I’m a poker junkie, nay, a poker whore! Just in case you were wondering.
I was playing online and came across a table that lists the odds of drawing to various hands in Texas Hold 'em. Most of the adds make sense to me, but I didn’t understand this one:
Straight Flush: 1 in 9148
versus
Royal Flush: 1 in 40,390
Why the disparity? Should my chances to draw any straight flush be equal to the chances to draw a royal flush? Does the difference in odds have to do with the fact that the Royal isn’t an open ended straight? But then if that’s the case, shouldn’t a low straight flush (A-5) have about the same odds of being drawn, that is, 1 in 40,390?
Help me out with this and I’ll give you a cut of the prize when I win the next pot.
I am not sure I understand what you are saying. It seems you are asking “Why are my odds of drawing a specific kind of straight flush less than drawing any straight flush.”
The answer, it would seem, is that there are many possible straight flushes, and only four royal flushes. In fact, I would have thought the odds would be even more disparate.
Ok, I’ll give this one a shot, I can’t back this up with mathematical facts though.
A straight flush is 10,J,Q,K,A all of one suit. Out of the 52 cards in a deck, only 20 of them can be used to make a royal flush. However, to make a straight flush, in theory any of the 52 cards can be used.
You could also state the odds this way. The odds of ** any specific ** flush occuring is basically 1 in 40,390. Whether it be a a royal flush or a low flush, or even 6,7,8,9,10. However, the odds of ANY flush occuring are much less because you’re not picky about which flush you’re getting. I hope that makes a little sense.
So, if they wanted, the casino could be celebrating their 56,789th hand of poker. To celebrate, if any person playing the game gets a 56789 flush they win one million dollars or something. Well, the odds of this happening are 1 in 40,390, not 1 in 9,148.
There are 36 straight flushes but only 4 royal flushes (that’s NOT counting the ROYAL as a straight flush, in which case there are 10 straight flushes).
They give the odds of ANY straight flush, that is, a straight flush from A-5, 2-6, 3-7, . . ., 9-K.
The odds of a royal come from only making one with 10-A. There are 4 of these.
The odds of any PARTICULAR straight flush (say, 5, 6, 7, 8, 9) are the same as making a Royal, but that’s not what they’re giving you.
Well, one given combination of 5 cards is no more likely than any other combination of 5 cards. So my chances of getting a Royal Flush in hearts is just as likely as me getting an Ace to 5 spade straight. But you’re not asking about individual combinations, but different types of combinations.
A straight flush is a particular kind of combination, and there are many different ways to achieve it, 40 in all, including the royal flushes. A royal flush is a more specific kind of combination, and there are only 4 ways to get it.
Is this making sense?
Basically, the reason the straight flush has better odds is that there are more ways of constructing one. However, the chance of creating any one particular hand is no more likely than creating any other particular hand. Microstates vs. Macrostates.
This seems pretty logical to me. A Royal FLush is a PARTICULAR TYPE of straight flush, basically, one in which you have all high cards in the deck, so the odds are going to be lower. If you compared the odds of say a Royal Flush to another PARTICULAR straight flush, the odds would be the same or similar.
The essence of this being that a royal flush is the only particular kind of straight flush that is singled out for special notice. You could have a similar discrepancy between the odds for four of kind (any card value) versus the odds for 4 aces, but there’s not much interest in thinking about it that way. In contrast, the royal flush has a certain mythos about it which induces extra attention and mention.