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# Bad Beat Jackpot Odds

## Introduction

"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.

1. 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.
2. Both the bad beat and winning hand must make use of both hole cards.
3. 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.