high hand royal flush odds

[hoopking]

party poker recently started a high hand jackpot. it pays only for a royal flush. i was hoping someone could tell me the odds of hitting a RF by the river if i always see the flop with suited faces, and stay in if there is still a chance to make RF. im looking to find a minimum jackpot where the extra 50 cent rake becomes profitable. ty

[deacsoft]

I'll get you started with this:
If you hold A-Ks the odds of flopping a royal flush are 19,599 to 1 (against).

[hoopking]

10 royal flush starting hands out of 169 possible starting hands. i come up with 331223.1 to 1 against flopping RF if i play suited face starters every time. im not sure how to combine the odds of hitting on the turn and river or both if i need runner-runner.

[Cobra]

Lets say you start with two cards to the Royal flush.

There are now 50 remaining cards.
47 of them are blanks.
3 are the remaining Royal cards which you must get.

There is (50c5) = 2118760 boards from the 50 remaining cards

There is 1*1*1*(47c2) = 1081 boards that give the royal

Probability of Royal is 1081/2118760 = .0510% or 1 in 1960

Cobra

[Cobra]

Obviously if you flop 0 or 3 cards to the royal flush these hands are self explanatory.

But let say you flop one to the royal needing two more

Prob = (2c2)/(47c2) = 1 in 1081

Lets say you flop two to the royal leaving you one left.

Prob = 1*46/(47c2) = 1 in 23.5

Cobra