Poker with a modified deck

[jason1990]

If anyone has the time and desire to work this out, I am curious what the result is.

Suppose you play poker with a deck that has 5 suits and 10 ranks in each suit. The possible hands are the ordinary poker hands plus 5 of a kind. For each possible hand, what is the probability you will be dealt that hand. (Assume you are dealt only 5 cards; that is, we're not talking about a stud or draw or holdem type structure.)

Incidentally, the particular probabilities are not what I'm curious about. I'm curious about the relative likelihood of the various hands.

Also, what about a deck with only 3 suits and 18 ranks in each suit? There is a thread on this in Poker Theory, but I'm sure we can be more mathematical about it here.

Another interesting question: what if there are 8 suits with 6 ranks in each suit? In this case, where does high card rank? Is it still the lowest ranking hand? If so, then in a holdem style game, this hand could not occur. If not, how does that affect which 5 cards out of the 7 make up your hand?

This leads to a more general question. In any kind of deck (modified or not) we can rank the hands under the assumption that we are dealt only 5 cards. Then we could rank the hands under the assumption that we are dealt 7. (For example, the probability of a flush would be the probability that, among your 7 cards, there is a 5-card combination which is flush. These probabilities, of course, would no longer add up to 1, but they would still provide a relative ranking.) For which decks do these rankings agree? (The most important one being the standard 52-card deck.) When they don't agree, does it make sense to modify the hand rankings in a holdem game? Or should they still stay the same as in a straight 5-card game?

[Phat Mack]

This doesn't answer your question directly, but has some interesting stats and discussion of five-suited thirteen-ranked decks.

http://www.stardeck.com/

[TOmCowley]

Is somebody playing Discordian Poker?

I worked this out with a friend on a cross-country flight about 12 years ago (yeah, we were really bored nerds). We even invented the antiflush for draw poker, 1 card of all different suits. I don't have the results anymore obv, but I worked it out by hand, so it couldn't have been that hard.

[tek]

I think the 5th suit should be the Skalnsky. Then you could have a straight or flush Sklansky high. And the Sklansky would get the first chip in a race off in tourneys. [img]/images/graemlins/grin.gif[/img]

[AngryCola]

[ QUOTE ]
I think the 5th suit should be the Skalnsky. Then you could have a straight or flush Sklansky high. And the Sklansky would get the first chip in a race off in tourneys. [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

If you held the nut Sklansky flush, you could say to your opponents-

"I have the best hand."

"Do you see why?"

"I'll let others elaborate."

[blank frank]

Since this sort of question keeps coming up, I went ahead and wrote an excel spreadsheet to calculate the odds of poker hands for odd decks. You choose the number of ranks, the number of suits, and the number of decks shuffled together, and it spits out the probabilities. You can get it at my web page. Click on the link for poker probabilities.

Now, as for comparing rankings between a five and seven card hand, they are not identical for a standard 52 card deck. As you can see from the tables on my site, you have about a 17% chance of getting nothing (high card) with seven cards, and a 44% chance of getting a pair. Should we change the rankings for seven stud? No. If you say that high card is better than pair in a seven card game (and it would even be better than two pair), everyone would call their pairs as high card. But then pairs would become incredibly rare, as you would only call a pair when you three pair among your seven cards. Then you would have to change the rankings back. And so on and so forth.

The point is that probability is not the be all end all of ranking poker hands. You can see this even in five card hands. Two pair aces high beats two pair eights high, even though it is more likely.