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View Full Version : Why does a flush beat a straight in holdem?

GrunchCan
09-16-2005, 12:37 PM
Two players are dealt drawing hands in HE. One is dealt suited cards. The other is dealt connecting cards of different suits that don't match the opponent's suit.

The flop comes and hits both opponents - both have thier best draw. There are 9 cards that will improve the flush draw, but only 8 at most that will improve the straight draw. Very often, only 6 will improve the straight.

It seems to me that it is much easier to make a flush than a straight. Is my suspicion correct?

kyro
09-16-2005, 12:40 PM
I don't think so. I think you're ignoring a lot of PF possibilities. I don't have exact numbers, but my guess is there are more ways to get connectors than suited cards.

*Edit* And by connectors I mean cards that can make a straight.

Koss
09-16-2005, 12:46 PM
You're more likely to be dealt a suited hand than connectors, but this doesn't count 1 &amp; 2 gappers. But you are still more likely to have a straight than a flush in holdem. Holdem is really no different than 7 card stud. You get 7 cards, it doesn't matter which 2 you start with and what they are. Straights just have a higher probability of occuring when you deal out 7 cards. Obviously you are more likely to hit a flush draw than a straight draw, but I'm pretty sure you're more likely to flop the straight draw.

LetYouDown
09-16-2005, 01:15 PM
[ QUOTE ]
*Edit* And by connectors I mean cards that can make a straight.

[/ QUOTE ]
You can make a straight without any cards in your hand. You can also make 4 card straights. In community card games, you have to take into consideration that the board can play (i.e. have a flush or a straight on it).

My quick math came up with (preflop combinations):

There are 192 directly connected cards, including suited cards. There are 176 one gap cards, including suited cards. Removing suited connectors, you have 144 connectors and 132 one gap cards. There are 312 combinations of suited cards, including connected. Removing suited connectors, there are 268 combinations of suited cards.

bizaff
09-16-2005, 01:31 PM
Koss touched on this, but I'll expound a bit. The poker hand rankings (excluding high card only hands) are ordered by how likely they are given any random 5 cards.

In hold em, when you flop a flush draw, you have 9 outs. When you flop an OESD or double gutter, you only have 8 outs.

The odds of flopping a flush draw: 8.1:1.
The odds of flopping a straight draw: 6.7:1. (connecting)

You're more likely to flop the draw, but slightly less likely to hit it.

09-16-2005, 02:37 PM
[ QUOTE ]
Why does a flush beat a straight in holdem?

[/ QUOTE ]
Because flushes are rarer than straights:

Seven Cards
Hand............Combinations
Royal Flush.........4,324
Straight Flush......37,260
4 of a Kind.........224,848
Full House........3,473,184
Flush.............4,047,644
Straight..........6,180,020
3 of a Kind.......6,461,620
Two Pair..........31,433,400
One Pair..........58,627,800
High Card.........23,294,460

mosdef
09-16-2005, 03:36 PM
[ QUOTE ]
One Pair..........58,627,800
High Card.........23,294,460

[/ QUOTE ]

which begs the question: why isn't ace high worth more than 1 pair in hold em or 7 card?

Siegmund
09-16-2005, 07:37 PM
[ QUOTE ]

which begs the question: why isn't ace high worth more than 1 pair in hold em or 7 card?

[/ QUOTE ]

If it were, ace high would be more common than one pair.

No matter what hand rankings you use, if you *first* announce the rankings and *then* let players choose which cards in their hand to play, the lowest-ranked hand is no longer guaranteed to be the most common. The raw poker ranks are based on 5-card straight poker, no draw, no community card, no extra cards, no choices. As soon as you give the players choices of how to improve their hand, they will climb as far up the announced rank chart as they can. Want an extreme example? Look at Chinese Poker. The back hand (think of it as the best 5 cards out of 13 dealt to you, though there are reasons to not always choose the best 5) is usually a flush or a full house; only three of a kind has virtually no chance of winning.

Most common example of this is adding a joker to the game - which makes high pairs vastly more common than low pairs, and three of a kind more likely than two pair. People use bugs instead of jokers in an attempt to preserve the rank-frequency relationship better.

mosdef
09-16-2005, 09:52 PM
i know. i was being sarcastic. sorry, my bad.

09-17-2005, 03:33 AM
For those who couldn't follow Siegmund's excellent response:

Because you're choosing five cards out of 7. All one pair hands are also a high card hand, because you can choose a different card to the pairing one. Same for some flushes, straights, and two pair hands.

So the actual number of high card hands possible when choosing 5 cards out of 7 is far higher than any other combination. The number quoted above is the number of hands which can't make any other combination except high card.