Poker odds

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I'm neither a gambler or a mathematician but I do have this little poker game I like to play with. I've noticed that a flush pays out more than a straight and I can't figure out why.

The way I see it, there are 8 cards that can complete a straight (if I'm dealt, say, 6-7-8-9) but there are 9 cards that can complete a flush (if I'm dealt four of the same suit).

So why does a flush pay out more than a straight?

Explain like I'm not a gambler or a mathematician, please.

Thanks!

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Type: Question • Score: 5 • Views: 4,139 • Replies: 20

@boomerang,

Simple. There are a more ways to make a straight than there are to make a flush.

You are only thinking about the last card after you already have four. This is not the right way to think about it (although having four cards of the same suit is very nice). You are more likely to have four cards to make straight anyway.

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@maxdancona,

If you deal out 5 cards from a deck, there are 5148 ways to make a flush. There are 10,240 ways to make a straight.

http://en.wikipedia.org/wiki/List_of_poker_hands

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@maxdancona,

Okay, that makes sense.

But how would you play a hand against someone if you were dealt 5-6-7-8-Q and they were dealt four diamonds and a club?

Wouldn't they have a better chance of getting a flush than you would a straight?

If you were playing on my little poker machine, where you're only playing against yourself, and you were dealt either of those hands, wouldn't you have a greater chance at the flush than the straight?

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@boomerang,

Yes. they would would have a better chance of getting a flush than a straight at that point.. But this is a completely different question than your first question.

If one person has 5678 and the other person has 4 diamonds, than clearly at that point the flush is more likely than the straight (assuming no other diamond is has been shown). But consider the odds if the first person got 5679 (now only 4 cards will complete the straight).

The odds are set by the likelyhood of you getting a certain hand before any cards have been dealt. Once you have already dealt four cards the odds of any certain hand clearly changes. Any time a new card is shown, the odds of each particular hand changes.

And consider the odds of getting four of a kind with five cards if the first four cards dealt are 2222. In this case the odds are 100%. This doesn't mean that a straight beats it.

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@boomerang,

To answer the question how I would play...

The rote answer is "It depends". This is kind of a cliche in the poker world.

Expert poker players (which I don't claim to be although I am studying to get better) laugh at the question "How would you play this...." because there are so many factors that go into such a decision, such where you are sitting, how your opponents are playing and what the stakes are.

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@boomerang,

boomerang wrote:

But how would you play a hand against someone if you were dealt 5-6-7-8-Q and they were dealt four diamonds and a club?

Well, there are additional factors. How many of your cards are diamonds? What are the values of the opponents cards? Stud or draw poker?

Sure, the opponent has a chance of completing the flush, and you have a chance of completing the straight, but both of you also have chances of getting pairs.

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I get that if you're playing against someone else that the odds would be dramatically different but I'm talking about a game that you play just against yourself. I know all of the cards that have been dealt in the hand so I know what is left in the deck.

I'm wondering why in this particular game why the odds on a flush are higher than on a straight when you have a better chance of getting a flush.

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@boomerang,

boomerang wrote:

I'm wondering why in this particular game why the odds on a flush are higher than on a straight when you have a better chance of getting a flush.

Once you know what cards have been dealt, you're better able to calculate the odds of completing the combinations.

In the case you described, the player with four of the same suit was simply dealt a good hand, and they have a good chance of completing the flush.

That's different from saying "a flush is less common than a straight, so therefore a flush beats a straight."

This is why poker is considered a game of skill, rather than a game of chance. You have to constantly recalculate your odds of winning a hand against your opponents odds of winning the hand, based on available information.

1 Reply

@DrewDad,

I think I get it.

Maybe this particular game has some kind of glitch where it deals out near flushes at about the same rate as near straights so it skewed my perception of the odds.

1 Reply

@boomerang,

boomerang wrote:

I'm wondering why in this particular game why the odds on a flush are higher than on a straight when you have a better chance of getting a flush.

The short answer is that you have already beaten the odds in getting four cards of the same suit. That is less likely than getting four to a straight.

Let's try a football analogy. Suppose the Patriots (good team) are playing the Jets (sucky team). The Pats are favored. But if the Jets are up by two touchdowns at the end of the third quarter, the Jets are going to favored from that point to win. Because the Jets beat the odds in the first three quarters, the revised odds are now in their favor. That doesn't change the betting line from the beginning of the game just like it doesn't change the poker payouts.

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@boomerang,

Is it possible that your mind is tricking you? Intuition in poker is usually wrong.

There are a couple of ways you could be mistaken.

1. Some of these games have you look at some cards and then choose whether you want to keep playing or not.

It could be that you are folding (choosing not to play) more possible straights than possible flushes. Remember that many of the possible straights are "inside straights" meaning missing a card in the middle rather than at the ends. Remember that the odds we calculated only apply starting from before any cards are dealt (once you see cards, the odds all change).

2. And, of course, you could just be being misled by your expectations. Your intuition is designed to look for patterns, and quite often it finds a bogus pattern. Once your intuition locks itself into a mathematically incorrect pattern, it is difficult to see the correct one.

Of course, it is possible that the game is fixed (i.e. not truly random). You would have to do an experiment to determine if this is true or not

If you want to do the experiment, you need to take your intuition out of the picture. The way I would suggest is the following.

1. Play the game 100 times (which is pretty good considering the hypothesis).
2. Never fold. Play every hand to its end.
3. Count the number of straights and flushes under these conditions.

If under these conditions there are the same number of straights and flushes, I would strongly suspect the game is fixed.

2 Replies

@maxdancona,

It may interest you that in real poker, many people overestimate the probability for flushes. Of course this leads to mistakes.

This is one way that bad players lose money. And, once they realize that someone is doing this, a good player will make money off of this error.

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@maxdancona,

That would be an interesting experiment. Maybe I'll give it a try. I usually just fiddle around with this thing while the coffee is brewing or I have something on the stove though. I sensed a pattern of how straights and flushes showed up and started mentally keeping track so I know it wasn't accurate but it seemed to play out the way I anticipated.

Because there is no money at stake I sometimes just challenge myself to try to make something from whatever I'm dealt -- I have to keep something - but I don't hold straights unless they're open at both ends and I don't keep flushes unless I have four of the same suit on the first deal.

This game is super, super simple. It deals you a hand, you discard, it redeals -- that's it. There's no upping your bet or unknown cards in play.

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In poker...it is almost ALWAYS better to go with the shot that has the better odds...and if the pot warrants taking those odds.

In this particular case...you do not a pot odds to consider...so the only reasonable choice is to go with the greater odds...by keeping the four diamonds.

In a game where you are playing against others...theoretically you are supposed to calculate the odds of making the hand (getting the flush) and see if those odds are less than the amount you would have to invest to remain in the pot.

Calculating pot odds is a bitch!

1 Reply

Here’s an interesting question.

Are the odds more in your favor of getting a royal straight flush…

…or of getting 10 and 6 of spades; the 4 of hearts; the Jack of Clubs and Ace of Diamonds?

Answer given by running your cursor over the post.

ANSWER: the odds of getting a royal straight flush are much better...4 times better.

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@Frank Apisa,

I disagree with you Frank. My game is tournament NLHE. There are lots of times when the right thing to do is against the odds (at least the odds of the cards). Unless... of course you are defining "odds" much more broadly than the chance to make a hand.

There are lots of factors like Bubble play to consider. In a tournament you are trying to reach the point where you win some money even if you don't win 1st place. This often makes you avoid taking some risks even though the pot odds say you should. And conversely this makes a good player make bets when she doesn't have the odds in her favor knowing that someone "on the bubble" is likely unwilling to take any risks.

I have been in situations where the correct play was to make a sizable bet, even though looking at my cards I knew I had zero chance of winning. In these situations I knew that based on the circumstances my opponent was in a position where she was very unlikely to take the risk.

1 Reply

Unless you are playing stud poker, you don't know what you opponent(s) have in their hands. Your decision has to be based solely on what is n your own hand.

1 Reply

@maxdancona,

maxdancona wrote:

I disagree with you Frank. My game is tournament NLHE. There are lots of times when the right thing to do is against the odds (at least the odds of the cards). Unless... of course you are defining "odds" much more broadly than the chance to make a hand.

There are lots of factors like Bubble play to consider. In a tournament you are trying to reach the point where you win some money even if you don't win 1st place. This often makes you avoid taking some risks even though the pot odds say you should. And conversely this makes a good player make bets when she doesn't have the odds in her favor knowing that someone "on the bubble" is likely unwilling to take any risks.

I have been in situations where the correct play was to make a sizable bet, even though looking at my cards I knew I had zero chance of winning. In these situations I knew that based on the circumstances my opponent was in a position where she was very unlikely to take the risk.

Tournament play is a special consideration. The object in tournament play is to be in at the end...preferably in the first position. Even approaching the bubble causes a considerable adjustment in play...and as the bubble is approached, some tourneys travel about at the speed of the last two minutes of a football game.

And for sure there are times where bluffing requires for odds to be ignored completely. It is interesting that most pros suggest that less advanced players DO NOT BLUFF enough. Daniel Negranu once mentioned that when playing non-tourney...if you are not "caught" bluffing reasonably often, chances are you are not bluffing enough.

But for the most part...pot odds are going to dictate a "see!"

And in the subject question...absolutely the answer is to take the higher odds "for." (This would not necessarily hold in a tournament...or even at table play.)

But as described with the object simply to fill the possible flush or possible straight...if you were to put yourself into the situation one million times going for the flush...and one million times going for the straight...

...and it will be no contest whatever. The "going for the flush" will win considerably over the "going for the straight."

Quote:

I have been in situations where the correct play was to make a sizable bet, even though looking at my cards I knew I had zero chance of winning. In these situations I knew that based on the circumstances my opponent was in a position where she was very unlikely to take the risk.

There is no "zero chance"...which is why you sometimes make a sizable bet. If you drive someone out of the hand...you win...and it doesn't matter that there was zero chance if the hand went to a show down. All poker players have done that...and probably all have at times rued doing it when playing against a lousy player who is more likely to chump-see than a good player.

1 Reply

@Frank Apisa,

I play lots of tournament Hold 'em myself, Max...and I have a lot of affection for Omaha hi-lo.

Great games all.

Robert went pro at one time. Never have heard how he fared.

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