The question is?

The_Don90

Ok this was a question i was asked last night at a live game which i was running.

I was asked has anyone ever seen the unltimate cooler

Q or K high straight flush v a Royal flush.

I could only answer honestly which was a NO. However i was woundering have any of you guys seen it. Also for the math guys what are the odds of this happening?

MereNovice

I believe that the odds of this happening in a heads-up game are as follows:

A. For one player to have an ace and make a royal flush while his opponent has the 9 of the same suit.
2*2*1/13*46/51*2*1/50*46/49*5*4/48*3/47*2/46*1/45 which is about 3,734,238 to 1.

(i.e. 2 players * 2 cards to hold ace * probability of an ace * probability of a card that is not KQJT9 of same suit * 2 cards to hold 9 * probability of a 9 * probability of a card that not AKQJT of same suit * 5 ways to draw 4 cards from 5 * probability of KQJT of same suit * probability of one of the other three cards * probability of one of the other two cards * probability of last card to make royal flush)

B. For one player to hold AKs and make a royal flush while the other player to hold 98 of the same suit.
2*2*1/13*1/51*2*1/50*1/49*3/48*2/47*1/46*10 which is about 351,184,469 to 1.

(i.e. 2 players * 2 cards * probability of an ace * probability of K same suit * 2 cards * probability of a 9 * probability of 8 of same suit * 10 ways to draw 3 cards from 5 * probability of KQJ of same suit * probability of one of the other two cards * probability of last card to make royal flush)

C. The combined odds (i.e. the chances of either happening) are 3,694,949 to 1.
As always, I am happy to be corrected.

Tikay10

Wiiiii - MereMaths Geek is back!

Happy days. The Forum was not the same without you.

unknown_username

If one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.
 
It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K.

In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush.

It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush.

These are because there CANNOT be two straight flushes of different suits in Holdem.  This would require a total of 10 cards in play, an the board plus two sets of hole cards add up to only 9.  (The answer is, of course, different in Omaha.)

Sorry, Mere Novice, but

unknown_username

I went out of the wcoop main event with quad kings against quad aces. Not quite straight flushes but the effect on me was just as bad (

SHANXTA

In Response to Re: The question is?:

If one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.   It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K. In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush. It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush. These are because there CANNOT be two straight flushes of different suits in Holdem.  This would require a total of 10 cards in play, an the board plus two sets of hole cards add up to only 9.  (The answer is, of course, different in Omaha.) Sorry, Mere Novice, but
Posted by metaraptor

If the board is KQJT all spades, player A has a royal with the As, player B has a straight flush to the King with the 9 spades.

How is the answer different in omaha? When you can still only use two hole cards, so 2+2+5 community cards still equals 9!

The_Don90

In Response to Re: The question is?:

If one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.   It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K. In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush. It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush. These are because there CANNOT be two straight flushes of different suits in Holdem.  This would require a total of 10 cards in play, an the board plus two sets of hole cards add up to only 9.  (The answer is, of course, different in Omaha.) Sorry, Mere Novice, but
Posted by metaraptor

Hold em

Player one 9d 8d (reasonable raise calling hand)

Player two Ad Ks

Flop
10d Jd Qd

Turn
Kd

River
Xx

Impossible i think not

Machka

In Response to Re: The question is?:

If one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.   It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K. In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush. It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush. These are because there CANNOT be two straight flushes of different suits in Holdem.  This would require a total of 10 cards in play, an the board plus two sets of hole cards add up to only 9.  (The answer is, of course, different in Omaha.) Sorry, Mere Novice, but
Posted by metaraptor

Unless we are talking Omaha then surely the board could be

10JQKx of hearts

I could hold  the Ah and the villan 9h

I have the royal flush and he has a straight flush to the K.

dylan12

I have lost with a st8 flush once online v a Royal Flush

I have had Quads 4 times live and lost twice to Royal Flushes, ffs I run good!!

unknown_username

Now I start to see ...

A)   Why I keep losing money with my K high straight flushes!

   Why it is inadvisable to go for a bar lunch on Saturday and log back in to a Poker site!

I shall now go and cringe in embarrassment and a very dark room with a very large cup of coffee.  Sorry and Thanks to All.

P.S.  Next time you meet me at the tables, remember that because I am an idiot, I may be unable to fold high straight flushes even when they are beat!!!

batman4

the real question is--what is the mathematical equation of Infinity ?

unknown_username

Ahhh, the coffee is starting to work.  Try this ...

In a sensible game like Omaha, if one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.
 
It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K.

In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush.

It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush.  These are because there CANNOT be two straight flushes of different suits.  This would require a total of 10 cards in play, and the board plus two sets of hole cards add up to only 9.

(The answer is, of course, different in silly games like Holdem where you don't need to use both your hole cards, so can share 4 common cards.)

... if my brain is still absent, could someone please recommend something better than coffee???

MereNovice

In Response to Re: The question is?:

If one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.   It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K. In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush. It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush. These are because there CANNOT be two straight flushes of different suits in Holdem.  This would require a total of 10 cards in play, an the board plus two sets of hole cards add up to only 9.  (The answer is, of course, different in Omaha.) Sorry, Mere Novice, but
Posted by metaraptor

but???

I think that I set out the necessary conditions pretty clearly.  :-)))

TINTIN

In Response to Re: The question is?:

In Response to Re: The question is? : If the board is KQJT all spades, player A has a royal with the As, player B has a straight flush to the King with the 9 spades. How is the answer different in omaha? When you can still only use two hole cards, so 2+2+5 community cards still equals 9!
Posted by SHANXTA

seen this in a freeroll, player a had sat out all tourney and had 40 chips left and was allin player b flated to try and eliminate him, board ran kqjt all spades player b had 9s the unlucky guy sat out had the ace of spades. didnt know wether to laugh or cringe

The_Don90

In Response to Re: The question is?:

Ahhh, the coffee is starting to work.  Try this ... In a sensible game like Omaha, if one player has a Royal Flush, it is IMPOSSIBLE for any other player to hold a straight flush to the K.   It possible for another player to hold a straight flush to the Q IFF ("if and only if") the hole cards held by the player with the Royal Flush are the A,K. In general, the highest possible straight flush held by the second player is to the card one rank lower than the lower of the two hole cards held by the player with the Royal Flush. It is also the case that if you hold any straight flush and at least one of yor hole cards is the 10 or higher, then it is IMPOSSIBLE for any other player to hold a higher straight flush.  These are because there CANNOT be two straight flushes of different suits.  This would require a total of 10 cards in play, and the board plus two sets of hole cards add up to only 9. (The answer is, of course, different in silly games like Holdem where you don't need to use both your hole cards, so can share 4 common cards.) ... if my brain is still absent, could someone please recommend something better than coffee???
Posted by metaraptor

I believe you are correct for Omaha. NO biggy i guess thats where you play most so thats the rules youll be used to.