Hot Roll Poker. Drew to 4OAK from holding 3, what are the odds?

So I was playing Hot Roll Poker, and had no multiplier, playing Triple Play nickel Bonus Poker Deluxe. I was dealt three 8s, held the 3OAK, but was amazed when I drew 4OAK on EACH of the 3 hands. The win was just $60, but I just want to know what the odds were of that happening. I figured this is the go to place to find out, since there seem to be a lot of math wizards on here. :)

I just wish that would've happened later in the evening when I was dealt four 2s on five play triple double bonus with an 8x multiplier. I drew only one kicker out of 5 hands, but that still made for a nice $1,440 payoff!

Assuming each of the three hands is a separate line as far as the draw is concerned, of the 47 cards remaining in the deck, the probability that the fourth 8 is one of the two cards you will be dealt is 2/47, so the probability of doing it three times is (2/47)³ = about 1 / 12,978. To put it in perspective, the probability of making a Royal from a 3-card draw is 1 / 16,215.

Quote: ThatDonGuy

Assuming each of the three hands is a separate line as far as the draw is concerned, of the 47 cards remaining in the deck, the probability that the fourth 8 is one of the two cards you will be dealt is 2/47, so the probability of doing it three times is (2/47)³ = about 1 / 12,978. To put it in perspective, the probability of making a Royal from a 3-card draw is 1 / 16,215.

If you look over on the NOT QUITE A ROYAL thread, RS holds a 3 of a kind and doesn't improve.....ON 50 PLAY

ODDS?

https://wizardofvegas.com/forum/gambling/big-wins/20177-not-quite-a-royal/16/#post520541

Quote: AxelWolf

Quote: ThatDonGuy

Assuming each of the three hands is a separate line as far as the draw is concerned, of the 47 cards remaining in the deck, the probability that the fourth 8 is one of the two cards you will be dealt is 2/47, so the probability of doing it three times is (2/47)³ = about 1 / 12,978. To put it in perspective, the probability of making a Royal from a 3-card draw is 1 / 16,215.

If you look over on the NOT QUITE A ROYAL thread, RS holds a 3 of a kind and doesn't improve.....ON 50 PLAY

ODDS?

https://wizardofvegas.com/forum/gambling/big-wins/20177-not-quite-a-royal/16/#post520541

When holding trips, there are 47*46/2 = 1081 total combinations.

Quads: 1*46 = 46 (46 choices for kicker)
Full House: 10*6 + 2*3 = 66 (6 choices for pairs when all 4 cards are available in a rank, 3 choices when you throw away a card)
No Improvement: 1081-46-66 = 969 combos

No improvement 50 hands in a row: (969/1081)^50 = 0.0042160345 = 1 in 237.2

I would have guessed much rarer.

I've seen a neighbor pull off the 3 for 3 quad hit. He didn't even flinch when he did it.

One of my most surprising hits was on Ten-Play, DJATC saw this one, in fact. I held a Pair of Eights on a Ten-Play game that we will not discuss and connected for Quads twice.

nCr(2,2)*nCr(45,1)/nCr(47,3) = 0.0027752081406105

Above represents the probability to connect on one hand, so if I use the Vassar Stats Binomial Distribution Calculator, rounding to .00277521:

I end up with 0.00034148799842914634 for two or more out of ten or 1/0.00034148799842914634 or 1 in 2928.361 (Rounded)

I thought that was a much rarer occurrence than it actually is, I think most people tend to think that about these sorts of things when they happen. It turns out I have had rarer hits, such as pulling Quad Deuces whilst holding a single deuce, which I've done two (and possibly more) times, but I only remember two times.

I've also pulled a Royal holding two, which again, is rarer than the hit detailed above.

Quote: tringlomane

Quote: AxelWolf

Quote: ThatDonGuy

Assuming each of the three hands is a separate line as far as the draw is concerned, of the 47 cards remaining in the deck, the probability that the fourth 8 is one of the two cards you will be dealt is 2/47, so the probability of doing it three times is (2/47)³ = about 1 / 12,978. To put it in perspective, the probability of making a Royal from a 3-card draw is 1 / 16,215.

If you look over on the NOT QUITE A ROYAL thread, RS holds a 3 of a kind and doesn't improve.....ON 50 PLAY

ODDS?

https://wizardofvegas.com/forum/gambling/big-wins/20177-not-quite-a-royal/16/#post520541

When holding trips, there are 47*46/2 = 1081 total combinations.

Quads: 1*46 = 46 (46 choices for kicker)
Full House: 10*6 + 2*3 = 66 (6 choices for pairs when all 4 cards are available in a rank, 3 choices when you throw away a card)
No Improvement: 1081-46-66 = 969 combos

No improvement 50 hands in a row: (969/1081)^50 = 0.0042160345 = 1 in 237.2

I would have guessed much rarer.

I've seen a neighbor pull off the 3 for 3 quad hit. He didn't even flinch when he did it.

Yes I thought it would've been much rarer as well.