straight vs. flush

[edog743]

Why does a flush pay more than a straight when a open ended sraight draw is one less card than a flush draw dealt with four cards to the flush? am I missing something here if so please tell me

[New2vp]

There is a game that is an anomaly that pays the same for straights and flushes called either U.S.A. poker or All-American poker.  What we learn from that game is that, other things like payoff being equal, straights are 17% easier to come by than flushes are.In most games the frequencies of the two final hands are nearly equal; e.g., in 9-6 jacks or better, we get straights less than 2% more often than we get flushes.  But that is because strategy is adjusted in favor of the higher-paying hand.Dealt straights are about twice as likely as dealt flushes (10,200 different combinations vs. 5108).It remains true, as you stated, that given 4 cards in your hand to a flush or a straight, it is easier to draw to fill the flush or the straight; but over all possible dealt hands, the straight is the easier hand to end up with.You didn't ask about wild games, but here frequencies of hands don't always stay in the proper hierarchy; as a matter of fact, there have been some theorems proposed that prevents the frequencies from getting smaller as the value of the hand gets larger.For example take a full-pay single Joker Kings or Better game.  Even though trips pay twice as much as two pairs, trips occur 21% more often than two pairs.If you were to try and fix this and have two pairs pay more than trips, you would fail to get the frequencies in order, unless you imposed rules that prevented the user from making the wild card whatever benefits them most.For example, if two pairs were worth more than trips (because two pairs is the less frequent outcome), with a hand like Jok-7-6-6-2, you would want the Joker to represent a 7 (or 2) instead of a 6, because that would pay more.  What would happen here is that many of the hands that used to end up as trips would instead end up as two pairs and the overall frequencies of two pairs would increase enough to make trips the rarer hand.Of course, then you would want trips to pay more, but we already know when that is the case, trips is the more frequent result.  A little paradox.Most vp software doesn't allow this, instead always forcing our example hand to be 3 sixes regardless of whether two pairs pay more or less than trips.

[shadowman]

I think it's due to a flush being considered the better hand in standard poker (a flush always beats a straight). Hence, it deserves a better payout.
 
There is a game or two where they pay the same. Some deuces games and All American for example.


 
When bonus games were introduced they also made certain quads pay more than a SF yet the quads occur more often.

[edog743]

Thank you for your answers guys