Poker Paradoxes ?

[blank frank]

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Hence, in this particular game it is impossible to rank traditional poker hands in a fashion that gives us a continuous increase in hand power with hand rareness.

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Yeah, I got that. But since we don't rank hands that way in the first place, why should we be worried that we can't? Why should we consider it a paradox at all?

[soko]

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I was once told that in seven card it is more likely to end up with at least a pair then it is to have only a high card. I don't know how much truth their is to it but it may apply to this situation.

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A 5 card poker hand has a tiny tiny percentage greater than 50% of only having a high card

[eurythmech]

We do rank hands like that in the first place, imo.

Sure, an ace-high straight is both the most common straight and the highest straight. Hoever, that's not how I look at it.
I look at it this way:

We have different "classes" of hands, ranked according to rareness:

Straight flushes
quads
.
.
.
pairs
N/A

And within each class, different hands are ranked according to the arbitrary "rank strength" of different cars. Arbitrary because there are four of each rank, but they are all of different worth.

In the above example, we have one of few examples where we cannot rank the classes according to rareness. No matter what we do, we will end up with a discrepancy. This is the only discrepancy I know of at a "class level" (other discrepancies occur on the sublevel, the one guided by the rank of the individual cards) that is unavoidable. There are however such discrepancies that CAN be avoided, but which are still in effect. For instance in soko/Canadian Stud/Scandinavian Stud where the bottom ranking goes pair<fourstraight<fourflush<two pair when it should be pair<two pair<fourflush<fourstraight.

[JoshuaD]

An Ace high straight is just as common as a King high straight.

[cpk]

Even better--there are many fewer 7-high flushes than A-high flushes. [img]/images/graemlins/smile.gif[/img]

But, yes, categories of hands are ranked from rarest to commonest. Ranking hands within categories is simply arbitrary.

[eurythmech]

Hehe, straights, what was I thinking?
I meant flushes of course.

[blank frank]

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This is the only discrepancy I know of at a "class level" (other discrepancies occur on the sublevel, the one guided by the rank of the individual cards) that is unavoidable.

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No, this is not one of the few, or the only one, it is one of the vast majority. There is no stable ranking of hands on the class level in seven card stud, in texas or omaha holdem, or in five card draw. In seven stud, pairs are more common than high card. But if you switch the rankings around, everyone will start calling their pairs as high card hands, making pairs rarer (non existant actually). You can switch the ranking back and forth and never reach stability. As hold'em is basically a seven stud variant, this holds there too. You have the same thing in five draw: after the draw pairs are more common than high card. But if you switch the rankings, everyone will start ditching their pairs at the draw, and pair will become less common than high card.

Any time you introduce enough choice into a poker game to affect the rankings, you'll have this situation. But the fact that changing the benefits of certain choices will change the choices that people make is not a paradox, it is just common sense.

So to say that we rank poker hands by the probability that they occur runs counter to observed practice. In practice, we rank poker hands by the probability that they will occur in five random cards with no wilds. Excluding, of course, games with non-standard hand rankings like three card guts.

[eurythmech]

While what you say about pairs being more common than no pair hands in 7CS is of course true, I still don´t think this is quite the same. In the case with the joker, we have this paradox regardless of what five cards we choose. The 7CS "paradox" only occurs because we have a larger number of cards to choose from.

[italianstang]

That flashing banner ad on the top gave me an instant headache.

[OneCentRob]

Sorry to hear about your headache. You can remove the flashing adverts by selecting "remonve advert" from next to the banner.