Straight flush got beat......I felt bad.

[2LIN]

I've seen some quad hands deal out a bad beat here and there, but I've only seen this once. This was at one of our neighborhood hold-em series poker tournaments. The flop comes out 7H, 10H, 7S. The turn is 9H. The river is 8H. One guy goes all-in, eight of us get out of the way except the last guy who makes the call. The all-in guy flips a 6H and shows a straightflush to the ten..........The caller flips over the jack of hearts. We all could not believe what we just saw!
 

[Martini]

Are you saying that after the River was dealt that eight of you got out of the way? So in other words the entire table saw all streets?

[Dr. Neau]

And 2LIN, sorry to stomp on your first post...

...but not a bad beat given the information.

[2LIN]

No. not everyone stayed in. A couple other guys stayed in till the all in. Figured a straight flush by then, but was not expecting the other guy to call and have a higher straight flush.

[2LIN]

I thought it was a shoe in for the straight flush. To get beat by a higher straight flush.......i don't think that we thought it would happen. But, it did. There was only one card out there that could have beaten him, the Jh. I know HE didn't expect that! In Omaha, i could see more possibilities like a higher straight flush with almost all the cards dealt out.

Bad beat or not, we all felt bad for him.   

[Martini]

I thought it was a shoe in for the straight flush. To get beat by a higher straight flush.......i don't think that we thought it would happen. But, it did. There was only one card out there that could have beaten him, the Jh. I know HE didn't expect that! In Omaha, i could see more possibilities like a higher straight flush with almost all the cards dealt out.

Bad beat or not, we all felt bad for him.   

Actually it would be significantly harder to be beat by a higher Straight Flush in Omaha since you have to use two cards.

[2LIN]

Well, with Hold'em, you can use more than three cards on the board, but you only get two cards. With Omaha, you have to use only three on the board, but you get four cards to pick from. Does someone have statistics for chances of getting a straight flush in Omaha vs Hold'em? That would be interesting. 

[Martini]

Well, with Hold'em, you can use more than three cards on the board, but you only get two cards. With Omaha, you have to use only three on the board, but you get four cards to pick from. Does someone have statistics for chances of getting a straight flush in Omaha vs Hold'em? That would be interesting. 

I haven't done the long form math but after running some initial numbers it appears you are right. I stand corrected. The extra two cards you get in Omaha provide enough extra combinations to outweigh the fact that a SF over SF hand in Hold'em could be made with more different patterns i.e. 5c6c7c or 5c6c7c8c or even 5c6c7c8c9c with the losing player playing the board and the winner holding the Tc. There is also a deduction for any of the Omaha hands holding one of the three consecutive cards necessary for a SF over SF but that still is not enough either. Makes sense I suppose since all other hand over hand combinations are more likely to happen in Omaha so I don't know what I was thinking.

[Dr. Neau]

But when you're thinking other hand situations with straights and 4 to the straight on the board (like the example) you get to use one of your two hole cards in substitution of a board card, which *really* opens up the chances.

Here's what I think:
- With A run of 3 on the board, Omaha holds the greater chance of a straight flush over straight flush.  You need 2. You have to play 2. But you have 4 to choose from. In Hold'em, you have to use both yo hole cards.
- With a run of 4 on the board, Hold'em holds the clear advantage. You can play 1 or 2 to do it. In Omaha, you still need to play 2. I think your chances of having 1 of the needed cards out of your 2 are far greater than having the exact 2 needed cards out of your 4.

[Martini]

Yeah, that was my thinking. For SF over SF in Omaha you can only do it with with a run of three middle cards with two connectors on either end. According to ProPokerTools.com, a middle run like a 678 will generate at least 600K combinations due to the extra two cards in hand. And while Hold'em gets extras like runs of four, runs of five, discontiguous runs, runs that include the Deuce and King on board, and other fringe cases they only add in combinations on the order of thousands and can't catch up to the head start that Omaha gets. Again, I didn't do a conclusive math breakdown but the back of the envelope calculations don't look good for Hold'em having more ways to lose with a SF.

[2LIN]

I tried to look up the probabilities for both, but I found nothing, or no site, that would give me side by side stats. I was searching for something like: 1 in 600,000 for hold'em and 1 in 500,000 for Omaha. I can't believe that info was not all over the place. If you find something, please post it.

 

[Martini]

I went to ProPokerTools.com.

Here is a simulation of a SF over SF in Omaha: http://propokertools.com/simulations/show?g=oh&s=generic&b=7s8s9s+**&d=&h1=4s5s+**&h2=TsJs+** which stopped after running through 600K simulations and that alone is enough. The actual number of combos I think should be (the 52 cards minus the seven known cards on the board and in the hands leaves 45) * 44 * 43 * 42 * 41 * 40 for each of the unknown cards. That number alone is over 5 billion.

In Hold'em with a board containing 7s8s9s ? ? and two hands holding 4s5s and TsJs there are 1980 ways of that happening (45 * 44) for the two other board cards. It gets a little better with 6s7s8s9s ? and 5s ? versus Ts ? which gives 91,080 combos. And if you put 5s6s7s8s9s with any two cards versus Ts ? then you can add on 45,540 more. There are more cases like a 4s6s7sTs ? with 3s5s versus 8s9s also.

This is a simplification and doesn't cover all the cases (like the fact that 2s3s4s on board can never result in a SF over SF in Omaha though it could in Hold'em) but the pattern is already clear that Hold'em hands add on combinations in the thousands or tens of thousands and will never reach the billions that Omaha has.

[Dr. Neau]

I went to a piece of paper.

I focused on the odds of hitting the low end of the straight flush with a 5-8 on the board.

In Hold'em, your odds are 4.255%.  One of your two cards needs to be the 4s.
In Omaha, your odds are 0.555%.  Two of your four cards need to be the 3s & 4s.

[Martini]

But there are more ways to have 3s and 4s in hand with four cards though, no? Since four cards are accounted for on the board shouldn't it be 4*(1/48) + 3*(1/47) = ~14.7%?

[Dr. Neau]

But there are more ways to have 3s and 4s in hand with four cards though, no? Since four cards are accounted for on the board shouldn't it be 4*(1/48) + 3*(1/47) = ~14.7%?

You don't add them together.

Essentially, for Omaha, you have to do this...the situations are:
XY-- (1/47 * 1/46) = 0.04625*
X-Y- (1/47 * 45/46 * 1/45) = 0.04625%
X--Y = (1/47 + 45/46 + 44/45 * 1/44) = 0.04625%
-XY- = (get the idea....)
-X-Y
--XY
Then you do the same, swapping X & Y.

Essentially, the odds are 12 / (47 * 46) = 0.55504%

Note, you also have to discount the fifth, blank, board card.

[Dr. Neau]

And I'm not going to get into the odds in Omaha for SF over SF, because it's already clear to me that it's much harder to even hit a SF in Omaha than it is in Hold'em (assuming 4 on the board).

But remember this.  If player A has a straight flush, there's also a chance that one of his other two hole cards is one of the two cards someone else would need to hit the high SF...

[Dr. Neau]

And just for kicks, here are the odds with 3 to the SF on the board of a given player completing the SF.

Hold'em:
1/47 * 1/46 * 2 * 3 = 0.278%

Omaha:
1/47 * 1/46 * 12 * 3 = 1.665%

[Martini]

Then wouldn't that imply that Set over Set is more rare in Omaha too?

[Dr. Neau]

No.  The key point with 4 on the board to a straight flush is that in Hold'em you only need 1 card to complete it, but in Omaha you still need 2.

[Dr. Neau]

Lemme ask you this.

Assuming you play both Hold'em and Omaha...

Think about how you feel in Hold'em when that 4th heart comes down on the river.

Now compare that to how you feel in Omaha when that "dreaded" 4th heart comes down on the river.

[2LIN]

The dreaded 4th heart in Omaha is inconsequential unless it completes the SF that you did'nt have with the 3 previous cards. Right? Like a flop of 6,7,K of hearts, and the turn or river is a 5H with your hand being 8,9 of hearts. I don't get the feeling of one or the other being different. If I make a straight flush in either one........I'm happy!

[Dr. Neau]

Thus the quotes around "dreaded", Jack.

That's the point.  If you've got the low SF in Hold'em after the flop and the turn comes in at the high end of the SF, then you're not quite as confident.

If you've got the low SF in Omaha after the flop, you're feeling pretty good, and if the turn comes in at the high end of the SF, you're probably just as confident.

[Martini]

No.  The key point with 4 on the board to a straight flush is that in Hold'em you only need 1 card to complete it, but in Omaha you still need 2.

But you have more cards available to have those two needed cards. Taken to the extreme, imagine a game where there is no stub and one player has the normal four cards but the other player has the remaining cards in the deck. Clearly there is a higher chance that you are up against a higher SF despite the fact that villain needs two exact cards to beat you. I know that example is a stretch but it underscores the principle that the number of cards available can outweigh the requirement to use exactly two cards. Now exactly where the tipping point is I don't know for sure but I think four cards is enough.

[Dr. Neau]

Okay...just for you.

In both scenarios, board is 3s-4s-5s-6s-blank. And we're heads up.

Hold'em
I have low end with 2s-blank.
There is a 4.44% chance you hold the 7s for the top end (2/45).

Omaha
I have the low end with As-2s.
There is a 0.66% chance that you hold both the 7s and the 8s for the top end. (12/(43*42)).

stats don't lie.

[Martini]

I think we're talking about different things. I believe the odds of ANY SF over SF is higher in Omaha than in Hold'em. That includes the scenarios where there are three to the SF on the board as well as four (or even five) to the SF on the board.

[2LIN]

That is what I was trying to ask. SF over SF Omaha vs. Hold'em 3 or 4 cards on the board.
I do love trying to understand the stats though.

[Dr. Neau]

With 3 to the SF on the board in Hold'em...if you have the low end there's a 0.101% chance that you'll be beat by your heads-up opponent.

With 3 to the SF on the board in Omaha...if you have the low end there's a 0.664% chance that you'll be beat by your heads-up opponent.

[2LIN]

With 3 to the SF on the board in Hold'em...if you have the low end there's a 0.101% chance that you'll be beat by your heads-up opponent.

With 3 to the SF on the board in Omaha...if you have the low end there's a 0.664% chance that you'll be beat by your heads-up opponent.

 

Cool! I love it!

Can you figure that same scenario with 4 cards on the board, and come up with a percentage?

[Dr. Neau]

With 3 to the SF on the board in Hold'em...if you have the low end there's a 0.101% chance that you'll be beat by your heads-up opponent.

With 3 to the SF on the board in Omaha...if you have the low end there's a 0.664% chance that you'll be beat by your heads-up opponent.

 

Cool! I love it!

Can you figure that same scenario with 4 cards on the board, and come up with a percentage?

Sure:

Okay...just for you.

In both scenarios, board is 3s-4s-5s-6s-blank. And we're heads up.

Hold'em
I have low end with 2s-blank.
There is a 4.44% chance you hold the 7s for the top end (2/45).

Omaha
I have the low end with As-2s.
There is a 0.66% chance that you hold both the 7s and the 8s for the top end. (12/(43*42)).

stats don't lie.

[2LIN]

Ok. so, Hold'em goes way up to 4.44% with 4 cards and Omaha stays virtually the same with 3 cards or 4 cards at 0.66%.
correct?

[Wedge Rock]

Holy carp!

I thought the dedicated dealer threadjack was TLDR...  Jeesh!