Skip to Content
 

Texas Hold 'Em with 5 Crowns deck odds

5 replies [Last post]
Mon, 10/10/2005 - 20:56
ACG
Offline
Joined: 12/31/1969

Hi! I have a Five Crowns deck at home (5 suits, 11 cards per suit). I was wondering what Texas Hold 'Em would be like with 5 suits. So I computed the odds. Strange things happen. Unless my math is wrong:

1. Ace high beats one pair -- pairs are much easier to get.

2. A new type of hand exists: a "rainbow" or anti-flush. That is, five cards of five suits.

3. A [non-rainbow] full house has the same likelihood of occurring as a rainbow three-of-a-kind. A tie between a full house and a three of a kind in this case goes to the player with fewer chips. (If there are three 5's on the board, who wins: a guy with 8 8 or a guy with 9 7 who happens to make a rainbow? We're comparing apples and oranges)

Here are the hand rankings as I see them, from weakest to strongest.

One pair
Zero pairs
Two pairs
Three of a kind
Rainbow with pair

Rainbow zero pairs
Straight
Rainbow with two pairs
Rainbow three of a kind/full house

Four of a kind
Flush (yes, flush beats four of a kind: fewer carts per suit, more suits)
Rainbow full house
Rainbow straight
Rainbow four of a kind

Royal rainbow (king-high: there's no ace or 2)
Straight flush
Five of a kind
Royal flush

What do you think?

Thanks in advance,

ACG

Top
Mon, 10/10/2005 - 21:54
#1
markmist
Offline
Joined: 12/31/1969
Texas Hold 'Em with 5 Crowns deck odds

Very interesting. Have you actually tried it out?

Here are my suggestions: I like your idea of having a rainbow - it seems like it should be a legitimate hand. However, some of the other rainbow hands don't really belong as hands (why use rainbow and a pair, if a flush and a pair is not a hand in regular poker?) Also, zero pairs and one pair should both probably not be listed as hands.

I would make it:
High Card
Two Pairs
Three of a Kind
Rainbow (regardless of numbers)
Straight
Full House
Four of a Kind
Flush
Straight Flush
Five of a Kind
Royal Flush

Now it would be even more interesting to know the odds for 4 card or 6 card hands with the Five Crowns deck.

Top
Tue, 10/11/2005 - 11:15
#2
ACG
Offline
Joined: 12/31/1969
Texas Hold 'Em with 5 Crowns deck odds

A straight flush combination is a separate hand in regular poker, so you can combine two types of hands. A full house is a pair and three of a kind.

Also, keep in mind that you can't have a pair and flush at the same time -- the two cards making a pair must be of different suits, wrecking the flush but still leaving open the possibility of a rainbow.

ACG

Top
Tue, 10/11/2005 - 13:31
#3
markmist
Offline
Joined: 12/31/1969
Texas Hold 'Em with 5 Crowns deck odds

ACG wrote:
A straight flush combination is a separate hand in regular poker, so you can combine two types of hands. A full house is a pair and three of a kind.
ACG

Ok, you have a point. However, I think I would still leave out a majority of the rainbow combinations as it is too many combinations to remember and in my opinion would make things too complicated.

No hurt giving it a try though. Tell me how it goes!

Top
Tue, 10/11/2005 - 14:00
#4
TrekNoid
Offline
Joined: 10/02/2009
Re: Texas Hold 'Em with 5 Crowns deck odds

I like the added elements of Five of a Kind and I like the idea of a Rainbow, but I only like the Rainbow idea where all five cards make the match...

So, I would drop:
Rainbow with Pair
Rainbow with two pairs
Rainbow three of a kind
Rainbow four of a kind

I might also drop the Rainbow full house just because suits don't normally have any affect on a Royal Flush...

Flushes and Straights Flushes are hands where suits come into play, so I'd put Rainbows in the same category.

So I'd keep these hands:

Rainbow (as opposed to a flush)
Straight rainbow
Royal rainbow

TrekNoid

Top
Wed, 11/02/2005 - 21:00
#5
ACG
Offline
Joined: 12/31/1969
Texas Hold 'Em with 5 Crowns deck odds

I've found a site with the rankings for 13x5 poker are. The rankings are listed below, highest to lowest.

They use and rank all of the rainbow hands I have.

My calculations for 11x5 are parentheses. The 13x5's are not in parentheses.

5 of a kind (5 of kind)
straight flush (straight flush, though theirs includes royal flush)
rainbow 4 of a kind (rainbow 4 of a kind)
rainbow straight (rainbow straight, though theirs includes royal rainbow)
rainbow full house (rainbow full house)
4 of a kind (I had flush -- but I've calculated they switch)
flush (I had 4 of a kind)
full house (full house ties rainbow 3 of kind )
rainbow 3 of kind (rainbow 3 of kind ties full house)
rainbow 2 pairs (rainbow 2 pairs)
straight (straight)
3 of a kind (rainbow 0 pair)
rainbow 0 pair (rainbow 1 pair)
rainbow 1 pair (3 of a kind)
2 pair (2 pair)
1 pair (0 pair)
0 pair (1 pair)

I just checked my math on the 3 of a kind vs. rainbow 1 pair and I believe my rankings are correct for both cases. I believe the website may be incorrect (though flush and four of a kind do swap with 13 cards).

3 of a kind odds for 13x5: 13 values to pair * 10 suit combos in pair * (12 choose 2 = 66) values for the other two cards * 5 suits * 5 suits = 214,500 -- maybe 200K without rainbows

Rainbow 1 pair for 13x5: 13 values to pair * 10 suit combos in pair * [at this point the three suits are forced, envision them in alphabetical order] * 12 [values for third card] * 11 [values for 4th card to not make pair] * 10 [values for 5th card] = 171,600

According to these calculations, 3 of a kind loses to Rainbow 1 Pair in 13x5 as well as in 11x5.

ACG

Top
Syndicate content


forum | by Dr. Radut