I don’t quite have the math skills to figure this out, but I’m curious.
Back in the early 20th century someone apparently tried to make five-suit bridge a thing by simply adding thirteen additional cards to the standard deck of a fifth suit. In the USA they were usually called “Eagles,” in the UK "crowns or “royals.” For the sake of unanimity I am going to suggest we call our fifth suit “Stars.” So you have an ace of stars, king of stars, etc. I don’t know what color it’ll be but in poker only suit matters, color doesn’t.
How would this change the ranking of hands?
Currently it’s
Royal Flush
Straight Flush
Four of a Kind
Full House
Flush
Straight
Three of a Kind
Two Pair
One Pair
Just your high card
Would using five suits alter this in any way?
Note that I read somewhere that someone came up with additional hands for such a system, including a “flash” - one of each suit - but at first let’s deal with ranking the existing hands. Would it change?
Obviously five of a kind is now possible. Is that above or below a straight flush?
Four of a kind would be easier - after the first card, for each subsequent card dealt there are proportionately more cards left with the same rank than other ranks. Full house, three of a kind, pairs would all be slightly easier for the same reason.
I’m too lazy to work out the probabilities exactly, but my guess is that the order of hands wouldn’t change. With 4 suits, a flush is twice as easy as a full house, so I don’t think adding the fifth suit is going to change the probabilities enough to make a flush harder.
Poker Hand No of Combinations Probability
--------------------------------------------------------
Royal Flush 5 0.0000006053
Five of a Kind 13 0.0000015739
Straight Flush 45 0.0000054480
Four of a kind 3,900 0.0004721614
Flush 6,385 0.0007730129
Full House 15,600 0.0018886455
Straight 31,200 0.0037772909
Three of a Kind 214,500 0.0259688751
Two Pair 429,000 0.0519377502
Pair 3,575,000 0.4328145854
No Pair 3,984,240 0.4823600514
Total 8,259,888 1.0000000000
Is a Royal Flush really anything other than an Ace high straight flush? Why would it beat 5 of a kind which is less likely than a straight flush. It only beats 4 of a kind now because a straight flush of any description is less likely than 4 of a kind.
The distinction between royal flush and straight flush is actually important in five suit poker. In normal poker, a straight flush is much, much less likely than quads. In five suit poker, though, a straight flush is more likely than five of a kind, which in turn is more likely than a royal flush, so there’s some value in distinguishing to make the hand rankings a bit more logical and interesting.
But that is entirely arbitrary. Any individual straight flush, for example 6,5,4,3,2, is harder to get than 5 of a kind. So why not make it the best hand in the game?
You are just saying, a straight flush doesn’t beat 5 of a kind - unless it’s this straight flush.
I agree. Conversely - if a Royal Flush is distinct from other flushes, why are all rankings of 5-of-a-kind hands grouped as one category? Why not make 5 Aces a standalone category, which should then beat a Royal Flush.
I’m with you guys — it doesn’t make a lick of sense for me to differentiate one special type of straight flush from the others. A five of a kind beats a royal flush in a wild card game (unless you have house rules to the contrary) so why not here? In this game, I’d consider aces-high five-of-a-kind the equivalent hand to royal flush in four suit poker. Hell, give it a fun name like a High Five (okay, kinda silly for poker) or an Ace of Aces or something.
Just to clarify, that table was for informational purposes only (mea magna culpa!!)—I am not advocating that “royal flush” be a special hand that beats five-of-a-kind, nor would that be my first instinct were I to run such a game. There are 50 straight flushes in total: 10 different straights (A–5, 2–6, …, 10–A) times 5 different suits.
It’s three-card brag that has some “special” types of hands: 333 is the highest three-of-a-kind and A23 the highest straight.
I mean, since you’re making up completely new hands I think the 4 and Jack of clubs, Ace of diamonds, 9 of hearts, and 5 of stars should be the highest hand. Only one way to make it, so it’s more rare than your proposed hand.
The royal flush is kind of an odd case, because the actual rules for poker don’t list it as a distinct hand, but a lot of people think it is. And for normal poker, the distinction doesn’t matter, because there’s no difference between the highest value of the best hand, and a distinct and even better hand.
With poker variants such as this one, though, there can be a distinction between those two, because the straight flush (inclusive of ace-high straight flushes) is no longer the best hand.
I think it’s best to follow the hands as defined in the actual rules, not the hands in popular perception, because that’s consistent with how all other hands are treated. We don’t say that a full house aces over kings is higher than a straight flush, just because there are only 24 ways to make a full house aces over kings and 40 ways to make a straight flush. We just say that aces over kings is the highest possible full house, which matters when two different people both have full houses, but doesn’t make any kind of full house better than any kind of straight flush.
Or, to look at the altered game, we could say that a royal flush, the highest possible straight flush, is rarer than just any old five of a kind… but we could also say that five aces, the highest possible five of a kind, is rarer than the royal flush.
Think of it like a grand slam in baseball: it’s a thing people talk about, but the official rules don’t have to say anything about it (what it is, how many runs it’s worth, etc.) or distinguish it from other types of home runs.
Since we have everything else taken care of, by the way, there are 13^5 = 371293 different ways to make a flash, since you can choose one of 13 hearts, 1 of 13 stars, etc. Based on @DPRK 's table, this would put it in between two pair and three of a kind.
There’d also be combinations of the flash with most of the other hands: You could have a flash pair, a flash two pair, a flash three of a kind, a flash straight, a flash full house, and a flash four of a kind (flash five of a kind wouldn’t need a new entry, because all five-of-a-kinds would automatically be flashes). I’m too lazy to calculate those right now, though (well, I think a flash straight would be 1200 combinations, between four of a kind and straight flush). Though I wouldn’t be surprised if those weren’t in the same order as the corresponding non-flash versions of the hands.