Odds Of Getting 4 Of A Kind Texas Holdem

4/12/2022by admin

In poker terms, the river is the name for the fifth card dealt, face-up on the board. In total, there are 2,598,960 possible poker hands with 52 cards. The odds of getting four of a kind in Texas Hold ‘Em is 4164 to 1. Probability that there will be a 4 of a kind on the board in the form MMMMX is P=.00004495. Adding all 5 of these probabilities gives us a total probability that there will be any 4 of a kind on the board when holding a non-pair in the hole, or P=.0002297. Analyze paired hole cards. Scenario 1: XMMMM. Start with paired hole cards P.

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

Odds Of Getting 4 Of A Kind Texas Holdem Games

Bad Beat HandType 1Type 2Type 3
Any full house0.002033290.000503050.00049508
Full house, three 3's or higher0.001895120.000469780.00046204
Full house, three 4's or higher0.001751590.000434440.00042728
Full house, three 5's or higher0.001603330.000397060.00039028
Full house, three 6's or higher0.001449650.000357410.00035145
Full house, three 7's or higher0.00129360.000317670.00031266
Full house, three 8's or higher0.001134920.000277750.00027355
Full house, three 9's or higher0.000973790.000237720.00023445
Full house, three T's or higher0.000811130.000197590.00019503
Full house, three J's or higher0.000647630.000157080.00015509
Full house, three Q's or higher0.000485330.000118380.00011682
Full house, three K's or higher0.000325610.000081300.00008033
Full house, three A's or higher0.000169640.000046080.00004579
Full house, aces full of 3's or higher0.000160040.000043500.00004322
Full house, aces full of 4's or higher0.000149860.000040800.00004052
Full house, aces full of 5's or higher0.000138980.000037970.00003763
Full house, aces full of 6's or higher0.000127490.000035040.00003469
Full house, aces full of 7's or higher0.000115800.000032330.00003203
Full house, aces full of 8's or higher0.000103470.000029570.00002925
Full house, aces full of 9's or higher0.000090670.000026730.00002645
Full house, aces full of T's or higher0.000077140.000023830.00002359
Full house, aces full of J's or higher0.000062860.000020640.0000204
Full house, aces full of Q's or higher0.000047930.000017380.00001721
Full house, aces full of K's or higher0.000032300.000014080.00001402
Any four of a kind0.000016010.000010860.00001081
Four 3's or higher0.000014370.000009960.00000992
Four 4's or higher0.00001270.000009000.00000902
Four 5's or higher0.000010990.000008050.00000804
Four 6's or higher0.000009340.000007050.00000707
Four 7's or higher0.00000780.000006130.00000611
Four 8's or higher0.00000640.000005250.00000519
Four 9's or higher0.000005190.000004390.00000435
Four T's or higher0.000004140.000003590.00000357
Four J's or higher0.000003170.000002870.00000285
Four Q's or higher0.000002460.000002260.00000224
Four K's or higher0.000001930.000001800.00000179
Four A's or higher0.000001570.000001490.00000147
Any straight flush0.00000120.000001220.00000121
Straight flush 6 high or higher0.000001050.000001070.00000105
Straight flush 7 high or higher0.000000890.000000910.00000090
Straight flush 8 high or higher0.000000730.000000740.00000074
Straight flush 9 high or higher0.000000560.000000590.00000058
Straight flush T high or higher0.000000410.000000430.00000042
Straight flush J high or higher0.000000280.000000270.00000027
Straight flush Q high or higher0.000000120.000000120.00000012

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.

Brian Alspach has a very good page on Texas Hold'em, including a section on the Bad Beat Jackpot at Party Poker.

Odds of getting 4 of a kind in texas holdem

Odds Of Getting 4 Of A Kind Texas Holdem Online


Written by: Michael Shackleford

acejackjb
What are the exact odds of making any four of a kind versus any two,three,four or one specific four of a kind, holding a pocket pair in Texas Holdem?
buzzpaff
16.473429

Odds Of Getting 4 Of A Kind Texas Holdem Game

acejackjb
I believe you gave me the odds of holding a pocket pair. What are the odds of making four of a kind?
buzzpaff
.00327
acejackjb
Odds of getting 4 of a kind texas holdem online
Thanks, would it be correct to say that .00327* number of players* hands dealt=probability of someone hitting four of a kind?
buzzpaff
No it would not. Was hoping someone would challenge my answer. I have absolutely no idea !
Kind
acejackjb
I believe you are very close!
buzzpaff
You are new here or you would know I just make up numbers. ME, I am not. SIGH
Nareed
Has anyone else noticed a pattern where a new user, with a handle all in lower case, asks a very specific question on a topic, comments on replies, and then is never heard from again?
Not that I mind. But if it's just one person, there's no need for the multiple identities.
dwheatley

Odds Of 4 Of A Kind In Texas Hold'em

It looks like the probability of being dealt a pocket pair (0.0588) then getting 4 of kind in the next 5 cards (0.00816) is about 0.00048, or 1 in 2083.
You can estimate the probability of anyone getting 4 of kind using your formula, but I don't think it's exactly correct

Odds Of Getting 4 Of A Kind Texas Holdem Free

Wisdom is the quality that keeps you out of situations where you would otherwise need it
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