Odds Of Hitting Quads In Texas Holdem

Just anecdotal but I was playing live at a casino last week and I flopped quads twice and hit quads on the turn another time in a 5 hour session. That probably represents about 160 - 175 hands. Sometimes the laws of probability can seem to be violated over a small sample size.

Here are some important probabilities in Omaha that returns in different situations. Knowledge about probabilities will help you to better evaluate situations in poker. You will , for example, know when you should call and when you shouldn't, and, vice versa, know when to fold and when the odds are in your favor.

Table 1. **Playing situations**
Drawing hands probabilities	Odds	Percent
Double wraparound straight draw (e.g. hand: 9-8-5-4, flop: 7-6-x)	0.48-1	68%
Wraparound straight draw (e.g. hand: 8-5-4-x, flop: 7-6-x)	0.67-1	60%
Straight flush draw	0.84-1	54%
Hitting a full house with three pairs	3-1	24%
Hitting a full house with two pairs	5.1-1	16.5%
Hitting quads with a set	21.5-1	4.5%

The odds in this Texas Hold'em odds table are unlikely to directly help your overall strategy, but they are pretty interesting nonetheless. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with.
In that scenario, quad eights will lose approximately 1 out of 190,476 hands. (By the way, this is for any 7-card game which means Texas Hold 'em OR 7-card stud.) I was surprised with that number. I thought it would actually be much, much lower odds. (In other words, much harder to hit.).
With 7 cards to choose from in hold'em, your hole cards and the board, the odds of making quads is about 1 in 595. (13. (48 choose 3)) / (52 choose 7) which = 0.7 or 1 in 595. This is over the entire 7 cards. So for another person to have quads in the same hand we figure out how many possible hands are left.

Starting hands

There are many starting hands in Omaha (16.432 if not all suit combinations are counted), which makes it difficult to get an overview. Table 2 will hopefully increase that overview a bit.

Table 2. **Starting hand versus average hand**
Situation	Percent
A-A-K-K double suited to win against average hand	73%
A-A-K-K rainbow to win against average hand	68%
A-A-7-7 double suited to win against average hand	72%
A-A-7-7 rainbow to win against average hand	67%
A-A-J-T double suited to win against average hand	76%
A-A-J-T rainbow to win against average hand	71%
J-T-9-8 double suited to win against average hand	56%
J-T-9-8 rainbow to win against average hand	49%

Comments

Exemple of a double suited hand: Q♥ A♥ 2♦ K♦
Exemple of a rainbow hand: Q♥ A♣ 2♠ K♦
The best Omaha hands are less bigger favorites against an average hand compared to Texas Hold'em.
In Texas Hold'em, common knowledge is that A-A is very big favorite against all other hands. In Omaha, A-A as a part of a hand is far from that strong. In general, an A-A-x-x hand versus a random four-card hand is a 70-30 favorite in average (if all the starting hands that are normally folded are excluded, the A-A-x-x hands will be even less favorites).

Made hands versus draws

A typical feature in an Omaha Hi game is a set against a hand with several drawing possibilities. The made hand will not be a very big favorite (sometimes it is an underdog), so the recommended strategy is to play fast and bet/raise the pot in these situations.

Table 3. **Made hand versus drawing hand**
Situation	Percent
Top set against flush draw	70%-30%
Middle set against flush draw	70%-30%
Top set against flush draw + two pairs	68%-32%
Set against wraparound straight draw	52%-48%
Set against double wraparound straight draw	53%-47%

No decimals are used. The numbers are only approximal.

Odds Of Making Quads In Texas Holdem

Comments

Factors that can affect the odds are for example blocking cards.

Flush draws versus straight draws

In Omaha, hands with flush draws are often more likely to win than straight draws.

Table 4. **Drawing hands**
Situation	Percent
Flush draw against wraparound	60%-40%
Flush draw against double wraparound	55%-45%

No decimals are used. The numbers are only approximal.
Odds of hitting quads in texas hold

Comments

Since that many cards are in action, there are often combined possibilities, which makes it hard to give general percentages. A hand with a flush draw has mostly something else, like a pair or a straight draw as well.

Odds Of Flopping Quads In Texas Holdem

Odds Of Hitting Quads In Texas Hold'em

1 percent (1-in-100): Percentage of time that no player holds an Ace or a King at a table in a 10-handed game
1 percent (1-in-100): Percentage of time that if you hold two suited cards, you’ll flop a flush
6 percent (about 1-in-20): Percentage of time that five community cards will give pocket suited cards a flush
6 percent (about 1-in-20): Percentage of time that you’ll be dealt a pocket pair
8 percent (about 1-in-12): Percentage of time that you’ll hit at least trips after having a pair on the flop
12 percent (about 1-in-8): Percentage of time that you’ll flop trips if holding a pocket pair
12 percent (about 1-in-8): Percentage of time that two more cards will flop in the same suit as a suited pocket pair
19 percent (about 1-in-5): Percentage of time that the five community cards will at least trip your pocket pair
32 percent (about 1-in-3): Percentage of time that you’ll pair one of your cards on the flop (with no pocket pair)
33 percent (about 1-in-3): Percentage of time that you’ll make a full house or better after having trips on the flop
35 percent (about 1-in-3): Percentage of time that you’ll make a flush on the turn or river if you have four cards to a flush after the flop