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Interrobang!?
04-14-2003, 11:39 AM
If you created a deck of cards that featured a new, fifth suit (say, Potions) and a full run of 13 cards (ace through king) of that suit, what effect would it have on regular poker hands? Would the hierarchy of winning hands have to be changed because the odds of making those hands changed?

Assume that, whatever variation of poker you're playing, the rules remain the same -- 5-card draw still gives each player 5 cards, etc. And, as usual, the suits themselves have no rank (hearts doesn't beat spades, for example), so potions could be either red or black.

I'd guess that flushes would become more difficult to achieve, and that hands involving pairs and threes of a kind would become a bit easier to achieve. A full house would be less powerful. And where would five of a kind rank?

yabob
04-14-2003, 12:29 PM
Your intuition is correct concerning the probability of being dealt a flush, as opposed to a straight.

With a normal deck, the number of combinations for straights and flushes are:

straights - 9 * 45
flushes - 4 * C(13,5)

where we are only counting aces on one end - use 10 instead of 9 if you wish to count aces on either end. C(13,5) is meant to indicate "combinations of 13 things taken 5 at a time" - 13!/(5!*8!). We are also not worrying about the 36 (or 40) possible straight flushes being counted in both. Remember I'm doing combinations here - unordered.

straights - 9 * 55
flushes - 5 * C(13,5)

So there are 5/4 the number of "flush" combinations, and (5/4)5 the number of "straight" combinations.

I leave it to others to exhaustively go through the rest of the list.

yabob
04-14-2003, 12:38 PM
BTW, if you are going to redesign the playing card deck, I would say it makes more sense to increase the suit length to 15 and keep 4 suits. This results in a 60 card deck, and 60 divides evenly by 2,3,4,5 or 6 - having a lot of factors is an advantage in designing card games. For starters, a 52 card deck can't be dealt out evenly to 3, 5 or 6 players.

I leave it as an exercise for the student to calculate poker hand probabilities for that deck, as well. Not to mention designing a bridge game with 3 sets of partners, or two trios for tables of 6.

knarf
04-14-2003, 12:47 PM
I've heard of 65-card Star Decks, and here they are: http://www.stardeck.com/

And the odds too: http://www.stardeck.com/ranks.htm#rank