Why does a flush beat a straight?

[dark_horse]

harder to pick up a flush draw? because once you have a flush draw vs open ended, you're less of a dog to make the flush.

fewer card combinations make a flush?

[RoundTower]

If you are dealt 5 cards, it is less likely that you will have a flush than a straight.

[JohnnyHumongous]

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If you are dealt 5 cards, it is less likely that you will have a flush than a straight.

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It's actually 50% as likely, if I remember correctly.

[The Goober]

Well, lets try to do the math. There are 10 possible straights, 5-high through A-high. For each straight there are (4^5) possible ways to make it, since each card can be of any suit. Subtract out the 40 straight flushes, and we get

number of straights = 10*4^5 - 40 = 10,200

For flushes, there are 4 suits, and for each suit there are 13 choose 5 ways to make a flush (and again we take out the striaght flushes)

number of flushes = 4 * C(13,5) - 40 = 5,118

So, yeah, it looks like there are almost exactly twice as many ways to make a straight as there are to make a flush.

Edit: there are 40 possible straight flushes, not 10

[jba]

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harder to pick up a flush draw? because once you have a flush draw vs open ended, you're less of a dog to make the flush.

fewer card combinations make a flush?

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yes it is fewer card combinations to make a flush.

a better question is, why does AA22x beat 4433x? There are many ways to have aces up (aces over kings, aces over deuces, etc), and only "two ways" to have fours up (fours over threes, fours over twos).

similarly, why does A2346 flush beat 75432 flush? There are many ways to have an A high flush, but very few ways to have a 7 high flush.

[Abbaddabba]

If you were to enumerate the possible holdings that could result in a flush from 5 cards dealt, those would be accurate.

Would it change anything if you were to enumerate the potential 5 card holdings from 7 cards? My guess is that it would. A straight seems as though it would become relatively more likely (compared to a straight) as more cards are added.

If you have 4 to a straight, and 4 to a flush both after 5 cards - which is more likely to complete their draw after a 6th? There are 9 for a flush and a weighted average of 4 or 8 to complete the straight. That will continue to be true if you were to miss on the 6th, but were to redraw on the 7th.

As more cards are drawn, a flush becomes relatively more probable. It may be the case that after 7, there is still a higher probability of a straight - but if you were to have enough draws, i think it would work in favor of a flush.

[semipro]

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[ QUOTE ]
harder to pick up a flush draw? because once you have a flush draw vs open ended, you're less of a dog to make the flush.

fewer card combinations make a flush?

[/ QUOTE ]

yes it is fewer card combinations to make a flush.

a better question is, why does AA22x beat 4433x? There are many ways to have aces up (aces over kings, aces over deuces, etc), and only "two ways" to have fours up (fours over threes, fours over twos).

similarly, why does A2346 flush beat 75432 flush? There are many ways to have an A high flush, but very few ways to have a 7 high flush.

[/ QUOTE ]

Because once you make your two pair, straight, or flush, it comes down to a matter of ranking your cards, not necessariliy the probability of specific hands, because per your above example there are as few possibilities of making AA22x as there is of making 3344x.

[Wacken]

:S
why does AA beat 22 ? There are equal chances for both !

[jba]

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:S
why does AA beat 22 ? There are equal chances for both !

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because A is a higher rank than 2. You're correct that the chances are equal.

the question is, why is aces up better than fours up, when aces up is more statistically likely. (not equal, as in the case of your example). There are many more possible card combinations that result in aces up vs. fours up.

edit: format

[jba]

[ QUOTE ]

Because once you make your two pair, straight, or flush, it comes down to a matter of ranking your cards, not necessariliy the probability of specific hands, because per your above example there are as few possibilities of making AA22x as there is of making 3344x.

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No. I just threw out AA22x as an example, my point is it is easier to get aces up than it is to get fours up.

A better example may be to show you

KKQQx

which is beat by

AAKKx
AAQQx
AAJJx
....
AA22x


as you can see, there are many more combinations of aces up than there are of kings up. yet, aces up is a better hand.

KKQQx *should* beat AA22x, but it doesn't.