pokerguy
Joined: Jul 10, 2015
• Posts: 3
July 10th, 2015 at 2:55:19 AM permalink
Hi all,

My first post here, so first thing first, congrats to the wizard for great site, I love the odds :)!
I'm hoping to find some help here as I don't manage to calculate myself following probabilities....

The number and probabilities for holdem hands in a 52 cards decks are the following. (ty google:))

hand number Probability
straight flush 41,584 .00031
4-of-a-kind 224,848 .0017
full house 3,473,184 .026
flush 4,047,644 .030
straight 6,180,020 .046
3-of-a-kind 6,461,620 .048
two pairs 31,433,400 .235
pair 58,627,800 .438
high card 23,294,460 .174

Does someone know what they are with a 36 cards deck ?
I mean if:
- the deck is 36 cards 6,7,8,9,T,J,Q,K,A and 4 suits heart diamond, spade and clubs
- I take 7 cards of the deck
- out of these 7 what is the probability for each poker hands (5 cards)
- where here A,6,7,8,9 is the lowest straight possible and T,J,Q,K,A is the highest straight possible

Pokerguy
chaunceyb3
Joined: Feb 22, 2013
• Posts: 346
July 10th, 2015 at 8:24:47 AM permalink
Sounds like you are referring to Six Plus Hold' em, a game popular in Macau and elsewhere.

I can't tell you the exact probabilities, but in this game, a flush beats a full house, and three of a kind beats a straight.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
July 10th, 2015 at 10:21:14 AM permalink
A game in which A,6,7,8,9 is a straight should offend anyone's poker sensibilities.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
beachbumbabs
Joined: May 21, 2013
• Posts: 14234
July 10th, 2015 at 11:27:59 AM permalink
Quote: MathExtremist

A game in which A,6,7,8,9 is a straight should offend anyone's poker sensibilities.

Got my attention. lol...
If the House lost every hand, they wouldn't deal the game.
Joined: Jul 3, 2015
• Posts: 30
July 11th, 2015 at 7:53:05 AM permalink
I'll do a couple now.

N(flush) = 4*[C(9,5)*C(27,2) + C(9,6)*27 + C(9,7)] = 46530
P(flush) = 46530 / C(36,7) = 47/8432 =~ 0.5574%

N(boat) = 9*8 * C(4,3)*C(4,2)*C(28,2) = 653184
P =~ 7.82%, about 14x as frequent as a flush which is why it's worth less.
pokerguy
Joined: Jul 10, 2015
• Posts: 3
July 12th, 2015 at 2:59:12 AM permalink

Thx for your stats even if now I'm even more confused that before. :)
Below is what I have for full house(boat) and flush....you'll see my results are not quite same as yours. :)
I'm really not sure who is right or wrong...that's why I'm hoping to find some input here.

N(Flush) = (4*(C(9,7)-(4+7+10))+(4*(C(9,6)-(5+14))*27)+(4*(C(9,5)-6)*C(27,2))=175560
P(Flush) = 175560 / C(36,7)) = 175560 / 8347680 = 2.103%

N(Full house) = (C(9,2)*C(4,3)*C(4,3)*28)+(9*C(8,2)*C(4,3)*C(4,2)*C(4,2))+(9*8*C(7,2)*C(4,3)*C(4,2)*4*4)= 633024
P (Full house) = 633024 / (C(36,7) = 633024 / 8347680 = 7 .583%

Still explains why Full house is worth less :)

Hope someone can help here. :)
Joined: Jul 3, 2015
• Posts: 30
July 12th, 2015 at 11:46:39 PM permalink
Sorry, both of my stats are wrong. For the flushes I forgot to subtract straight-flushes. For the boats I double-counted the cases of trips+twopair and I forgot to count the cases of double-trips.

N(straight flush) = 4*[C(31,2) + 5*C(30,2)] = 10560
P = 2/1581

N(flush) = 46530 - 10560 = 35970
P =~ 0.4309 %

N(boat) = 653184 - 3*C(9,3)*C(4,3)*C(4,2)^2 + C(9,2)*28*C(4,3)^2 = 633024

Since we still disagree on the flushes, I'll look at it again tomorrow.

Edit: In your flush calculation, where does 4+7+10 come from, and 5+14 and 6?
JB
Joined: Oct 14, 2009
• Posts: 2089
July 13th, 2015 at 12:55:39 AM permalink
I calculate the following:
Best 5-Card Hand Combinations Probability
Royal Flush 1,860 0.000223
Straight Flush 8,700 0.001042
Four of a Kind 44,640 0.005348
Full House 633,024 0.075832
Flush 175,560 0.021031
Straight 1,169,940 0.140152
Three of a Kind 607,200 0.072739
Two Pair 3,157,056 0.378196
One Pair 2,316,600 0.277514
High Card 233,100 0.027924
Totals 8,347,680 1.000000

My analysis assumed that standard poker hand ranking applies. For example, 89TJQQQ is a Straight, not Three of a Kind.
Results were calculated by writing a program which iterated through all combin(36,7) hands and determined the best 5-card hand.
Joined: Jul 3, 2015
• Posts: 30
July 13th, 2015 at 1:08:04 AM permalink
Oh, for my flushes I wrote 4*[...] but in my calculator I forgot the 4 so my result was off by a factor of about 4. Now that I typed it correctly (and subtracted straight flushes), I too get an answer of 175560 combos.
pokerguy
Joined: Jul 10, 2015