Originally posted by sonhouse
I think you would be talking about the wild cards, the number of them in a deck, 2, I think, would screw up the statistics of the hand expectancy vs not using wild cards.
I have now idea what that would be but it looks like that would add another level of statistics to be dealt with.
Actually, thinking about wild cards, in dealer game, the dealer als ...[text shortened]... like, 2's, whatever the dealer specifies, that would certainly add another level of statistics.
OK, that's the basic reason, and here's a detailed answer.
Everyone who has two pair, say AAJ52, using one wild card deuce, also has three of a kind, and will choose that if it beats two pair as it does in no-wild poker. But that makes two-pair rarer, because only natural two-pairs will be played as two pair. But if you rank two pair as beating 3 of a kind because it is more rarely played, everyone will choose two pair over three of a kind with a BBCD2 hand, and the reversal reverses again. So with deuces wild there is no rational odds-based basis for ranking the hands. The odds reversal also affects 4 of a kind.
This table is from: http://www.play-poker-card-games.poker.tj/probabilities-holding.html
I hope this table prints OK. The page before it, Using Wild Cards, is also relevant.
Probability without wild cards Probability with deuces wild
One pair 1 in 2.4 1 in 2.1
Two pairs 1 in 21 1 in 27
Three of a kind 1 in 47 1 in 7
Straight 1 in 255 1 in 39
Flush 1 in 509 1 in 197
Full house 1 in 694 1 in 205
Four of a kind 1 in 4,165 1 in 84
Straight flush 1 in 69,974 1 in 638
Five of a kind n/a 1 in 3868
Royal flush 1 in 69,974 1 in 5370