Probabilies of flopped royal vs. straight flush

I am trying to determine the probability of the following occurrences in a Texas Holdem Game with 9 players.
On the flop:
Royal Flush versus queen high straight flush ( I.E board of 10 J Q suited versus AK and 89 of same suit)
On the turn:
Flopped Royal Flush versus 4 of a kind made on the turn
Flopped 4 of a kind versus turned 4 of a kind (pocket pair versus pocket pair)

Quote: Farley

I am trying to determine the probability of the following occurrences in a Texas Holdem Game with 9 players.
On the flop:
Royal Flush versus queen high straight flush ( I.E board of 10 J Q suited versus AK and 89 of same suit)

There are combin(52,3) = 22,100 different flops, of which four (one of each suit) is Q-J-10, so the probability of the three flop cards being Q-J-10 suited is 1/5525.

I'm not 100% sure I am calculating this right, but here goes...
The probability that any of the 18 hole cards is the Ace of that suit is 18/49.
The probability that that player's other card is the King is 1/48.
The probability that any of the 16 remaining hole cards is the 9 of that suit is 16/47.
The probability that that player's other card is the 8 is 1/46.
The probability that one player in a nine-player game has a royal on the flop and another has a Queen-high SF is the product of these five numbers, or about 1 in 97,551,242.

Where did this happen at?

Quote: MaxPen

Where did this happen at?

It didnt, just trying to determine the probabilities for promotional purposes.

I've seen a straight flush vs. straight flush bad beat jackpot once.

Quote: Ibeatyouraces

I've seen a straight flush vs. straight flush bad beat jackpot once.

Flopped?<---very uncommon, hence my inquiry in my first post.

I like to know the probability of that as well (IE and three suited connect cards with each player holding the two straight flush cards for either side.)

with all 5 board cards, ive seen straight flush versus straight flush (each player using both hole cards) quite a few times in 25 years or so in card rooms

Quote: Farley

It didnt, just trying to determine the probabilities for promotional purposes.

There is a point in time that an outcome is so unlikely that a promotion based on it is BS.

Quote: MaxPen

There is a point in time that an outcome is so unlikely that a promotion based on it is BS.

I agree, players would recognize that point and it would likely have little affect. Trying to find the median.

Currently the Bad Beat is AAA1010 or better losing to 4 of a kind or better, both cards must play.
Objective:
To add additional value to the jackpot ( I.E adding 5K 10K 15K ...or up to 50 or 100K) depending on the hands that qualify and when those hands are made.

Hi all. I should have stumbled upon this forum sooner.

Quote: ThatDonGuy

about 1 in 97,551,242.

I agree.

4 * C(9,2) / C(52,7) / C(7,3) / 3!!

Numerator: 4 suits, 1 valid flop combo for each suit, C(9,2) possible player matchups, 1 combo for the hole cards

Denominator: 7 cards dealt out of 52, then C(7,3) choices for which 3 are on the flop, then 3!!=3 possible ways to distribute the 4 hole cards between the 2 players involved (when it doesn't matter who gets the Royal and who gets the other).