Please could someone settle a disagrement.....

[Pepsi]

Im having a debate with a friend and I need your help.
Are the odds of hitting a royal flush in hold em, the same, higher, or lower than in 7 stud?

[moomoocow]

If both are played out to the end- both players have 7 cards to work with - so they are the same for any one player in any one given hand.

Per round of stud, many more cards are dealt out - and I'm probably going to guess that it is more liekly to see straight/royal flushes in stud than it is in hold'em.

Intuition speaks,

moo -

[xniNja]

It depends how you phrase/think about the question. My intuitive answer, based on how I perceive the question, would have to be Hold'Em.

For a "player" to make a royal flush in 7-card stud he must be dealt exactly the highest 5 cards of any given suit. This is a small % that I probably wouldn't have even gotten right when I took statistics.

For a "player" to make a royal flush in Hold'Em... He could have 1-2 of the 5 highest cards and then would need 3-4 of the rest out of the 5 cards on the board. However, since the board is common... say 4 people went in with AK suited (unlikely but possible) they all have the same shot at making the royal flush before the flop. I think this would mean a significantly higher percentage overall. Follow me?

Edit: Nevermind. I thought about this some more. The % is the same... in 7-card stud 4 people could have AK suited face down and it would be the same scenario... I left my above post in-tact for educational purposes =P

[danzasmack]

Before I waste my time with the math, does this sound right:

for a full game of texasHE:
P(royal flush on board) + P(4 cards to RF & 1 player has the card) + P(3 cards to RF & 1 player has the 2 cards)

Where 7 card stud: P(1 player receives the 5 necessary cards to get a royal flush)

Obviously, if it is 1 player, it's the same thing, because only 7 cards are seen.

[xniNja]

I think that's conceptually accurate, but the original responder was saying that P(r-board) + P(4 /> 1) + P (3 /> 2) in hold'em is the same as P(1->5) in stud.

Now that I think about this, yet again, I need to make another revision. The probablity, overall, is higher in stud because each player can end up with the royal flush mutually exclusive of the rest. Agree?

Edit: For stud it's P(1 player gets the 5 cards he needs) + P(2 players get the 5 cards they need) + P(3->5) + P(4->5) ... which would be higher than Hold'Em. Does that make sense?

[Pepsi]

Thanks for all your help guys.

Anyone with any other views?

[Rasputin]

Are we talking about one specific player or are we talking about any random player at a given table?

If it's one specific player, I don't see how it could be different. Seven cards are seven cards.

If it's any random player at a table then I think it's got to be hold'em simply because you can fit more players at a table.

[LetYouDown]

If the board contains a royal flush at a full Hold 'Em table, do you consider that 10 royal flushes?

[AaronBrown]

If dealt to completion, a single player has exactly the same chance of getting a royal flush in seven-card stud or hold'em. There are 4,324 ways to get a royal flush out of the 133,784,560 seven card hands. A seven card stud player must play 30,940 hands on average to get one. A single hold'em player will have to wait just as long.

If we play 21 times that number of hands, 649,740, each of the players at a stud table will have had 21 royal flushes with average luck. There is virtually no chance that two or more of these will occur on the same hand.

The same 649,740 hold'em hands will produce, on average, one hand with a royal flush on the board. Then everyone at the table will get credit for a royal flush. Each hold'em player, on average, will also get 20 royal flushes that do not have to be shared because one or two of the cards are in his hand. So each hold'em player will get the same 21 as the stud players; but will get 20 individual and one shared instead of 21 individual.

[Pepsi]

Thanks all.
My answer was the same and my friends was hold em so I think I win. /images/graemlins/laugh.gif /images/graemlins/laugh.gif