This is a discussion on In need of some accurate probabilities within the online poker forums, in the General Poker section; 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 


#1




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, AAAAKKKKQQQQJJJJ. 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 44J or QQ3. 
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#2




Quote:
1. How often should ( in all probability ) the flop ( flop only, not turn or river ) contain any of the top 4 ranked cards, AAAAKKKKQQQQJJJJ. 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 44J or QQ3.[/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) 
#3




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 
#4




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.

#5




re: Poker & In need of some accurate probabilities
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#8




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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. 
#9




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 3P(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% 
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