In NLH, what are the odds of the board ending up XXXYY if I hold XY? How rare is this versus other remote outcomes in NLH?

Just curious because I've never seen this before, nor has anyone I know.

You have not played enough and neither has anyone you know apparently.

In any case, we need more specifics. Are you asking, "What is the probability that I get dealt XY and the board ends up XXXYY?" Or are you asking, "What is the probability, given that I already have XY, that the board ends up XXXYY?"

They are different questions. For that matter, is order important? You wrote XXXYY, implying that you make quads on the flop and then pair your other hole card on the turn and river. Does that sequence have to happen? Or can the flop come YYX with an X turn and X river to meet your qualifications? It makes a difference. Further, does it matter that it comes XXXYY. Would YYYXX not suffice?

If you start with XY, the board will be either XXXYY or YYYXX with a probability of (2x4)/C(50,5) = 1/264845 or 264844 to 1 against ( if every unseen card is equally likely ).

Sorry for poor wording in the original question. This is what I wanted to know. Thanks for the response. It is far less remote than I'd imagined - glad I asked.

I honestly don't remember having seen this, although I guess I can't rule out that it happened but was subsequently forgotten because it doesn't exactly leave the lasting impact of a Royal Flush.

Isn't the correct answer [2 * C(3,3) * C(3,2)]/C(50,5) = 6 /2118760 ~ 1 in 353126.6?

Sorry to be a nit.... just trying to learn this stuff.

Yes, of course you're right and I must have been half asleep!

The true probability of this happening is much lower than what has been calculated because not all hands go to the river. Most don't. And when you consider the fact that you have XY on an XXXYY board it is even more unlikely that another person will get to the river with you because they're unlikely to have a strong hand (because its hard to hit that board when there's only one Y left in the deck).

Probability of that happening is lower than flopping a nut flush or a nut full on the flop.

But the question should be, how much can you make out of flopping XXXYY when holding XY. If either X or Y is a paint, then more than likely you will not get so much action. In other words, your profit will be very little to none. And in most cases, they'll fold and you'll have to muck. Either that or you can show your hand to boost your "ego".

The only time you'll receive action is if XXXYY is X is something like 10 or J. AND your opponent better be holding some sort of hand like K/K or A/A. A novice player might chase with Q/Q but advanced player might even muck it. Of course, a drunk player will go all in and it'll be bingo time for you. But in most cases (in cardrooms), you would only be able to pick up what's already in the pot and small chance that you'll double it.

The closest thing this has happened to me was last weekend when I went to a local casino. Mind you, I played from 12Pm to about 1AM (13 hours). The table was going at the rate of 30-40 hands per hour. so out of 390-560 hands, i picked up the closest thing to your example. I was holding Jc/Qc under the gun. The table was loose-aggressive. In most cases, I may have folded, but I called UG. The person in the cut off raise 3x BB and button called, and pretty much everyone called. the flop comes Qs/Jh/Qh. BB and SB checked. I like to check-raise with loose-aggressive people and cut off person was loose-aggressive. So I checked. it went all the way to the cut off person who raised 3x the blind. the button called. BB and SB folded. I raised him 3x his bet. now everyone folded and action was back to him. he actually folded! I know i should have just called but i was stupid and after playing about 7 hours straight I made a stupid mistake. Luckily (yes I said luck), the button got up from the chair and stared me down. Of course, I played possum. the button was a lovely whale who got a sugar daddy, so she was donating the table. she didn't believe my check-raise and think i was semi-bluffing for a flush draw. She smooth called me. Now the turn come another Qd. So the board is now Qs/Jh/Qh/Qd. As a good boy as i was (to pretend like I was chasing a flush), I checked. She saw it as a weakness, and bet the same amount I raised on the flop. I took about 30 seconds and called. the river was a Ah. Now it's the best time for me to bet all in. So I did. She snap call me. she showed J/J cause she was so happy and thought that she had the best hand. I showed my J/Q and took a huge pot.

I understand her action on the flop. But if I was her, I would have folded on the turn as I was playing solid and only semi-bluffed while I was playing at the table. Of course, maybe she's just playing very stupid cause she got a sugar daddy. But that was the only time I got a huge pay off and I really doubt that will ever happen again.

so my point is the possibility of flopping what I had was about 0.18%-0.26%. I know my answer is not very solid because it may be a sampling error but that's the closest thing I can come up with. Now to hold XY and having XXXYY on the board will be MUCH MUCH lower. So my advice, is to act like a dummy when you flopped on against an aggressive player and put up standard raises against calling stations