Flushes v. straights

[TaintedRogue]

I can imagine how many times this question has been asked, as I asked it on RGP years ago........Why is a flush considered a better holding than a straight, when it is harder to flop an open-ended straight draw than it is to get a flop with 2 to your flush? Not only that, in some of the instances when you do flop an open ended str8 draw, you will drawing to the low end of the str8, as when you have 65 and the flop come 78K.

If I remember correctly, the answer is that there are more ways to get the nut straight, then there is the nut flush. Such as, 65 can flop 74 or 43. 65s cannot be the nut flush.

Anyone know the true answer?

Thanks,
Ken

Flush > Straight

I think the rankings come from the game of five-card draw (or stud), because there are more combinations of straights than there are flushes, making the flush worth more. There are more flushes than full houses, more full houses than quads, etc.

No, the numbers come from holdem, where you choose 5 cards out 7. Here's the table:
<font class="small">Code:</font><hr /><pre>
hand number Probability
straight flush 41,584 .00031
4-of-a-kind 224,848 .0017
full house 3,473,184 .026
flush 4,047,644 .030
straight 6,180,020 .046
3-of-a-kind 6,461,620 .048
two pairs 31,433,400 .235
pair 58,627,800 .438
high card 23,294,460 .174
</pre><hr />
Note there are far more high card numbers than any others, the number above is the number of high card hands left after selecting a 5 card hand of pairs and two pairs (which also make high card hands).

See http://www.math.sfu.ca/~alspach/comp20/ for the math.

[BigBrother]

If I read that link correctly, It is based on Stud, not Hold'em.

Has anybody seen the math broken out for 10-handed Hold'em, where the 10 sets of 2 hole cards are combined with the single set of 5 board cards?

The frequency will be exactly the same, you're choosing 5 cards out of 7, dealt randomly. The fact that everyone shares a flop is irrelevant, it's the same as having a seven card hand and just changing the last two. Because the flop is random is every time, this evens out to the same numbers/frequency for each of the hand ranks.

[BigBrother]

Got it, thx.

I guess where the hold'em math gets different is : If I can make a hand of rank X on a board of YYYYY, what is the probability that one of the other random hands can make a hand of rank Z.