what's better - 5 of kind or straight flush (wild cards involved, obv)

[scotty-win]

In games like Follow the Bitch, for example, where you have wild cards, what's better - 5-of-kind or a straight flush? My home's game had the rule that quints win, but I wanted to find out from a mathematical perspective what's the rarer hand? (and I don't feel like figuring it out myself)

[elwoodblues]

My understanding is that when the hands were originally ranked 5 of a kind was the best hand. It was a more rare hand in that when these rankings occurred if wilds were used it was usually just 1 wild card (1 of 52, not 4 of 52) which made 5 of a kind actually more rare. Now, the "standard" way to rank is still w/ 5 of a kind the greatest despite the fact that a straight flush is more rare with multiple wilds (as opposed to just one.)

[scotty-win]

thanks - so you're saying that a straight flush is more rare if you have more than one wild (in our case, all queens and all 8's were wild), but 5-of-kind is still higher ranked?

[elwoodblues]

I'm fairly certain that is correct.

[headtrauma]

I believe 5 of a kind is still rarer with multiple wild cards, because the wild cards can also be used to complete a straight flush.

[ran]

To get 5 of a kind with only one wild, you have a 52/52 x 4/51 x 3/50 x 2/49 x 1/48 = 0.0004001% chance. This assumes no draws.

A straight flush with no wilds is 0.0014%, clearly easier than 5 of a kind. Wilds would make it easier, obv.

Quints with 8 wild cards (two ranks - all queens and eights, for example) would be (8/52 x 7/51 x 6/50 x 5/49 x 4x48 = 0.002155% (chance of getting five wild cards)) + (44/52 x 11/51 x 10/50 x 9/49 x 8/48 = 0.111% (chance of getting five of a kind with four or fewer wild) = 0.113% chance of getting quints with eight wild cards.

Some other stats

[ QUOTE ]
5 card poker probabilities if one ordinary Joker is added to the deck

(Computer program and data by Bill Butler)

Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 13 0.00000453
Royal straight flush 24 0.00000836
Other straight flush 180 0.00006272

5 card poker probabilities if two Jokers are added to the deck

(Computer program and data by Bill Butler)

Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 78 0.00002466
Royal straight flush 84 0.00002656
Other straight flush 540 0.00017075

5 card poker probabilities with Deuces (2’s) wild

(Computer program and data by Bill Butler)

Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 672 0.00025856
Royal straight flush 484 0.00018623
Other straight flush 2,068 0.00079570

5 card poker probabilities with 2 Jokers,
One-eyed Jacks, and Deuces (2’s) wild
(8 out of 54 cards are wild)

(Computer program and data by Bill Butler)

Poker Hand Nbr. of Hands Probability
---------------------------------------------------
5 of a kind 8,348 0.00263968
Royal straight flush 2,674 0.00084553
Other straight flush 11,950 0.00377864

[/ QUOTE ]

[ran]

Cliff notes:

With one wild, SFs are 15.69 times more common than quints.

With two wild, SFs are 8 times more common than quints.

With four wild, SFs are 3.8 times more common than quints.

With eight wild, SFs are 1.75 times more common than quints.

Clearly, as the number of wild goes up, quints become more common. (Guessing) somewhere around ten wild, quints would be more common.

[Lottery Larry]

[ QUOTE ]
I'm fairly certain that is correct.

[/ QUOTE ]

No, it isn't. 5K is still harder to get that a straight flush, even with wildcards... though I haven't done the math if you have double-digit wild cards.

[Lottery Larry]

[ QUOTE ]
Now, the "standard" way to rank is still w/ 5 of a kind the greatest despite the fact that a straight flush is more rare with multiple wilds (as opposed to just one.)

[/ QUOTE ]

No, 5k is still ranked higher because it's still harder to get.

[Dru]

I play str8 flush higher, but only t avoid controversy, my 5-card deuces wild game requires wilds to be played in their suit. IE, 2 of spades, can only be a spade in a flush hand.