dumb question from a newbie about hand rankings

I did a search and I haven't really seen this addressed-perhaps someone would assist/link/answer

it has been my understanding that the hand rankings in poker were/are determined by their relative scarcity- the rare the hand-the higher it's ranking-is this correct?

if so, maybe someone could explain to me how and why four of a kind is not the highest ranked hand, rather than the commonly accepted and agreed upon straight flush-with the royal being the highest-

there are 10 straight flushes per suit-using the ace for both high and low-yet there are only thirteen quads-
even allowing for the royals(4) that still leaves 36 straight flushes as compared to the 13 quads-making
the four of a kind much rarer by a factor of almost 3x.

how did the hand rankings come to be agreed upon, and more importantly, why so?

[mrmazoo]

For each rank, there are 48 ways you can make quads, for a total of 48 x 13 ranks = 624.

Remember, JJJJ2h is not the same as JJJJ2c or JJJJ7d.

The hand strengths ARE in order of least to greatest possiblity as mentioned above. but remember that the probabilites were calculated as in dealing 5 cards randomly out of the 52 card deck.

as for actual card ranking (like ace high beating queen high, or a pair of 8s beating a pair of 4s), that of couse was arbitrarily chosen since having any pair or straight or flush is just as likely as any other ranked hand of the same type.

You can't get all of those straight flushes in one hand. You can only get two per suit for a total of 8. Whereas it's possible to get 13 four of a kind per hand.

I haven't done the math myself but I believe that the straight is easier to get because you're more likely to get a draw early in the hand.

Let's say your first card is an 8. There are 32 cards that can still help your straight (4 each 9 thru Q, 4 each 4 thru 7). However, if your first card is a diamond only 12 can help.

But once you get to the last card and you have a four flush, 9 cards can help, whereas with an open-ended straight only 8 help. For a close-ended or gut shot only 4 help.

of course I didn't consider the other cards-a very important factor- thanks mr. mazoo for explaining quickly and concisely.

[UATrewqaz]

The harder it is to make a hand the better it is

I believe at some point in time straights beat flushes until it was show with math that straights are actually easier to make.

[Cooker]

[ QUOTE ]
The harder it is to make a hand the better it is

I believe at some point in time straights beat flushes until it was show with math that straights are actually easier to make.

[/ QUOTE ]

This is not quite true. It is true that the broad catagories are correct, but often there are problems within the catagories. For instance, it is obvious that there are more A-high flushes than T-high flushes. Similarly there are many more A-high high card hands than there are 7-high high card hands.

[GMan42]

Another wrinkle in this whole thing (I love useless theoretical discussions like this) is that the rankings' relative scarcity change a lot based on how many cards are dealt. In a 7-card game like 7CS or Hold'em, straights and flushes move much closer together in frequency compared to a 5-card game, and if I'm not mistaken, one pair hands are actually more common than high-card hands (although changing hand rankings to reflect this would be silly). If you dealt a game where each player had 10 cards, it would be extremely difficult not to make a straight or a flush, and high-card hands become even rarer than 4 of a kind.

[eisanm]

Your math on the probabilities is wrong, it's more complicated than that.

Either way, the hand rankings were agreed upon based on the probability of being dealt one of those hands in a five card game and they have not been adjusted since, so it is possible they are "incorrect" from a probabilistic point of view in Hold'em of 7card stud for example. Not to mention Omaha.

For the math about quads vs straight flush, a quads is easier to make and this is partly because it only requires 4 specific cards whereas the straight flush requires 5 specific cards, this has been mentioned above in an example with JJJJ7d and JJJJKh (I don't remember the exact cards) .
I have a book which tells a bit about the history of poker but not much about the math. I could probably calculate this more precisely but I won't spend the time.