- Answers to these and similar questions about Texas Holdem poker probabilities and odds can be found here. This collection of Texas Hold'em odds also contains the probabilities for several long-shot scenarios like set over set, flush over flush and other rather unlikely scenarios. If you're missing a probability, just leave a comment below!
- Quads over quads! Played some poker after a month long break. Nice greeting with a juicy 1outer to the river.
Introduction
Poker Odds Quads Over Quads
'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.
Following are the rules for a type 1 bad beat.
You have reached the maximum of 5,000 Players Club points per day. You can keep playing as much as you'd like, of course! Points will resume counting after midnight Pacific. I'll have you know I graduated top of my class at Upswing Poker, and I've been involved in numerous secret home games, and I have busted opponents over 300 times. I am trained in piosolver and I'm the top player in the entire Northeast US live 5-10 scene.
- 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.
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 |
Methodology
Following are the rules for a type 1 bad beat.
You have reached the maximum of 5,000 Players Club points per day. You can keep playing as much as you'd like, of course! Points will resume counting after midnight Pacific. I'll have you know I graduated top of my class at Upswing Poker, and I've been involved in numerous secret home games, and I have busted opponents over 300 times. I am trained in piosolver and I'm the top player in the entire Northeast US live 5-10 scene.
- 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.
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 |
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. Poker table flip top dining.
Brian Alspach has a very good page on Texas Hold'em, including a section on the Bad Beat Jackpot at Party Poker.
Poker Quads Over Quads 2
Written by: Michael Shackleford
