In need of some accurate probabilities

Hi, I am in need of some very accurate probability percentages to help me in a test I am considering carrying out. I would be grateful if someone with the know how could post here, and if possible, someone else can confirm the figures quoted. Thanks.

I am interested in probabilities for the following scenario ................

The game - No limit hold'em
The format - Heads up ( 2 player cash games )
The area - The flop

I wish to know the correct probability percentages for the following .......

1. How often should ( in all probability ) the flop ( flop only, not turn or river ) contain any of the top 4 ranked cards, AAAA-KKKK-QQQQ-JJJJ.

2. How often should the flop contain 2 suited cards, ie 2 diamonds.

3. How often should the flop contain 3 cards of the same suit, ie 3 clubs.

4. How often should the flop contain a pair, ie 4-4-J or Q-Q-3.

Crystal Blue said:

Hi, I am in need of some very accurate probability percentages to help me in a test I am considering carrying out. I would be grateful if someone with the know how could post here, and if possible, someone else can confirm the figures quoted. Thanks.

I am interested in probabilities for the following scenario ................

The game - No limit hold'em
The format - Heads up ( 2 player cash games )
The area - The flop

I wish to know the correct probability percentages for the following .......

Click to expand...

I'm taking these numbers from the book "Texas Hold'em Odds and probabilities Limit, No-Limit, and Tournament Strategies". From the section " The Flop, Probability of Hitting Certain Hands on the Flop" I'll word it the way they do.

1. How often should ( in all probability ) the flop ( flop only, not turn or river ) contain any of the top 4 ranked cards, AAAA-KKKK-QQQQ-JJJJ.

Sorry, havent found this one yet

2. How often should the flop contain 2 suited cards, ie 2 diamonds.

Two suited cards hitting a flush draw. PROB .11 ODDS 8to 1

3. How often should the flop contain 3 cards of the same suit, ie 3 clubs.

Two suited cards hitting a flush. PROB .008 ODDS 124 to 1

4. How often should the flop contain a pair, ie 4-4-J or Q-Q-3.[/quote]

Two cards such as AK flopping trips PROB .014 ODDS 70 to 1

now they dont mention full ring, 6 max or heads up, and I took these numbers right from a chart (didnt calculate myself)

Thanks guys..............
Well, I found this and it does answer some of my questions. Although I think it is a chart that accounts for 50 cards remaining in the deck. What I am really after is a breakdown from 48 remaining cards in the deck before the flop and also assuming that each player has a random holding.

I can't seem to find anything with regards to the numbers for the frequency of the top 4 ranks hitting the flop. Maybe if I explain it the following way someone might be able to help.

If any Ace, King, Queen or Jack = T
How often should the flop contain XXX
How often should the flop contain TXX
How often should the flop contain TTX
How often should the flop contain TTT

I'm not great at probability figures and that's why I started this thread. I am unsure if the information I am looking for is too big of an ask, or for that matter, if it's a simple question which I should be able to figure out for myself. I have searched for the complete answers with little or no success and that's why I'm asking here. Is there anyone out there with the answers? Please let me know, cheers.

Crystal Blue said:

Thanks guys..............
Well, I found this and it does answer some of my questions. Although I think it is a chart that accounts for 50 cards remaining in the deck. What I am really after is a breakdown from 48 remaining cards in the deck before the flop and also assuming that each player has a random holding.

Click to expand...

I'm definately not a numbers person but I think the chart you have is what you want. Heads up, yes there are 48 card left preflop, but i dont think you take your opponents cards into the mix (not 100%). When your figuring odds you take your cards and the board cards (if any) into account. When your at a full ring table you don't factor in 9 players x 2 cards and subtract 18 and board cards when making your decisions??? I dont think.

Ahhh, I'm hearing you RichKo, that's something I didn't even consider. Yeah, it's 2 random hands I want to work from so what you say may hold true. Thanks.

Hopefully someone else will confirm or deny whether my info is good or not.lol

RichKo said:

When your at a full ring table you don't factor in 9 players x 2 cards and subtract 18 and board cards when making your decisions??? I dont think.

Click to expand...

I think I would for flushes and the like but many disagree. I just figure that if I need one card of a suit to make my flush and 18 cards have already been dealt, then I doubt there are 9 of the suit I need left in the deck. More than likely, a few of my suit have already been dealt to other players besides me and the board; therefore my odds are worse than 9/47 -- they are more like 5/29. But these odds are very close, so maybe it's just easier to calculate from 47.

As for the OP, I think the question is a matter of straight probability equations. Unfortunately, it's been many years since I studied this and I can't remember how to add or multiply running cards. If I find some time I might go back and relearn it. It's something like (chance of first card being A,K,Q,J out of 52 cards times (or plus) chance of second card being A,K,Q,J out of 51 cards, times (or plus) chance of third card being A,K,Q,J out of 50 cards, etc., etc. Sorry I can't remember any more than this right now.

flop containing just one a,k,q, or j:
P(first card) + P(second card) + P(3rd card) - P(any 2 together or all 3) = 16/52 + 16/52 + 16/52 - (0.09 + 0.09 + 0.09 + 0.025) = 0.9 - 0.295 = 0.605 = ~60%

flop containing 3 of the same suit:
1/1 (first card can be any suit) x 12/51 x 11/50 = 132/2550 = .05 = ~5%

2 of the same suit but not 3: looks complicated but it isnt
P(card1 and card2 - P(1,2 and 3)) + P(1 and 3 - P(1,2 and 3)) + P(2 and 3 - P(1,2 and 3) = (600/2550 - 132/2550) x 3 = 468/2550 x 3 = 1404/2550 = 55%

flop containing a pair (but not trips): think about it like this. (X = paired cards, B = blank) XXB XBX BXX these are the 3 possible combos for a pair on board on the flop, so for XXB calculate the P(1 and 2) - P(1,2,3) becuase trips doesn't count so you have to minus the chance of trips coming

P(1 and 2 -P(1,2,3)) + P (1 and 3-P(1,2,3)) + P (2 and 3 -P(1,2,3)) = (1/1 x 3/51 - (1/1 x 3/51 x 2/50)) x3 = (3/51 - 6/2550) x3 = (150/2550 - 6/2550)x3 = 144/2550 x3 = 432/2550 = ~17%

Excellent stuff there Spranger, thank you most kindly.