Need someone to calculate the probability for flopping this set of hands:
555 QQ
555 KK
555 AA
555 5x
Hand #1301109150 · Replay Poker
In other words what are the odds of you flopping the 1st, 2nd, 3rd, and 4th nuts in the same flop.
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Asking AI which is always sketchy, but at least a starting point.
- Flop = 555: ~0.082%
- Case 5 in play: ~50%
- AA, KK, QQ in three hands: ~0.0003%
Combined odds: ≈ 1 in 300,000 to 500,000 hands
Yeah, I have it at around 1 in 100 million.
Odds of aces is about 1 : 39 or 2.57%. We can just cube that to find the odds of 3 people AA, KK, QQ (it won’t be exact, but close enough).
We don’t actually need to worry about the last player - they can have at most 4 ways to make quads on a tripple board. That means there’s 12 / 36 options for the first flop card, 2/35 for the second and 1/34 for the last. Which is about 1 in 1800. 1800 * 39^3 is approx 100,000,000
Seems way too high!
Did you consider it being a seven-player table at the time?
Makes a difference if you consider the above compared to 4 players.
Someone will most likely have a 5.
In general, in Omaha, one must assume they have the nuts.
So, not a stretch of the imagination having the 5, AA, & KK - not rare at all.
Only the QQ, added to the mix, would make it slightly rare at best.
Using the eyeball test to make a rough estimate, and seeing your calculation, the difference is
cavernous
Something seems off here.
All we need is another mathematician to comment.
(Also, the flop could be 222,333,444,555,666,777,888,999,101010, and JJJ.
Making it more common!)
It actually doesn’t make a difference because I worked the other way around. If you assume the 4th player always has 4 unpaired cards and no A, K or Q (ie the best possible chance of making quads), then you only need to calculate how likely the board is to run out with the remaining 3 of any one of those 4 cards.
Like you say, none of individual elements of this hand are rare, it’s just the combination of all of them happening at once that make it a long shot.
I calculated the odds of AA vs KK vs QQ more precisely and that gives final odds of about 1 in 80 million - the same ballpark as the quick and dirty calculation.
Interesting note, if you actually multiply all the AI supplied odds together you get around 1 in 800 million. I’m pretty sure the odds it gives for AA, KK and QQ is off by a factor of roughly 10 though, so that would give 1 in 80 million.
Flopping 555 - odds are 1 in 5,525
Flopping any 3-of-a-kind - odds are 1 in 425
This according to AI
I’ve found that A.I. questions have to be specific otherwise it will be sketchy.
A.I. Question:
what’s the odds of having the flop a full house and you have pocket pairs with 4 out of 7 players playing after the flop in omaha 8
A.I. Answer:
Odds of Flopping a Full House with a Pocket Pair in Omaha 8
In Omaha 8, you’re dealt four hole cards, and you must use exactly two of them with three from the board. So when you say “pocket pair,” I’ll assume you mean at least one pair among your four hole cards.
If You Hold a Pocket Pair (e.g., 8:spade_suit: 8:diamond_suit: X X):
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Odds of flopping a full house: ~0.98% or 1 in 102
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Odds of flopping quads: ~0.2%
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Combined odds of full house or better: ~1.2%
These are per-hand odds, and they don’t change based on how many players see the flop. However, with 4 out of 7 players continuing, the dynamics shift:
Strategic Implications in Multi-Way Omaha 8 Pots
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More players = more potential low hands, which can split the pot.
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Your full house may not scoop unless no qualifying low hand exists.
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Board texture matters: If the flop is paired and low-heavy (e.g., 2♣ 2♦ 5♠), your full house might be vulnerable to better boats or low draws.
Bonus: Full House Odds by Hole Card Structure
| Hole Card Structure | Flop Full House Odds |
|---|---|
| One pocket pair | ~0.98% |
| Two pocket pairs | ~2.5–3% |
| Three of a kind (rare) | ~4.5% |
| Two pair (non-paired hand) | ~16.5 |
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Odds of flopping a full house: ~0.98% or 1 in 102
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Odds of flopping quads: ~0.2% or 1 in 500
So, wouldn’t the odds be: .0098 x .0098 x .0098 x .002 = 1 in 531,241,234.52?
No, because the odds of flopping a full house aren’t independent. Essentially this would be factoring in the odds of have a paired or tripled flop 3 times instead of once. We also only want to count tripled flops because 3 players can’t make a boat if the flop is only paired, and we specifically need the pocket pairs to be AA, KK and QQ.
I don’t think the odds would change because you want AA, KK and QQ. The odds of a pocket pair are still .0098. Now if it’s necessary to only have these cards then the odds are even greater.
But isn’t this what has happened in this hand and isn’t this the question being asked?
The odds of AA are the same as the odds for any other specific pair, but that’s not the same thing as just a pair in general (which is 13 times greater).
No, there’s only a single shared flop. You’ve emphasized the wrong part of what I was saying.
That’s why I wrote if he was specifically requiring AA, KK and QQ, the odds would be even greater than the 1 to 531 million odds. Offhand, I’d think it would even be more than 13x of that amount. I guess I could ask my A.I.
Your still missing that there’s a shared flop. You can’t just multiple 0.0098 together 3 times because of that. 0.0098 x 0.0098 x 0.0098 gives you the odds of someone flopping a boat 3 times in a row, which is a very different question.
From the A.I. response, the odds shouldn’t change based on the how many players see the flop. I’m not following your point which is just fine, I guess.
Your odds of flopping a boat don’t change, but the odds of 3 people flopping a boat at the same time is not the same as someone flopping a boat 3 times in a row. If the flop is not paired, the chance of having a boat goes to zero for everyone. If the board is tripled, any pocket pair is now a boat.
(1) I think it still is the same since in omaha 8 and given the hand situations dealt, given a flop of a set, the odds of a pocket pair is still .0098 whether it’s one or three players.
(2) Exactly my point if there are pocket pairs.
This is the way I’m interpreting the A.I. response.
Yeah, I think I’m off by a factor of 24, because we don’t care who has what hand. I try and figure it out exactly when I get the chance, but it’s probably going to end up being 1 in a few million or so I think.
No, that’s the odds of flopping a boat. Let me explain it this way…
Imagine a game where everyone flips their own coin, but there’s also a community coin that is part of their “hand”. The odds of someone have two heads is 1/2 x 1/2 = 1/4 - the odds of them flipping a head times the odds of the community coin being a head. Now, what are the odds of two players both having two heads? That’s 1/2 x 1/2 x 1/2 - the odds of the community coin by a head times the odds of each player having a head, not 1/4 x 1/4 (the odds of both players independently having two heads). There’s only 3 coins, so there can only be 8 possible outcomes.
You can only multiply probabilities together when they are independent, which is clearly not the case when we’re dealing with hands that all share the same flop.
But this is exactly what has happened in this hand. I think you are considering a completely different situation.
I thought I was trying to ask the question to A.I. with the same situation as the hand played out. A boat after the flop calculated the odds at .0098 given a pocket pair in omaha 8 doesn’t change, no matter how many players see the flop.
We didn’t have a single boat in this hand, we had three. The odds of a single boat don’t change, but the odds of a second or third player having a boat absolutely does.