which is harder get playing poker with wild 2s, 5 of a kind or royal fluch. has anyone got the maths on it?

Answer 1

With 4 wild cards, in a 5 card hand, there are 484 possible royal flushes, and 672 possible 5 of a kinds.

I will detail the 5 of a kinds.
There are 48 ways to make a 5 of a kind that involves only 1 deuce: 12 x 4. 12 is possible 4 of a kinds (other than deuce) and 4 are the possible deuces (1 for each suit).
There are 288 ways to make 5 of a kind with exactly 2 deuces: (12 x 4) x (1 x 6). There are 48 ways to make 3 of a kind (other than 3 deuces), 12 card values, each with 4 different ways to choose 3 suited cards (SpadeDiamondHeart, DHC, SDC, and SHC). Each pair of deuces can be chosen with one of 6 combinations of suits: SD, CH, SC, DH, SH, CD.
There are 288 ways to make a 5 of a kind with exactly 3 deuces: (12 x 6) x (1 x 4). The 6 and 4 once again relate to the suits.
There are 48 different ways to make a 5 of a kind with exactly 4 deuces. All 4 deuces must be used. The 48 are the remaining cards in the deck; any of which can be selected to make a 5 of a kind.
672 = 48 + 288 + 288 + 48

This presumes that you count ambiguous hands as 5 of a kind. For example, if you have 4 deuces and a Ten, that could be either 5 of a kind or a Royal Flush.

Answer 2

Your question has an elementary flaw. A flush with five cards in it would not all be royal since the Jack, Queen, King and Ace take four cards. The other one would therefore not be a 'royal' card. The flush in question is easier to obtain than the four of a kind plus the wild. That is assuming that you are waiting for a particular number, eg Aces. You could wait for any of the target cards to get the flush. If you're arguing over a won pot, those were two very good hands to be dealt simultaneously, I would say there is some cheating going on!!

Answer 3

royal flush defo