Tuesday, December 19, 2006

Question about ranking of poker hands

I can't figure out why a flush is ranked higher than a straight
in poker.

From personal experience, it's alot easier to get a flush
than it is a straight.

Using Texas Hold'em to illustrate. Assume your two hole
cards are suited and the flop comes with two more of the same
suit. The odds of a 3rd card of the same suit hitting to make
your flush is 1/4. Right?

Now let's say you have connected hole cards (e.g. 7-8) and
the flop comes 10-9-3. You have an open ended straight draw
and the possibility of getting that Jack or 6 to complete the
straight is 2/13. That's less probable than the 1/4 chance of
making a straight and this is for an open ended straight draw.
If you are looking for an inside straight draw (e.g. you hold 7-8
and the flop comes J-9-3, you need a 10) than it's an even
worse 1/13 chance.

Seriously, from experience it's alot easier to make a flush
than it is a straight. Hell, I'd guess that poker players make
flushes more frequently than a 3 of a kind yet that is also ranked
lower as a poker hand.

Any statisticians or poker experts care to enlighten me?


Charles Miller said...

Dealing five cards from a deck of 52, there are 10,200 possible hands that will give you a straight, and only 5108 flushes.

There are 54,912 three-of-a-kinds.

(Odds taken from: http://en.wikipedia.org/wiki/Poker_probability )

The problem with your analysis is that you start off with "Assume your two hole cards are suited and the flop comes with two more of the same suit.", which is a rare event that obviously skews the odds heavily in favour of a flush.

One reason you might see a lot of flushes is that there are so many people who will play any two suited cards, then hang on to flush draws without regard for the odds.

Wayland Chan said...

Thanks Charles, I suspected it had to do with my assumption. I guess part of my post was due to recent bad beats with guys chasing and hitting their flush when I've got a set.

Robert said...

While it is true that mathematically it is easier to get straights, your observations are also correct in that it is easier to get a flush.

The problem with the probabilities is that it doesn't take into account your starting cards and the cards that need to come to make your hand. For example, yes you could hold a 79 and still make a straight with them, but 4 of your outs MUST be an 8. A flush doesn't have this type of restriction and therefore the odds of a flush with your two cards being suited are higher than your two cards being able to make a straight.

Of course this assumes you are playing Hold Em type of games (omaha and texas hold em). Don't forget that the hand rankings apply to most forms of poker so if you were playing 5 card draw it is probably easier to get a straight than flush in practice where holdem is the opposite.