# Kings and Peasants

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#### Fan_of_EP

##### Rising Star
I good good help on my previous question on odds, so I'm hoping someone can solve this problem for me. I play cards with a group of buddies, and sometimes, just to make things more interesting, the dealer will call a game that has wild cards in it... and includes the hand of "5 of a kind"... (hey, don't judge us !!).

We always argue about where to place this "5 of a kind" hand in the proper ranking. I always argue that it should fall below a straight flush... they always argue it should be ABOVE the Royal Flush...ie: it is the highest hand possible.

Here's the game. You're dealt five cards. The lowest card in your hand is wild, as are all Kings. You have one chance to throw away the cards you do not like and redraw to fill your hand of five (ie: just like 5 card draw).

So... if you have 2S-10H-JackH-QueenH-King Clubs, you have a Royal Flush (the deuce of spades is wild because it is the low card in your hand, and the King is also wild. These two wild cards with your 10H, JH, QH makes the Royal).

Another example, you have a natural Full House 4H-4C-10D-10H-10C, the fours are wild, making your hand 5-of-a-kind (five 10's). Same for a natural 4-of-a-kind...it's an automatic 5-of-a-kind hand because the lowest card in your hand will be wild.

This might be a tougher nut to crack, given all of the possible hands when wild cards are being played. If anyone can help identify where in the ranking a 5-of-a-kind hand should be placed, along with a good explanation I can share at the table, please do let me know.

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#### KitaMB

##### Rising Star
When we play WC hands 5-of-a-Kind always trumps straight and royal flushes.

However, we play a lot of High-Straight-Flush run split pot games. So, there's a standard high hand winner, and then the player with the longest straight-flush run splits the pot. The disclaimer, when using wild cards, is that natural beats "aided" in the straight flush run.

EX: a natural 4-card run 8c:) would beat a better 4-card run that uses a wildcard.

#### Odysseus101

##### Rock Star
This might be a tougher nut to crack, given all of the possible hands when wild cards are being played. If anyone can help identify where in the ranking a 5-of-a-kind hand should be placed, along with a good explanation I can share at the table, please do let me know.

Ugh, you don't make it easy do you? So, with kings and little ones wild, and a draw of up to five cards, should five of a kind beat a straight flush? Is that the question? You couldn't start with something simpler?

The draw of up to five is the biggest complicating factor. It adds a choice between the events which is based on the players' assumptions. And this leads us right into territory explored by the Monty Hall paradox or Russell's Box explored in your previous thread.

Why don't you posit something less complicated, then your knowledge will be built up too and then maybe you can attack similar problems with confidence.

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#### nenkov407

##### Rock Star
A straight flush should be higher than a 5 of a kind. The odds of hitting a straight flush are way lower than hitting an ordinary full house (which in this case makes 5 of a kind).

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#### Prolaznik

##### Rock Star
A straight flush should be higher than a 5 of a kind. The odds of hitting a straight flush are way lower than hitting an ordinary full house (which in this case makes 5 of a kind).
Have you calculated that, or were you just assuming?

#### Odysseus101

##### Rock Star
Have you calculated that, or were you just assuming?

On a simple five card draw, there are more combinations for a full house than for a straight flush, so the odds of getting that full house are obviously better.

But with low card wild, any full house draw is automatically now five of a kind. This isn't a definitive answer on whether 5 of a kind should beat a straight flush, but it's a consideration for sure. The presence of wild cards, which might themselves also change upon the draw of up to five, make this problem very complicated.

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#### nenkov407

##### Rock Star
Have you calculated that, or were you just assuming?

I haven't calculated but in a normal poker game straight flush is higher than a full house. Also in my opinion a four of a kind should be considered higher than five of a kind since in normal poker four of a kind is higher than a full house where in that version with five of a kind it can be developed by an ordinary full house.

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#### Prolaznik

##### Rock Star
On a simple five card draw, there are more combinations for a full house than for a straight flush, so the odds of getting that full house are obviously better.

But with low card wild, any full house draw is automatically now five of a kind. This isn't a definitive answer on whether 5 of a kind should beat a straight flush, but it's a consideration for sure. The presence of wild cards, which might themselves also change upon the draw of up to five, make this problem very complicated.
I know all that, just wanted to know whether his claim is based on real calculations (see below).
However, I don't think the wildcards themselves complicate too much. If there wasn't a draw, it would be a hundred EUR job; I might even do it without any fee, just to satisfy the curiosity.
But drawing is a major factor - if someone offered 2K EUR fee, I'd decline flatly...

I haven't calculated but in a normal poker game straight flush is higher than a full house. Also in my opinion a four of a kind should be considered higher than five of a kind since in normal poker four of a kind is higher than a full house where in that version with five of a kind it can be developed by an ordinary full house.
You mean genuine quads is harder to get then "quints" with wildcards? Of course, but that's trivial. The question is:

IF the wildcards are here to stay, what's easier to get - quints or str8 flush?

@Fan_of_EP
It seems your game isn't well defined - smaller quints are obviously harder to get. So if you want to keep traditional relation (higher is stronger), you should differently define the wildcards...
For example:
b) Highest cards (instead of lowest)

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#### Fan_of_EP

##### Rising Star
I've been running some numbers, but not quite done yet. I'll post again over the weekend with what I've found, and hopefully generate some good comments from everyone.

#### Odysseus101

##### Rock Star
Not that I have any math to back it up, but just from pondering it I'm thinking that there are plenty of hands that could result in either a straight flush or 5 of a kind. So those would be discounted from any calculations? I mean, this is another complicating factor. Ideally, you'd want to calculate the number of potential quint hands and the number of straight flush hands, and assume that the one with the lower number should be the "better" hand. But depending on which is "assumed" to be the higher hand is certainly going to impact the choice of draw cards, right?

OP, this question is very likely beyond the ability of anyone here to give a meaningful answer.

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#### kidrock1211

##### Visionary
never played 5 of a kind so not sure but i would think it beats all:joyman:

#### Odysseus101

##### Rock Star
Here's an excellent article, simple but to the point, on the math of adding wild cards to a five card poker draw, and when that should lead to the reordering of what hand beats what.

http://datagenetics.com/blog/september32016/index.html

Check the "paradox" issue raised at the bottom. Even into this simple foray of adding wild cards like a joker or two, or making 2s wild, it gets murky.

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#### Prolaznik

##### Rock Star
Ideally, you'd want to calculate the number of potential quint hands and the number of straight flush hands, and assume that the one with the lower number should be the "better" hand.
That's precisely what I had in mind! (When I said it's a hundred EUR job)

But depending on which is "assumed" to be the higher hand is certainly going to impact the choice of draw cards, right?
Yes, but not too much. In vast majority of cases, you'll chase what's easier (what has a higher probability of getting), not what's stronger.