A question about WPT EP01-11 Partypoker million

[Blackwolf]

I just want to warn people that I am just trying to learn the maths... even the basic ones just to be more sure and calculate it alot quicker so basicly I am a noob at this /images/graemlins/laugh.gif

In WPT party poker million season 1 episode 11 at the break they ask what are the odds to flop a Royal straight flush with A /images/graemlins/spade.gifK /images/graemlins/spade.gif
Answer: 19599 to 1

Now I kinda dont agree on that since I got the impression that Crazy Mike (atleast I think he was first to publish the total amount of flops) counts the diffirent flops NOT to come exactly Q /images/graemlins/spade.gif J /images/graemlins/spade.gif T /images/graemlins/spade.gif but also like J /images/graemlins/spade.gif T /images/graemlins/spade.gif Q /images/graemlins/spade.gif since they fall in diffirent orders.
Ofc u need those exact 3 cards but those three cards can only make up a flop in 6 diffirent ways so shouldnt the odds in flopping a Royal Straight flush be more like 6 to 19600 or 3265 to 1 roughly?

Kinda hoping I am wrong and I will be corrected that way I learn more /images/graemlins/smile.gif Thanks for reading it threw!

[Orpheus]

First, a detail that trips some people up: all cards that aren't in your hand are unknown. Maybe they're in another hand, maybe they are undealt at the bottom of the deck. maybe they'll even end up on the board. Since we don't know, we must treat them all alike.

The math is simple:

There are 3 possible cards (out of 50) for the first flop card. Two remaining cards (out of 49) for the second flop card. and finally, just one remaining card (out of 48) for the last flop card.

(3/50) * (2/49) * (1/48) = .000051020408

since you asked about the ODDS, not the probability, you want the inverse of this. You can get this by inverting the three fractions. Can you see why?

(50/3) * (49/2) * (48/1) = (50*49*48)/(3*2*1) = 117600/6 = 19600

You'll note that it doesn't matter which card is dealt first, second or third. It only counts how many candidate cards are left after each successful card is dealt. The "6" in the denominator is the number of possible orders for 3 cards to be dealt. I hope this helps you see how the order is already accounted for.

[Blackwolf]

I understand completely. Thanks for explaining that so well I really do understand /images/graemlins/tongue.gif
Now I see where my thoughts are way off again thank you very much for the time /images/graemlins/smile.gif

But I still want to find a spot where they give the wrong advice /images/graemlins/wink.gif

[LetYouDown]

They've given the incorrect odds before. One had was something along the lines of "if you hold K-K, what are the odds that someone has A-A at a 10 person table?" or something like that. They didn't incorporate the fact that two people could have A-A and/or eliminate the K-K from the remaining cards. Either way, their answer was wrong. BruceZ proved this in a thread not too long ago.

[TomCollins]

They also claimed poker was legal in Texas.