More On The Silly Subject Of Hand Rankings

[George Rice]

Many many years ago I sat down with pen, paper and calculator and confirmed the hand rankings as just for five cards, six cards and seven cards. But I did notice that as the number of cards increased, certain hands increased in likelihood at a faster rate than others.

One of the posters sugested that flushes should be ranked lower than straights in holdem. Of course this is false. However, in card games with more cards this would be true. I don't remember if this happens with eight, nine or ten cards, but it does happen. Probably not eight or it might effect the rankings in draw poker (Although having eight cards to choose from is different than discarding three and drawing.). In Omaha, if you were allowed to use all four cards in your hand, then straights possibly should be ranked higher than flushes. Pineapple would be another game where this is close.

Another hand that overtakes its next higher hand is the no pair hand. I don't remember how many cards it takes to happen. It's probably in the same area.

Without doing any fancy probability calculations you can consider the following:

If I deal you 14 cards you are guaranteed to be holding a pair (ignoring any other hands you might hold).

If I deal you 15 cards you are guranteed to be holding either two pair or three of a kind.

If I deal you 17 cards you are guaranteed to be holding a flush.

It would take the same 17 cards to be guranteed to show me two different pairs.

The number of cards where you are guranteed to be holding three of a kind is the same number of cards you need to be guranteed to be holding a full house. That number is 27.

It takes 40 cards to be guranteed that you will be dealt four of a kind.

It takes a whopping 45 cards to be guranteed that you will be able to show me a straight. It takes the same 45 cards to be guranteed a straight flush too.

It takes 49 cards to be guranteed the royal flush.

Of course none of this is applicable to cards as played in casinos today. But you can see why straights and no pair hands become more rare than other hands as the number of cards increases.

Understanding this concept might help in certain home games where there are replacements and/or many board cards.