0000078 | 0.00000613 | 0.00000611 |
| Four 8's or higher | 0.0000064 | 0.00000525 | 0.00000519 |
| Four 9's or higher | 0.00000519 | 0.00000439 | 0.00000435 |
| Four T's or higher | 0.00000414 | 0.00000359 | 0.00000357 |
| Four J's or higher | 0.00000317 | 0.00000287 | 0.00000285 |
| Four Q's or higher | 0.00000246 | 0.00000226 | 0.00000224 |
| Four K's or higher | 0.00000193 | 0.00000180 | 0.00000179 |
| Four A's or higher | 0.00000157 | 0.00000149 | 0.00000147 |
| Any straight flush | 0.0000012 | 0.00000122 | 0.00000121 |
| Straight flush 6 high or higher | 0.00000105 | 0.00000107 | 0.00000105 |
| Straight flush 7 high or higher | 0.00000089 | 0.00000091 | 0.00000090 |
| Straight flush 8 high or higher | 0.00000073 | 0.00000074 | 0.00000074 |
| Straight flush 9 high or higher | 0.00000056 | 0.00000059 | 0.00000058 |
| Straight flush T high or higher | 0.00000041 | 0.00000043 | 0.00000042 |
| Straight flush J high or higher | 0.00000028 | 0.00000027 | 0.00000027 |
| Straight flush Q high or higher | 0.00000012 | 0.00000012 | 0.00000012 |
Chances Of 4 Of A Kind In Texas Holdem Game
Methodology
The above tables are the result of random simulations of about 2.5 billion rounds each.
Further Reading
The video poker variant World Series of Poker - Final Table Bonus features a bad beat jackpot. See my section on that game for more information.
Brian Alspach has a very good page on Texas Hold'em, including a section on the Bad Beat Jackpot at Party Poker.
Written by: Michael Shackleford
Pairs
It's always nice to start with a pair in the hole (especially the high kind) because they can often win without any improvement whatsoever. By the same token, an opponent's hidden pair can also often sneak up and beat you.
Here's some odds charts that can give you a way to not only estimate your chances of catching pairs, but to also get a feel for the likelihood of pairs in your opponent's hands.
Hey mobile users or anyone that would like to download, print or view the charts in more detail. Check out the Holdem pair pre-flop odds in high resolution universal .pdf format.
High Card Hands (Unpaired)
Whoever said that Holdem is a high card game was right. Much of the overall Holdem action involves two unpaired high cards like the typical hands illustrated above. These probability charts will give you some idea of what to expect to be dealt, and how many high card hands are likely to be out there against you.
Chances Of 4 Of A Kind In Texas Holdem Rules
Odds Of Flopping 4 Of A Kind In Texas Hold Em
To download, print or view the above chart in more detail, check out the Holdem high card pre-flop odds in high resolution universal .pdf format.